AN ABSTRACT OF THE DISSERTATION OF

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2 AN ABSTRACT OF THE DISSERTATION OF Christopher Wolf for the degree of Doctor of Philosophy in Statistics and Forest Ecosystems and Society presented on November 21, Title: Predator Conservation and Trophic Ecology. Abstract approved: Alix I. Gitelman William Ripple Many of Earth s terrestrial large carnivore species are threatened with extinction. As a result, some of the ecological effects associated with these species may be lost. With the goal of furthering large carnivore conservation research, I conduct three global scale analyses involving these species. First, I explore prey depletion as a threat to large carnivores, finding that loss of prey base is a widespread occurrence and that many prey species are themselves threatened with extinction. Second, I analyze how large carnivore species geographic ranges have contracted, linking range contractions to spatial covariates: rural human population density, cropland, and livestock (cattle) density. Finally, I explore options for large carnivore reintroductions, identifying hundreds of potential sites around the world (protected areas and low human footprint regions) where rewilding may have the greatest likelihood of success. In the second part of this dissertation, I transition to considering the basic ecology of predation, with a focus on statistically estimating functional response parameters, which are closely linked to food web interaction strengths. I first show how an observational

3 method for estimating these parameters may be extended using a Bayesian framework that incorporates multiple sources of uncertainty while producing biologically realistic credible intervals. I pay particular attention to the problem of prior selection for modeling multinomial predator feeding survey data, showing that a neutral prior is most appropriate. Finally, I consider prior choice in more general nonlinear regression settings, proposing two new prior distributions designed to have low frequentist-sense bias and unifying a set of non-informative priors for a particular function family. I compare these and other non-informative prior distributions using a simulation study and a case study involving whelk feeding behavior in a rocky intertidal ecosystem.

4 Copyright by Christopher Wolf November 21, 2017 All Rights Reserved

5 Predator Conservation and Trophic Ecology by Christopher Wolf A DISSERTATION submitted to Oregon State University in partial fulfillment of the requirements for the degree of Doctor of Philosophy Presented November 21, 2017 Commencement June 2018

6 Doctor of Philosophy dissertation of Christopher wolf presented on November 21, 2017 APPROVED: Co-major Professor, representing Statistics Co-major Professor, representing Forest Ecosystems and Society Chair of the Department of Statistics Chair of the Department of Forest Ecosystems and Society Dean of the Graduate School I understand that my dissertation will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my dissertation to any reader upon request. Christopher Wolf, Author

7 ACKNOWLEDGEMENTS Thank you Alix I. Gitelman, William Ripple, and Mark Novak for collaborating with me on my thesis research. I appreciate your insight, support, patience, and encouragement. Thanks also to the rest of my Ph.D. committee: Lisa Madsen, Deborah Rubel, and Dana Warren, and to the wonderful faculty, staff, and students in the departments of Forest Ecosystems & Society and Statistics. I especially want to thank my teachers in these departments: Matthew Betts, Glenn Howe, and Michael Nelson in FES and Yanming Di, Sarah Emerson, Claudio Fuentes, Yuan Jiang, Lisa Madsen, Paul Murtaugh, Cliff Pereira, Charlotte Wickham, and Lan Xue in statistics. Additionally, I thank the members of Mark s lab for including and supporting me. I also thank everyone at Oregon State University for creating a great learning environment. Lastly, thank you Mary Flahive and Bella Bose for teaching me how to do research as an undergraduate and encouraging me to pursue my academic goals. On a personal note, thank you to all of the friends I ve made in grad school. Thank you Mom and Dad for helping me get a great education and thank you Grandpa for going on nature walks with me a long time ago. Thank you planet Earth and all your teleological centers of life, including wolves, coyotes, whelks, and Siberian marmots. Finally, thank you Ruby and Tucker for being the best dogs ever!

8 CONTRIBUTION OF AUTHORS Chapters 2 and 3: Christopher Wolf carried out the data analysis and drafted the manuscript; William Ripple conceived of the project and helped draft the manuscript. All authors gave final approval for publication. Chapter 4: Christopher Wolf carried out the data analysis and drafted the manuscript; William Ripple conceived of the project and helped draft the manuscript. Chapter 5: Mark Novak and Alix I. Gitelman originally formulated the idea for the project, Christopher Wolf analyzed the data, and Christopher Wolf, Mark Novak, and Alix I. Gitelman wrote the manuscript. Chapter 6: Alix I. Gitelman, Mark Novak, and Christopher Wolf conceived of the project. With input from Alix I. Gitelman and Mark Novak, Christopher Wolf developed the methodology, conducted the simulations, analyzed the data, and drafted the manuscript.

9 TABLE OF CONTENTS Page 1 Introduction Prey Depletion as a Threat to the World s Large Carnivores Range Contractions of the World s Large Carnivores Rewilding the World s Large Carnivores Bayesian Characterization of Uncertainty in Species Interaction Strengths A Unification of Priors for Modeling Rare Events in Nonlinear Regression Conclusion Bibliography Appendices...4 A Supplementary Material for: Prey Depletion as a Threat to the World s Large Carnivores B Supplementary Material for: Range Contractions of the World s Large Carnivores C Supplementary Material for: Rewilding the World s Large Carnivores D Supplementary Material for: Bayesian Characterization of Uncertainty in Species Interaction Strengths E Supplementary Material for: A Unification of Priors for Modeling Rare Events in Nonlinear Regression...332

10 LIST OF FIGURES Figure Page 2.1 IUCN Red List conservation status of large carnivores prey Population trends of large carnivores prey Maps showing the percentages of large carnivore prey species with decreasing population trends for the five large carnivores whose prey have the highest percentages of decreasing trends Percentages of all 494 prey species that are threatened (top) or have decreasing population trends (bottom) Mean percentages (with standard errors) of prey species ranges occurring inside protected areas Range contraction maps for 25 large carnivores Percentage of historic range lost for each large carnivore Composite range contractions maps based on all 25 large carnivores Current and historic species richness histograms by region of the world Regions of the world with intact or no longer intact large carnivore guilds (one or more species) The 25 terrestrial large carnivore species in our analysis (Table 4.1) Histograms for human footprint (a spatial measure of human impacts on the environment) across the historic ranges of each large carnivore Potential sites for reintroducing large carnivores...80

11 LIST OF FIGURES (continued) Figure Page 4.4 The six largest protected areas inside the lost (historic minus current) ranges of each large carnivore species (only three were identified for the red wolf) Corridors among the 411 protected areas that we identified as candidate sites for large carnivore reintroduction based on the 25 largest protected areas for each large carnivore species Comparison of alternative non-informative priors in estimating the ratio of the proportions of feeding versus not feeding predator individuals Comparison of the frequentist and Bayesian approaches to estimating the per capita attack rates with which Haustrum scobina consumed its 8 prey species Posterior distributions for Haustrum scobina s per capita attack rate parameters (prey predator 1 prey 1 m 2 day 1 ) and their components ξ i = α i 1 1 using neutral c = 1 Dirichlet prior α 0 ν i η i 3 on feeding proportions Deterministic variation in per capita attack rates due to predator body size for the two prey species consumed by Haustrum scobina most frequently Nonlinear functions that we consider in our analysis Type I function simulation results based on 1,000 simulations for each parameter configuration...146

12 LIST OF FIGURES (continued) Figure Page 6.3 Type II function simulation results based on 5,000 simulations for each parameter configuration Type III function simulation results based on 1,000 simulations for each parameter configuration Parameter point estimates (posterior means) for the nonlinear function parameters of the Type I, Type II, and Type III functions fit to our example dataset of the proportion of Nucella ostrina individuals feeding on Lottia asmi (Table E.1)...149

13 LIST OF TABLES Table Page 2.1 The 17 obligate meat-eating carnivores with masses at least 15 kg Population trends of large carnivores prey The 25 large carnivore species in our analysis For each large carnivore species, the six largest protected areas where it has been extirpated (i.e. where we found no evidence in the literature of its current presence) Summary statistics for the datasets we use to estimate the per capita attack rates with which the intertidal predator Haustrum scobina fed on its eight prey species n 6.1 Values of i=1 y i = s for which the posterior distribution is proper (Type II function) Simulation parameters for our simiulations to assess the performance of sparse priors in estimating Type I, Type II, and Type III function parameters (Figure 6.1)...151

14 LIST OF APPENDIX FIGURES Figure Page A.1 Prey endangerment maps (complete set) A.2 Prey decreasing trend maps (complete set) A.3 Prey status by continent A.4 Prey population trends by continent A.5 Status of large carnivores preferred prey A.6 Population trends of large carnivores preferred prey A.7 Percentages of all 114 preferred prey species that are threatened (top) or have decreasing population trends (bottom) A.8 Preferred prey endangerment maps (complete set) A.9 Preferred prey decreasing trend maps (complete set) A.10 Major threats faced by large carnivores threatened prey A.11 Mass and order information for each large carnivore s prey species A.12 References to prey depletion in the literature A.13 Mass and order information for each large carnivores preferred prey species B.1 Predictor variables used in the model for predicting range contractions B.2 Percentage range contraction versus carnivore body mass B.3 Current and historic species richness histograms by biome B.4 Results for a generalized linear mixed model predicting the increase in the odds of range contraction per one standard deviation increase in each predictor variable while accounting for the other variables (estimates shown with 95% confidence intervals)...238

15 LIST OF APPENDIX FIGURES (continued) Figure Page B.5 Effects of cattle density, cropland, and rural population on the odds of species range contraction by region of the world based on a spatially explicit generalized linear mixed model with random slopes (and intercepts) by geographic region and random intercepts by species C.1 The six largest contiguous low footprint regions inside the lost (historic minus current) ranges of each large carnivore species C.2 Potential sites for reintroducing large carnivores C.3 All strictly (category I-III) protected areas inside the lost (historic minus current) ranges of each large carnivore species (without any manual validation) C.4 All contiguous low footprint regions inside the lost (historic minus current) ranges of each large carnivore species D.1 Average field covariates versus feeding proportions D.2 Given the skewed nature of prey-specific per capita attack rate posterior probability distributions, the distribution median serves as a more appropriate point estimate than the mean E.1 Estimation of β in the Type II function E.2 Type I function simulation credible interval coverage results based on 1,000 simulations for each parameter configuration E.3 Type II function simulation credible interval coverage results based on 5,000 simulations for each parameter configuration...345

16 LIST OF APPENDIX FIGURES (continued) Figure Page E.4 Type III function simulation credible interval coverage results base on 1,000 simulations for each parameter configuration E.5 Example posterior distributions for the Type I function using the information and log uniform priors (Section 6.2) E.6 Type II function quantiles using different versions of the functional uniform prior (FUP) E.7 Approximation error associated with approximating f(β) = 1 n {i=1}(1+βx i ) using g(β) = 1 n {i=1}(1+βx) E.8 Type II function simulation results based on 5,000 simulations for each parameter configuration (approximation priors)...350

17 LIST OF APPENDIX TABLES Table Page A.1 Diet study sources for the large carnivores A.2 Information on the 494 prey species in our analysis A.3 Analysis of the six most cited conservation-related articles for each large carnivore B.1 Sources of the historic range maps used in our analysis B.2 Summary data for large carnivore range contractions C.1 Photo credits for the images used in Figure C.2 The 25 largest category I-III protected areas in the lost (historic minus current) ranges of each large carnivore species C.3 The 25 largest contiguous low (bottom 10% within lost range) human footprint regions in each carnivore species lost range D.1 Summary of notation used in this manuscript D.2 Predator feeding survey results grouped by predator size class E.1 Example dataset used to estimate Type I, Type II, and Type III function parameters E.2 Parameter estimates for models fit using our example dataset (Table E.1)...352

18 To Mai DEDICATION

19 1 1 Introduction Unified by the theme of predator conservation and trophic ecology, this dissertation contains elements of statistics and ecology. In short, Chapters 3-5 deal primarily with ecology, but include some statistical analyses where appropriate. Chapters 6 and 7 deal with the development of new statistical methodology, but incorporate ecology as an area of application. A detailed overview of the dissertation s structure is presented in Section Background Early ecologists generally focused on the drivers of primary productivity (nutrient availability, light, temperature, and so on) in working to understand and predict ecosystem structure (Terborgh & Estes 2010, p. xiii). Reasons for this focus include the relative ease with which these factors can be measured and experimentally manipulated and the obvious importance of autotrophs like plants, without which, higher trophic levels would not exist (Terborgh & Estes 2010, pp. xiii-xiv). In contrast, many early ecologists devoted less attention to the roles of predators in ecosystems. In the scientific literature, Hairston et al. (1960) were among the first to argue that predation has a major impact on the biosphere. According to their Green World Hypothesis, predation on herbivores limits herbivory and thus keeps our world green. Key early evidence for the importance of predators came from Robert Paine s manipulative experiments in rocky intertidal ecosystems, where he showed that the removal of the keystone predator starfish Pisaster ochraceus led to major changes in the ecological community. Since then, there is a growing consensus that predation, especially by top

20 predators, can be a major force driving ecosystem structure and function and helping to maintain biodiversity at lower trophic levels (Estes et al. 2011). 2 Many predator species are highly endangered. For example, 66% of terrestrial large carnivores are threatened with extinction (Ripple et al. 2014). Even among less threatened species, range contractions and declines in abundances mean that their ecological effects may now be less common (Soulé et al. 2003; Morrison et al. 2007). Predator declines are part of a much larger biodiversity crisis, with the current species extinction rate estimated to be 100 to 1000 times higher than the pre-human background extinction rate (Pimm et al. 1995). At the same time, many questions remain about predator ecology and food web dynamics, including how to accurately forecast species abundances, how to determine the circumstances under which predators limit or regulate their prey, and how to quantify the effects of predation on ecosystem stability and resilience (McCann 2000). 1.2 Dissertation structure Motivated by the ecological significance and unique conservation challenges associated with predators, in Chapters 2-4, I conducted global analyses related to some of the most pressing issues in predator conservation. As predators are totally reliant on having a suitable prey base, in Chapter 2, I analyzed prey depletion as a threat to large terrestrial carnivores using diet meta-analyses from the literature. In Chapter 3, I analyzed how terrestrial large carnivore species geographic ranges have contracted over the last ~500 years. By linking range contractions to spatial environmental covariates (e.g. livestock density), this analysis provides insight into how further range contractions might be avoided.

21 3 In particular, the use of predator friendly agriculture methods could mitigate future range contractions in regions where livestock grazing is common. Then, in Chapter 4, I considered options for large carnivore reintroductions that could both promote these species ecological effects and reduce the likelihood of extinction for the most endangered species. Taken together, these chapters address key topics in the conservation of terrestrial carnivores at the global scale and include detailed discussions of specific management and policy steps that can help to ensure a future for these species and their ecological effects. In the next two chapters, I considered the basic ecology of predation from a statistical perspective. In Chapter 5, I developed new methodology for the estimation of functional response (per capita feeding rate model) parameters by extending the work of Novak & Wootton (2008). This new Bayesian method more accurately characterizes uncertainty in these parameters, which is essential for the probabilistic modeling of species population dynamics. I demonstrated the utility of the method by applying it to a case study dataset involving the intertidal predator whelk, Haustrum scobina. The rarity of prey in this predator s diet motivates my last chapter, Chapter 6, wherein I considered the Bayesian estimation of nonlinear functions where data are sparse as is often the case with predator feeding surveys. I focused on three nonlinear functions that are closely related to the Holling Type I, II and III functions, which are common functional response models (Jeschke et al. 2004). I proposed new prior distributions for use with the Type I and II functions that reduce the frequentist-sense bias of the posterior mean. I then showed that the Type II function priors are special cases of a more general distribution and used this result to examine posterior properness. Using a simulation study, I showed that the proposed priors have superior performance compared to other common non-informative priors. Most predators in nature are generalists feeding on a large number of different prey species that

22 4 are predominately rare. Hence, this chapter further contributes to our understanding of predators in nature. Taken together, these five chapters deal with both the applied conservation of predators and the basic ecology of predation. The development of new methodology with applications to species population dynamics and food web modeling can help to provide insight into the role of predators in determining the structure of ecosystems. Additionally, it is relevant to the conservation of predators in that a better understanding of their feeding behavior can help inform conservation decisions such as whether to reintroduce prey and predator species sequentially or simultaneously (Samhouri et al. 2017). Similarly, more effective predator conservation can benefit basic ecological research in the areas of food webs and predation, by providing more opportunities to study systems with intact predator guilds.

23 5 2. PREY DEPLETION AS A THREAT TO THE WORLD S LARGE CARNIVORES Christopher Wolf and William Ripple Wolf, Christopher, and William J. Ripple. "Prey depletion as a threat to the world's large carnivores." Royal Society open science 3.8 (2016):

24 6 2.1 Abstract Large terrestrial carnivores are an ecologically important, charismatic, and highly endangered group of species. Here, we assess the importance of prey depletion as a driver of large carnivore endangerment globally using lists of prey species for each large carnivore compiled from the literature. We consider spatial variation in prey endangerment, changes in endangerment over time, and the causes of prey depletion, finding considerable evidence that loss of prey base is a major and wide-ranging threat among large carnivore species. In particular, the clouded leopard (Neofelis nebulosa), Sunda clouded leopard (Neofelis diardi), tiger (Panthera tigris), dhole (Cuon alpinus), and Ethiopian wolf (Canis simensis) all have at least 40% of their prey classified as threatened (IUCN Red List status of endangered, vulnerable, or critically endangered) and all of these species except the Ethiopian wolf have at least 80% of their prey classified as declining. Of the 494 prey species in our analysis, an average of just 6.9% of their ranges overlap protected areas. Together these results show the importance of a holistic approach to conservation that involves protecting both large carnivores directly and the prey upon which they depend. 2.2 Introduction The large terrestrial carnivores are an ecologically important group of species. Many of these species have significant direct effects on their prey, which can lead to additional indirect effects. For example, wolves (Canis lupus) may reduce elk (Cervus canadensis) numbers directly or may change their behavior, leading to changes in plant species diversity, plant species abundance, and songbird communities (Hebblewhite et al. 2005). In Australia, dingoes (Canis dingo) can

25 7 limit fox (Vulpes vulpes) populations, indirectly benefiting numerous small mammals, many of which are endangered (Letnic et al. 2012). In addition, large carnivores can provide important ecosystem services. For example, in West Africa, lion (Panthera leo) and leopard (Panthera pardus) declines coincided with an increase in the abundances of olive baboons (Papio anubis) a species that can pose a threat to agricultural crops and declines in the abundances of small ungulates and primates (Brashares et al. 2010). Large carnivores are also associated with important economic and social human benefits due to their role as one of the primary drivers of wildlife viewing tourism (Lindsey et al. 2007). Tourism, including wildlife viewing, is especially important in the developing world where it is a significant or growing component of the Gross Domestic Product in 11 of the 12 countries that contain 80% of the world s poor (Ashley et al. 2000). Furthermore, many people derive value from knowing that large carnivores exist in the wild. This existence value is independent of value associated with wildlife viewing or other wildlife use (Stevens et al. 1991). Among mammals, the large carnivores form a highly endangered group, and the future of many of these species is uncertain (Ripple et al. 2014). Most of these species face multiple serious threats to their survival, 77% have declining populations, and 61% are classified as threatened by the International Union for Conservation of Nature (IUCN) (Ripple et al. 2014; International Union for Conservation of Nature 2017). Large carnivores are often persecuted by humans due to conflict over livestock and shared prey (Woodroffe 2000). Due to their charisma, endangered status and ecological significance, large carnivores have received considerable research effort (Gittleman et al. 2001; Ordiz et al. 2013; Ripple et al. 2014). Although direct persecution and habitat change have received much of the attention, the loss of prey is another potentially important threat to large carnivores. Globally, little work has been done on assessing the importance

26 8 of prey depletion as a threat to large carnivores (Ripple et al. 2014). Herein, we analyze prey depletion as a threat to large carnivore survival from a global, macroecological perspective. Abundant terrestrial mammalian prey are required for the survival of large carnivores (Carbone et al. 1999; Carbone & Gittleman 2002). In fact, there is a strong relationship between prey and carnivore abundance approximately10,000 kg of prey supports about 90 kg of large carnivore biomass regardless of species (Carbone & Gittleman 2002). When sufficient prey is unavailable, large carnivore populations will decline, possibly becoming locally extinct. This can be compounded by large carnivore conflicts with livestock, which increase as carnivores search for alternative food sources (Berger et al. 2013). Similarly, when large carnivores are forced to range more widely in search of prey, they may face greater exposure to anthropogenic threats including mortality on roads (Fahrig & Rytwinski 2009) and direct persection in regions with high human population densities (Woodroffe 2000). So far, research on prey depletion has generally focused on single carnivore species, with no comprehensive multi-species analysis. Research on tigers (Panthera tigris) suggests that prey depletion poses a major threat to their survival (Karanth & Stith 1999; Ramakrishnan et al. 1999; Chapron et al. 2008). Snow leopards (Panthera uncia) have also received attention in terms of loss of prey. Snow leopards occur in environments with relatively low productivity, leading to naturally low amounts of prey. Thus, they are particularly vulnerable to declines in prey. The snow leopard s range is primarily located in central Asia, where wild ungulates are declining due to competition with domestic livestock (Berger et al. 2013). In the Congo Basin rainforest, leopard abundances decline and diets shift toward smaller prey species in regions near human settlements due to exploitative

27 9 competition with bushmeat hunters (Henschel et al. 2011). In Africa, poacher s snares that are used to catch prey species often catch their predators as well since they are attracted to carcasses in snare lines, making the trapping of prey species both an indirect and direct threat to carnivores (Lindsey et al. 2013). Motivated by the status of large carnivores and the potential for loss of prey to threaten their survival, we assessed the endangerment status and population trends of the prey of large carnivores. In addition, we considered how prey endangerment varies across time and space. Given the wide array of serious threats faced by mammal and other species, we hypothesized that prey endangerment status has deteriorated over time. We further hypothesized that the prey of large carnivores are less endangered in the developed world as recent research indicates that carnivores in Europe are currently experiencing a recovery (Chapron et al. 2014). This hypothesis is consistent with the status of large carnivores improving in areas where the status of their prey improves. 2.3 Materials and Methods For our analysis of prey depletion, we focused only on terrestrial hypercarnivores as classified by Hunter (Hunter 2011) with mean adult body masses above 15 kg (Ripple et al. 2014). The hypercarnivores, also called obligate meat-eaters, are members of the mammalian order Carnivora that are dependent on meat for their survival. That is, their diets consist of at least 70% meat (Valkenburgh 2007). They form a group of 17 species in the carnivore families canidae, felidae, and hyaenidae (Table 2.1). The smallest species in the group are the dingo and Ethiopian wolf (Canis simensis) at 15 kg. The largest is the tiger at 161 kg (Ripple et al. 2014).

28 10 For our analysis, we used the endangerment status and trends of large carnivores prey as assessed in the International Union for Conservation of Nature (IUCN) Red List database (International Union for Conservation of Nature 2017) to quantify prey depletion. The IUCN Red List is widely recognized as the most comprehensive, objective global approach for evaluating the conservation status of plant and animal species (International Union for Conservation of Nature 2017). The endangerment status of all mammals were assessed in 2008 or later, making the data fairly current. Throughout our analysis, we used prey endangerment status and population trends as proxies for abundance since species abundances are generally not available at this scale (International Union for Conservation of Nature 2013). We constructed lists of the mammal prey species of each large carnivore to assess prey endangerment status using the single most comprehensive diet meta-analysis for each predator species (sources in Table A.1). These diet meta-analysis papers synthesize individual diet studies throughout a large carnivore s range. If multiple meta-analyses existed, we used the most recent one, provided it cited the earlier work. A few large carnivores, such as the Sunda clouded leopard (Neofelis diardi), have not been studied extensively, and lack diet meta-analyses. For these species, we searched Thomson Reuters Web of Science database for articles using their scientific names and built prey lists based on confirmed prey species according to the literature (Reuters 2015). In cases where a prey species group is listed as a genus, family, or other group of species within a genus or family, we included all prey in the group with ranges that intersect the predator s range. We excluded broader groups of prey like mammalian orders. We also developed lists of preferred prey species by noting which, if any, prey species were described as preferred by the authors of the diet meta-analysis papers.

29 11 After constructing the prey lists, we performed a basic assessment of the status of large carnivores prey by summarizing the IUCN Red List endangerment status and populations trends of the prey species for each large carnivore separately. Specifically, we recorded the percentages of prey for each large carnivore in each endangerment and population trend category. We considered threatened species to be those categorized as vulnerable, endangered, or critically endangered (Hoffmann et al. 2011). We used the Major Threat(s) sections of the Red List species fact sheets to manually determine the major threats faced by threatened prey species (habitat change, hunting for meat, etc.). In addition, we obtained prey body masses from Jones et al. (Jones et al. 2009) when available. We also split the large carnivore ranges by continent to better highlight spatial variation in prey endangerment. We summarized results for the predators with ranges overlapping each continent. For example, the Eurasian lynx (Lynx lynx) is included in the results for both Europe and Asia and the mountain lion (Puma concolor) in both North and South America. We then split the prey lists accordingly by constructing shorter prey lists corresponding to prey species overlapping each large carnivores range within a given continent. To visualize prey endangerment spatially, we used a Geodesic Discrete Global Grid System (DGGS) that divides the earth s surface into hexagons, each with area ~12,500 km 2 (Sahr et al. 2003; Sahr 2011). We retained only the hexagons whose centers occurred over land and not large bodies of water. For each hexagon, we determined the large carnivores and prey species with ranges that overlapped it, allowing us to map the proportion of endangered species across each large carnivore s range at the hexagon level. We used this mapping approach to emphasize prey species with smaller ranges and to reduce the impact of range map inaccuracies (Hurlbert & Jetz 2007).

30 12 To assess changes in prey endangerment, we obtained corrected 1996 IUCN endangerment statuses from (Hoffmann et al. 2011). For our analysis of changes in endangerment, we considered only prey species that were assessed in Mammal species endangerment information in the current IUCN Red List was last updated in 2008 or later, so we refer to current statuses as 2008 status when making comparisons across time. We also considered overlap between prey species ranges and protected areas using the World Database of Protected Areas (IUCN and UNEP-WCMC 2015). We used only protected areas with IUCN categories Ia, Ib, II, or III (the highest levels of protection) and polygon (rather than point) spatial information. We clipped each prey species range to these protected areas in order to determine total and percentage area overlap. We conducted a literature search to assess the extent to which prey depletion has been considered in large carnivore conservation research. For each of the large carnivore species in our analysis, we searched Thomson Reuters Web of Science database for articles with title including the carnivore s scientific or common name and topic conservation (Reuters 2015). After excluding articles not related to the large carnivore searched for, we classified the six most cited articles for each carnivore based on the extent to which prey was mentioned into three categories: not mentioned at all, mentioned without reference to prey endangerment, status or depletion, or mentioned in the context of prey status or depletion. 2.4 Results

31 13 All together, the prey lists contain 494 species, of which 123 species (25%) were threatened: 67 (14%) are classified as vulnerable, 44 (9%) endangered, and 12 (2%) critically endangered (Table A.2). Additionally, 37 species (7%) are data deficient. Overall, threatened large carnivores had more threatened prey, with an average of 27% of their prey threatened compared to 19% for non-threatened carnivores. The five large carnivores with the highest proportions of threatened prey were the clouded leopard (60%), Sunda clouded leopard (50%), tiger (50%), dhole (42%), and Ethiopian wolf (40%) (Figure 2.1). All other carnivores had less than 30% of their prey threatened (Figures 2.1, A.1). The five large carnivores with the highest proportions of prey with decreasing population trends were the Sunda clouded leopard (88%), tiger (81%), dhole (81%), clouded leopard (80%), and leopard (56%) (Figures 2.2, 2.3, A.2). Many prey species had unknown population trends. For example, 40% of the Ethiopian wolf s prey species have decreasing trends while the remaining 60% of its prey have unknown trends. At the continent level, prey endangerment rates were highest in Asia, South America, and Africa, where large carnivores had an average of 33%, 22%, and 18% of their prey threatened respectively (Figures 2.4, A.3). The corresponding percentages of prey with decreasing trends were 55%, 39%, and 37% (Figures 2.4, A.4). The preferred prey lists contain 114 species, of which 20 (18%) were threatened (Table A.2). Overall endangerment patterns for preferred prey species (Figures A.5-A.9) were similar to those for all prey species. The tiger and Ethiopian wolf have the highest rates of preferred prey endangerment 50% for both species (Figure A.5). The clouded leopard and Sunda clouded leopard were excluded

32 from the preferred prey analysis as their preferred prey species could not be determined from their diet study references. 14 Prey status declined from 1996 to 2008 for all but six of the large carnivores (Table 2.2). No large carnivore had a net improvement in prey species status. Only one of the 494 prey species improved in status. The primary threats faced by prey species were habitat change and hunting for meat, which threaten 19% and 16% of all prey species respectively (Figure A.10). The most common forms of habitat change threatening prey species were agriculture (12%) and deforestation (11%). Other common forms of hunting were hunting for body parts (10%), medicine (6%), and ornaments (5%). The extent to which prey were protected varied widely, with the 494 total prey species having an average of 6.9% of their ranges protected (Figure 2.5). The five species with the least protected prey were the red wolf (3%), snow leopard (3%), Eurasian lynx (4%), puma (4%), and clouded leopard (5%) (Figure 2.5). Of these five species, the red wolf, snow leopard, and clouded leopard were listed as threatened (Table 2.1). There is also wide variability in both prey species orders and masses (Figure A.11). Of the 494 prey species identified, masses were available for 360 (73%). These 360 prey species cover a large range of masses: kg (49 species), kg (50), 1 10 kg (125), kg (98), kg (33), kg (5). All together, the prey species span 16 different orders. The orders with at least five prey species were even-toed ungulates (Cetartiodactyla): 133, opossums (Didelphimorphia): 88, primates (Primates): 87, rodents (Rodentia): 73, rabbits,

33 hares and pika (Lagomorpha): 53, armadillos (Cingulata): 21, diprotodonts (Diprotodontia): 15, and odd-toed ungulates (Perissodactyla): Variability in prey consumed occurs both within and among large carnivore species. In terms of prey orders consumed, the four large carnivores with the greatest diet diversity were the leopard (7 orders), dingo (7), cheetah (6), and jaguar (5). The carnivores that prey on the fewest number of orders (2) were the African wild dog (Lycaon pictus), dhole, Ethiopian wolf, and Eurasian lynx (Figure A.11). In total, we obtained 100 articles for our literature search (Table A.3). Only four articles on the Sunda clouded leopard were found. Forty six of the articles mentioned prey endangerment status, prey depletion, or the importance of prey to large carnivores (Figure A.12). None of these 46 articles were about the Eurasian lynx, dingo, clouded leopard, or Sunda clouded leopard (Figure A.12). 2.5 Discussion Our results show that prey endangerment leading to loss of prey base is a common threat faced by many large carnivores. In particular, the clouded leopard, Sunda clouded leopard, tiger, dhole, and Ethiopian wolf all had highly threatened prey and were themselves threatened. With the exception of the Ethiopian wolf, all of these species have large portions of their ranges in Southeast Asia, where many prey species were endangered (Figure 3). Prey in Southeast Asia face many threats related to high human population densities, hunting, and habitat loss due to deforestation (Miettinen et al. 2011).

34 16 The continental results (Figures A.3 and A4; see also Figure 2.4) show that large carnivores prey were more threatened in the developing world than in the developed world. This may be a consequence of many historic prey species (e.g. megaherbivores) having already been extirpated from Europe and the Americas due to overhunting and other factors (Stuart 1991). Many of the remaining prey species have experienced major recoveries in the developed world to the point that some ungulate populations are now considered overabundant, especially in the absence of their native large predators (Bradford & Hobbs 2008). The recovery of prey populations in Europe may have contributed to the recent large carnivore recoveries observed there, although other factors including increased public tolerance played a role as well (Chapron et al. 2014). Similarly, the higher rates of prey endangerment in the developing world, particularly Africa and Asia, have likely contributed to carnivores being more endangered there, with 9 of the 11 large carnivores endemic to these regions classified as threatened. In developing countries, carnivores may be endangered by both prey depletion and threats like habitat loss that are also faced by prey species. The link between predator and prey endangerment provides additional rationale for conserving mammal prey species in the developing world. There is currently a funding mismatch with 32% of all threatened mammals found in the 40 most underfunded countries (Waldron et al. 2013). These 40 countries include Indonesia, Malaysia, and many others where large carnivores are present (Waldron et al. 2013). Moreover, spending on terrestrial reserves in developing countries is less than 5% of what is needed for effective conservation (Balmford & Whitten 2003). As poverty rates in the developing world decline, conservation funding may increase and people could become less reliant on consuming wild meat for survival (Bennett 2002). If this happens, prey populations could recover, and with supporting legislation and sufficient public tolerance, carnivores may

35 also recover, paralleling the pattern of prey recoveries followed by predator recoveries seen in Europe. 17 Large carnivore diets typically include a wide range of prey (Figure A.11). While large carnivores are generally reliant on large prey, the majority of prey species were under 10 kg. This suggests that smaller prey species can be important food sources for many large carnivores and prey depletion analyses should consider abundances of both small and large prey. Seven large carnivores had median prey masses below 10 kg: jaguar (.3 kg), Ethiopian wolf (.4 kg), dingo (.8 kg), red wolf (1.1 kg), snow leopard (1.5 kg), puma (4.2 kg), and clouded leopard (4.9 kg) (Figure A.11). These species may be particularly reliant on small prey. In some cases, this could be a result of larger prey tending to be more endangered. Other carnivores may also switch to consuming smaller prey when larger prey are scarce, potentially decreasing their extinction risk. For example, African wild dogs can subsist on small prey such as Kirk s dikdiks (Madoqua kirkii) when abundant in regions where larger prey are depleted (Woodroffe et al. 2007) and leopards may switch to consuming smaller prey when bushmeat hunting makes large prey scarce (Henschel et al. 2011). Low median prey masses may also be related to the inclusion of large numbers of small, rare prey in our original prey species lists. Restricting the analysis to preferred prey, just three carnivores had median preferred prey masses below 10 kg: Ethiopian wolf (.1 kg), red wolf (1.4 kg), and jaguar (4.0 kg) (Figure A.13). Relatively low observed diet diversity could be due to lack of information on prey (likely with the clouded leopards), natural specialization (e.g. Ethiopian wolf and rodents), or due to declines in prey populations in the past (e.g. gray wolf and Eurasian lynx in Europe) or past and present (possibly dhole). In any case, carnivores with low diet breadth may be more vulnerable to prey depletion as it

36 18 may be more difficult for them to switch to alternate prey when their preferred prey decline. In one study, rodents made up 88% of Ethiopian wolf diets by volume (Ashenafi et al. 2005). Ethiopian wolves are currently classified as critically endangered (CR) and their specialized diets consisting primarily of Afroalpine rodents may put them at greater risk of extinction. Although rodents are generally resilient species, the assessed rodent prey of Ethiopian wolves the giant mole rat (Tachyoryctes macrocephalus) and black-clawed brush-furred rat (Lophuromys melanonyx) are both threatened by livestock overgrazing of their habitat (International Union for Conservation of Nature 2017). Even large carnivores with high observed diet breadth can be vulnerable to prey depletion. Anthropogenic threats to prey species such as habitat loss due to humans and hunting for meat often affect a wide array of prey species in contrast to more specialized threats like certain viruses (Figure A.10). While nearly half (46%) of the articles found in our literature search mentioned prey status or depletion, the majority of these articles were not focused on preyrelated issues, but rather mentioned them briefly in passing, often when providing general conservation background information in the introduction section of the papers (Figure A.12, Table A.3). Our results exclude most articles on prey depletion as we only looked at the six most cited conservation articles for each carnivore. Several large carnivore species had specific conservation issues that dominated their search results. For example, the ecological effects of dingos, taxonomic issues associated with clouded leopards, and red wolves and hybridization Limitations

37 19 In our analysis, we have only considered terrestrial mammalian prey. The endangerment status of non-mammalian prey were not included in the results. However, a brief study of the predator-specific diet meta-analysis papers (Hayward 2006) suggests that non-mammals are generally not important food sources for large carnivores. We did not consider carnivores as potential prey for other carnivores as they are also seldom an important food source due to their naturally low abundances and other life history traits (Palomares & Caro 1999). Some of the prey species that were included in our analysis represent potential, rather than actual, prey. We attempted to assess the impact of excluding potential or uncommon prey by re-running key portions of our analysis on preferred prey only. Similarly, uncommon prey species may have been excluded from our analysis if they were not reported in our sources. Prey depletion is a function of declining prey abundances, which are difficult to measure at a global scale. This analysis is reliant on the use of prey endangerment status as a proxy for prey abundance. Species can be classified as threatened due to declining or very low abundance, making this a reasonable proxy variable (International Union for Conservation of Nature 2013). However, its use still represents a limitation of this analysis caused by the inability to measure abundances directly at this scale. Even accepting their use as a proxy variable, endangerment statuses also have the disadvantage that they are measured at the species level. This is a problem when endangerment varies across a species range. For example, a prey species may be very endangered in one part of the world and overabundant in another part. Given the number and ranges of species involved in this analysis, there does not appear to be a more accurate data source that can be used. While our results should be interpreted carefully due to this limitation, it is likely that using global rather than local prey endangerment information underestimates the extent of prey depletion. If a prey species has

38 20 several large, healthy populations, it is unlikely to be listed as threatened. On the other hand, it is common for prey species classified as least concern or near threatened to have threatened populations. This is particularly true in Africa where many non-threatened ungulates like bushbuck (Tragelaphus scriptus) are locally threatened at certain sites due to bushmeat hunting (Fitzgibbon et al. 1995). In addition, this is a predator-centric project. Prey endangerment is viewed here as a potential driver of predator endangerment. However, prey endangerment is an important problem in and of itself as a large portion of mammals (both predators and prey) are currently threatened (Schipper et al. 2008). Moreover, overabundant predators may be a driver of prey endangerment a possibility that was not explored in this project. We assumed that predators mammalian prey as reported in comprehensive diet meta-analyses (Hayward 2006) were representative of their historic prey. This may not be the case because historically preferred prey may now be too rare to appear in diet studies a shifting baseline problem (Papworth et al. 2009). For example, domestic animals recently made up an estimated 87% of the prey biomass of leopards in western Maharashtra, India (Athreya et al. 2016). In that study, the only wild prey found in leopard diets were rodents, small carnivores, primates, and birds (Athreya et al. 2016). Assessing prey preferences in such cases is problematic as historic prey may have been extirpated from the study area. This issue is partially mitigated by our use of diet meta-analyses that likely include some studies from remote regions with relatively limited anthropogenic impacts Conservation Implications

39 21 This analysis is the first of its kind and addresses an important conservation issue depletion of prey as a threat to large carnivores at a global scale. By analyzing the status of prey for all the large carnivores as a group, we found significant evidence that the loss of prey species is a widespread issue and identified five large carnivore species (Figure 2.3) that are particularly at risk. Of these five species, the clouded leopards are vulnerable and the tiger and dhole are endangered. The leopard is classified as near threatened rather than threatened, possibly due to the breadth of its diet or other unique circumstances. On the other hand, the leopard was the only large carnivore that worsened in status from 1996 to 2008, and may be further uplisted to vulnerable on the basis of declining populations (Jacobson et al. 2016). Our results suggest that prey endangerment may deserve further consideration in leopard conservation. While more work is needed to understand the extent to which these species are threatened due to prey depletion, our results indicate the importance of conserving prey to conserve large carnivores. Recognition of the widespread occurrence of prey depletion motivates a holistic approach to conservation over purely predator-centric approaches. One of the ways this could be achieved is by strengthening management of protected areas which protect predators, prey, and habitat. This is particularly important in Africa where many large carnivores reside and protected areas are often ineffective due to poaching, lack of funding, and rapidly growing human populations (Jacobson et al. 2016). In addition to strengthening management, enlarging and connecting existing reserves could help prevent isolation, reducing the impacts of harmful human-related edge effects (Watson et al. 2015). As large carnivores range widely, are often persecuted by humans, and are highly dependent on prey

40 availability, they can benefit greatly from expanded and strengthened protected area networks (Watson et al. 2015). 22 Large carnivores broad diets mean that prey conservation efforts aimed at ensuring a robust prey base will tend to be most effective when they do not benefit individual prey species alone. For ungulates, a particularly important prey source for many carnivores (Figure A.11), collateral conservation (e.g. habitat protection, snare removal, certain programs targeting other species) has been the primary factor preventing recent increases in endangerment (Hoffmann et al. 2015). More generally, large carnivores benefiting from prey conservation can also be viewed as a form of collateral conservation. Similarly, prey can benefit from conservation efforts aimed solely at their predators as predator populations often limit the abundances of competitively superior prey. While predator-centric conservation is certainly necessary (e.g. efforts to reduce hunting of threatened carnivores), ultimately, effective predator conservation cannot be accomplished without effective prey conservation (William J. Ripple et al. in press). 2.6 Data accessibility The datasets supporting this article have been uploaded as part of the supplementary material. 2.7 Competing Interests We have no competing interests. 2.8 Authors contributions

41 23 CW carried out the data analysis and drafted the manuscript; WR conceived of the project and helped draft the manuscript. All authors gave final approval for publication. 2.9 Acknowledgements We thank Peter Lindsey and Luke Hunter for reviewing a draft of the paper and providing helpful comments Funding We have no funding sources to report.

42 Figure 2.1. IUCN Red List conservation status of large carnivores prey. Status categories are: DD (data deficient), LC (least concern), NT (near threatened), VU (vulnerable), EN (endangered), CR (critically endangered). Carnivores are ordered by decreasing percentage threatened (VU/EN/CR) prey from the top down. The numbers of prey species are shown after the large carnivore names. 24

43 Figure 2.2. Population trends of large carnivores prey. Carnivores are sorted by percentage of prey with decreasing population trends. The numbers of prey species are shown after the large carnivore names. 25

44 Figure 2.3. Maps showing the percentages of large carnivore prey species with decreasing population trends for the five large carnivores whose prey have the highest percentages of decreasing trends. 26

45 Figure 2.4. Percentages of all 494 prey species that are threatened (top) or have decreasing population trends (bottom). 27

46 Figure 2.5. Mean percentages (with standard errors) of prey species ranges occurring inside protected areas. For example, the prey species of the dingo have an average of 13% of their ranges within protected areas. 28

47 Table 2.1. The 17 obligate meat-eating carnivores with masses at least 15 kg. Status is the IUCN Red List conservation status (2008 or later): LC (least concern), NT (near threatened), VU (vulnerable), EN (endangered), CR (critically endangered) (International Union for Conservation of Nature 2017). None of these species changed in endangerment status since 1996, except the dingo (which was not assessed at that time) and the leopard, which was classified as LC. Estimated current population sizes are from the IUCN Red List. Scientific Name Common Name Status Trend Family Population Size Acinonyx jubatus Cheetah VU Decreasing Felidae 6,674 Canis lupus Gray wolf LC Stable Canidae 168, ,000 Canis dingo Dingo VU Decreasing Canidae Canis rufus Red wolf CR Increasing Canidae <150 Canis simensis Ethiopian wolf EN Decreasing Canidae Crocuta crocuta Spotted hyena LC Decreasing Hyaenidae 27,000-47,000 Cuon alpinus Dhole EN Decreasing Canidae 4,500-10,500 Lycaon pictus African wild dog EN Decreasing Canidae 6,600 Lynx lynx Eurasian lynx LC Stable Felidae Neofelis diardi Sunda clouded leopard VU Decreasing Felidae 4,500 Neofelis nebulosa Clouded leopard VU Decreasing Felidae Panthera leo Lion VU Decreasing Felidae 18,726-31,395 Panthera onca Jaguar NT Decreasing Felidae Panthera pardus Leopard NT Decreasing Felidae Panthera tigris Tiger EN Decreasing Felidae 3,159 Panthera uncia Snow leopard EN Decreasing Felidae 4,080-6,590 Puma concolor Puma LC Decreasing Felidae 29

48 Table 2.2. Change in prey threat status. Total is the number of prey species LC- CR in 1996 and Declined/improved are the numbers of prey species that have declined/improved in status where LC < NT < VU < EN < CR. % Change is the net percentage change in prey endangerment. Species Total Declined Improved % Change Clouded leopard % Sunda clouded leopard % Dhole % Tiger % Leopard % Puma % Snow leopard % Dingo % Jaguar % Gray wolf % Cheetah % African wild dog % Ethiopian wolf % Eurasian lynx % Lion % Red wolf % Spotted hyena % 30

49 3. RANGE CONTRACTIONS OF THE WORLD S LARGE CARNIVORES Christopher Wolf and William Ripple 31 Wolf, Christopher, and William J. Ripple. "Range contractions of the world's large carnivores." Royal Society Open Science 4.7 (2017):

50 Abstract The majority of the world s terrestrial large carnivores have undergone substantial range contractions and many of these species are currently threatened with extinction. However, there has been little effort to fully quantify the extent of large carnivore range contractions, which hinders our ability to understand the roles and relative drivers of such trends. Here we present and analyze a newly constructed and comprehensive set of large carnivore range contraction maps. We reveal the extent to which ranges have contracted since historical times and identify regions and biomes where range contractions have been particularly large. In summary, large carnivores that have experienced the greatest range contractions include the red wolf (Canis rufus) (> 99%), Ethiopian wolf (Canis simensis) (99%), tiger (Panthera tigris) (95%), and lion (Panthera leo) (94%). The greatest range contractions occurred in Southeastern Asia and Africa. Motivated by the ecological importance of intact large carnivore guilds, we also examined the spatial extent of intact large carnivore guilds both for the entire world and regionally. We found that intact carnivore guilds occupy just 34% of the world s land area. This compares to 96% in historic times. Spatial modeling of range contractions showed that contractions were significantly more likely in regions with high rural human population density, cattle density, or cropland. Our results offer new insights into how best to prevent further range contractions for the world s largest carnivores, which will assist efforts to conserve these species and their important ecological effects. 3.2 Introduction

51 33 Large carnivores are among the world s most threatened species (Ripple et al. 2014). They face a wide variety of anthropogenic threats including persecution by humans, particularly over livestock related conflicts, hunting and trapping, and loss of prey base (Ripple et al. 2014; Wolf & Ripple 2016). Moreover, their unique life history characteristics (e.g. relatively long gestation lengths among carnivores) make them particularly vulnerable to anthropogenic threats associated with increasing human population densities (Cardillo et al. 2004). There is now extensive literature documenting the ecological importance of these species, with trophic cascades having been found for 7 of the 31 large carnivores (Ripple et al. 2014). However, research into the ecological effects of large carnivores has almost certainly been hampered by the limited knowledge available on the extent to which these species have undergone range contractions. Increases in species extinction risk are typically linked to the loss of individual populations and associated declines in geographic range (Ceballos & Ehrlich 2002). Thus, species range contractions are closely related to extinction risk and the analysis of range contractions can provide spatially explicit insight into what is happening to a species both at the level of individual populations and as a whole. They have major conservation value in terms of guiding efforts to limit further range contractions, and potentially, promoting range expansions within historic ranges. Analyses of range contractions often consider the spatial patterns of the contractions, with emphasis on the extent to which ranges contract toward their center (Lomolino & Channell 1995; Channell & Lomolino 2000a). Such analyses can inform conservation decisions regarding the most critical regions of a species range to protect (Channell 2004). An alternative form of range contraction analysis involves modeling the likelihood of range contraction using spatially varying predictor variables like human footprint metrics (Yackulic et al.

52 2011). Such models can help conservation researchers gain a better understanding of the roles and relative influence of potential drivers of range contractions. 34 There are several major multispecies range contraction results that include some of the extant terrestrial large carnivores. An extensive set (n = 173) of terrestrial mammals have together lost more than 50% of their historic range, with losses most severe in regions with high human population density (HPD) or other human impacts (Ceballos & Ehrlich 2002). Among 43 ungulate and carnivore species in North America, 17 species have experienced range contractions of at least 20%, and range contractions have been most common in regions with high human influence (Laliberté & Ripple 2004). Similarly, generally positive relationships have been found between human population density and the probability of range contraction for 10 large carnivores in portions of their range (Woodroffe 2000). Among 245 species spanning numerous taxonomic classes, most species tended to persist in the peripheral regions of their ranges rather than the historic core (Channell & Lomolino 2000b). However, among mammals, biome type has been found to be more predictive of the likelihood of range contraction than position within range (distance to historic centroid) (Yackulic et al. 2011). Currently, less than 21% of the world s land retains its historic large (> 20 kg) large mammal guild (Morrison et al. 2007). Moreover, large carnivore guilds have undergone a substantial loss in functional diversity since the late Pleistocene (Dalerum et al. 2009). While each of these range contraction analyses has included some of the large carnivores, no analysis has yet focused on range contractions of all extant terrestrial large carnivores worldwide. Here, we conduct the first such global analysis of large carnivore range contractions. We used historic and current range maps for the large carnivores ( 15 kg body mass) with reliable historic range

53 35 maps available. We excluded the otters (Lutrinae) and polar bear (Ursus maritimus) as these species are primarily aquatic and our analysis focuses on terrestrial species. We excluded the maned wolf (Chrysocyon brachyurus) as an accurate historic range map was not available for this species. This was the only species that we excluded from our analysis due to lack of a suitable historic range map. Guided by the range contraction literature, we split our analysis into several research questions and hypotheses. We hypothesized that range contractions have been greatest (in terms of numbers of species lost) in Sub-Saharan Africa, Southern Asia, and Southeastern Asia since these regions have historically contained many large carnivores. Given the similarities among large carnivore species, we hypothesized that they have had major range contractions regardless of life history traits. We further hypothesized that intact large carnivore guilds are very uncommon and occupy small fractions of their historic areas, with most intact guilds tending to contain few species and occurring at high latitudes where human influence is lower. Finally, we hypothesized that high human population density, cropland, and cattle density are all positively correlated with the likelihood of range contraction as prior analyses suggest human influence in general is a key driver of range contractions (Ceballos & Ehrlich 2002; Laliberté & Ripple 2004). 3.3 Methods Historic and current range maps We obtained current range maps for 24 of the 25 large carnivores in our analysis from the International Union for Conservation of Nature (IUCN) Red List (International Union for Conservation of Nature 2017). The current range map of

54 36 the dingo (Canis dingo) was provided by Letnic et al. (Letnic et al. 2012). For the current ranges using IUCN source maps, we treated the ranges as areas where species are classified as extant or probably extant (regardless of origin). For the historic range maps, we used maps from a variety of sources (Table B.1). We treated the historic maps as corresponding to approximately 1500 AD after Morrison et al. (Morrison et al. 2007). When comparing current and historic range maps, we frequently observed slivers (long regions of apparent range expansion next to historic ranges) and islands (isolated areas of apparent range expansion near historic ranges). As these slivers and islands are more likely artifacts associated with mapping errors than real range expansions, we extended the historic ranges to include all areas in the current range of each species. We made slight adjustments to the historic and current ranges near coastlines in order to align them with each other and a map of land, adding terrestrial regions within three 0.05 degree raster grid cells of each range and the ocean to each range. We then clipped ranges using species altitude limits from the Red List species fact sheets when these data were available. We did not do this for the Ethiopian wolf (Canis simensis) as its elevation limit appears to be for its current range only. Minor additional modifications were made to the historic range maps on a case by case basis (Table B.1) Mapping We added the species ranges (0.05 degree resolution) together to form composite richness maps corresponding to historic species richness, current species richness, species richness lost (historic minus current), and percentage of species lost. We

55 37 also quantified the change in large carnivore richness at the scales of biomes and geographic regions (Olson et al. 2001; United Nations 2013). We assessed the extent of intact carnivore guilds by defining regions with intact guilds to be those with zero carnivores lost. Geographic Information System (GIS) analysis was done in ArcGIS 10.1 and R (ESRI 2012; R Core Team 2013) Modeling range contractions We modeled range contractions for all species together using a residuals autocovariate (RAC) model (Augustin et al. 1996; Crase et al. 2012). We used composite species range maps at 50 km resolution because it was considered most appropriate given the accuracy of the historic range maps (Yackulic et al. 2011). Observations in our model were binary, with each observation corresponding to whether or not a species range had contracted from a 50 km x 50 km grid cell within its historic range. We included a spatial auto-covariate term in order to account for potential autocorrelation. The spatial auto-covariate was derived from the corresponding non-spatial generalized linear mixed model deviance residuals. Specifically, it was based on the average of the residuals for all grid cells within 300 km of each grid cell and was calculated using the spdep R package (Bivand et al. 2015). Additionally, we included random intercepts at the level of species to account for potential taxonomic dependence. We fit the models using the glmer function in the lme4 R package (Bates 2010 p. 4). For predictor variables, we used 2014 estimated cattle density (cattle per km 2 ) from the Food and Agriculture Organization s (FAO) gridded livestock of the

56 38 world database (Robinson et al. 2007, 2014), 2015 estimated rural human population density (HPD) (Salvatore et al. 2005), and cropland (Van Velthuizen 2007) (Figure B.1). All predictors were included in the model together and were standardized to have mean zero and standard deviation one so that estimated effect sizes were comparable. To explore the extent to which the estimated effects vary by region, we also fit a model including random intercepts and slopes by geographic region. We quantified the effect of these additional terms by calculating the change in conditional (i.e., accounting for the random effects) pseudo-r 2 using r.squaredglmm in the MuMIn R package (K. Barton 2016) and by calculating the random effect estimates (conditional modes). To visualize these results, the random effect estimates were added to the fixed effect estimates, with 95% prediction intervals constructed under the assumption that random and fixed effect estimates are independent. Finally, we quantified the effect of variability at the species level by looking at the difference between marginal and conditional pseudo-r 2 for our main model. 3.4 Results The compiled set of carnivore range contraction maps (n = 25) showed significant range contractions for many large carnivore species (Figure 3.1, Table B.2). The six large carnivores with the greatest estimated range contractions were the red wolf (> 99%), Ethiopian wolf (99%), tiger (Panthera tigris) (95%), lion (Panthera leo) (94%), African wild dog (Lycaon pictus) (93%), and cheetah (Acinonyx jubatus) (92%), while the six carnivores with the smallest range contractions were the Eurasian lynx (Lynx lynx) (12%), dingo (12%), striped hyena (Hyaena hyaena) (15%), spotted hyena (Crocuta crocuta) (24%), gray wolf (Canis lupus) (26%), and brown hyena (Parahyaena brunnea) (27%) (Figure 3.2).

57 39 With the exception of the red wolf, all 13 of the large carnivore species that experienced the greatest percentage range contraction are currently both threatened with extinction (IUCN Red List status Vulnerable, Endangered, or Critically endangered ) and have decreasing population trends according to the IUCN Red List (Figure 3.2). Overall, the extent of range contractions did not appear to vary substantially with large carnivore mass or taxonomic family although the hyenas experienced relatively minor range contractions as a group (Figure B.2). The composite range contraction maps showed the highest historic large carnivore richness in South and Southeast Asia (up to 9 co-occurring species) and Africa (up to 6 co-occurring species) (Figure 3.3). The greatest declines in average large carnivore richness were observed in Southeast Asia (2.9 species), Africa (2.9), and Asia (excluding Southeast Asia) (2.8), while the smallest declines were observed in Oceania (0.1), Europe (0.8), and the Americas (1.0) (Figure 3.4). In contrast, regions with high percentages of large carnivores lost were more uniformly distributed spatially, with particularly large areas where 100% of historic large carnivores have been extirpated occurring in Europe, the Eastern United States, and Southeast Asia (Figure 3.3). In terms of biomes, the greatest declines occurred in Tropical & Subtropical Dry Broadleaf Forests (3.0 species), Flooded Grasslands & Savannas (2.6), and Tropical and Subtropical Grasslands, Savannas and Shrublands (2.6), while the smallest declines occurred in Tundra (0.1), Boreal Forests/Taiga (0.4), and Temperate Conifer Forests (1.6) biome types (Figure B.3). Globally, large carnivores historically covered 96% of the world s land area, but intact large carnivore guilds now occupy just 34% of the world s land (Figure 3.5). The proportion of land covered by intact guilds varied substantially by

58 region: Oceania (89%), Europe including Russia (57%), Americas (48%), Southeast Asia (37%), Africa (8%), Asia excluding Southeast Asia (5%). 40 Our model results indicate that rural population density (average: 19 people/km 2, standard deviation: 48 people/km 2 ), cattle density (average: 9.9 cattle/km 2, standard deviation: 26 cattle/km 2 ), and cropland (average: 12%, standard deviation: 19%) were all positively associated with large carnivore range contractions (p < ) (Figure B.4). The estimated increases (with 95% confidence intervals) in the odds of large carnivore range contraction for 1 standard deviation increase in (log 1 plus transformed) rural population density and cattle density were 20% (17%, 24%) and 24% (21%, 27%) respectively. The estimated increase in the odds of range contraction per one standard deviation increase in percentage cropland was 72% (68%, 75%). The random intercepts by species explained 46.0% of the variability in the response (marginal R 2 : 29.1%, conditional R 2 :75.2%). The inclusion of random intercepts and slopes by geographic region (regions listed in Figure 3.4) increased the conditional pseudo- R 2 by 3.95% (from 75.18% to 79.13%). The random effect conditional modes (Figure B.5) indicate substantial variation by geographic region in the effect sizes. 3.5 Discussion Individual maps While range contractions of well-studied large carnivores like tigers are often noted in the literature (Dinerstein et al. 2007), our results show that major range contractions are common for most of the 25 large carnivores (Figure 3.1). Eighty eight percent (22/25) of the large carnivores had range contractions of 20% or

59 41 more (Figure 3.2). This is substantially more than the reported 40% (17/43) of North American carnivores and ungulates with range contractions of at least 20% (Laliberté & Ripple 2004) a difference likely due to the greater vulnerability of large carnivores to anthropogenic threats, many of which continue today. By giving historical context to current ranges, our results show the extent to which large carnivores have been extirpated from Europe despite recent reports of large carnivore recoveries there (Chapron et al. 2014). In certain cases, range contraction patterns appear to have occurred due to unusual, species-specific circumstances. For example, the red wolf s current range is due to a planned reintroduction and the dingo s current range is limited by barrier fencing spanning across parts of Australia. Moreover, the dingo s historic range is itself due to an introduction several thousand years ago. The unique circumstances for each large carnivore mean care must be taken when trying to interpret range contractions at the level of individual species. Therefore, we have emphasized composite range contraction maps and figures showing broad trends, changes in guilds containing many species, and modeling range contractions for all large carnivores pooled together Family and body mass The finding that species taxonomic family and body mass do not appear to be strongly predictive of range contraction extent (Figure B.2) appears to contradict previous work showing that extinction risk is higher for larger-bodied carnivore species (Purvis et al. 2000; Cardillo et al. 2004). It is possible that the lack of apparent relationship between species body mass and percentage range contraction is due to the limited number of observations (only 25 large

60 42 carnivores), which makes statistical hypothesis testing at the level of individual species difficult, particularly once spatial and phylogenetic dependence have been modeled. On the other hand, the lack of relationship could mean that extrinsic environmental factors (e.g. human, cattle density) are more predictive of range contractions than intrinsic factors (e.g. body mass). This is consistent with the more limited body mass range spanned by large carnivore species relative to the ranges spanned by the taxa considered in previous analyses (Purvis et al. 2000; Cardillo et al. 2004) Composite maps and results As expected, historic and current large carnivore richness are strongly correlated spatially (Figure 3.3). Large regions of the eastern United States and Europe have lost 100% of their large carnivores (Figure 3.3). The fact that this level of loss has not occurred in many other regions with high human population density suggests that there are other key drivers of carnivore conservation outcomes (e.g. human culture and intensive livestock), as supported by our model results (Figure B.4). The biomes where the lowest loss in mean large carnivore richness occurred tend to be those with low rural population densities and limited agriculture, consistent with general human impacts (including agriculture) being linked to range contractions (Figures B.1, B.3) (Sanderson et al. 2002) Guild analysis Large carnivore guilds, particularly those outside the far North have undergone substantial reductions in area since historical times (Figure 3.5). This is notable as conservation may be more readily accomplished at the level of whole predator

61 43 guilds. While carnivore species abundances may vary inversely due to competitive exclusion (Miquelle et al. 2005), there are also well-documented facilitative relationships among large carnivore species. For example through trophic cascades, gray wolves can indirectly benefit berry-producing shrubs, providing food for grizzly bears (Berger et al. 2001a). Many large carnivores (e.g. brown hyenas) benefit from scavenging carcasses left by other carnivore species (Pereira et al. 2014). Another intriguing possibility is that of interspecific cooperation among large carnivores. Gray wolves and striped hyenas have been documented travelling together, possibly cooperating to benefit from the wolves superior ability to subdue large prey and the striped hyenas better sense of smell and ability to break large bones (Dinets & Eligulashvili 2016). Facilitative interactions among large carnivores means that the extirpation of one or more species could negatively impact the others. Another reason to attempt conservation at the scale of guilds is that it is often easier to focus conservation efforts around certain flagship large carnivore species. While some of the most popular flagship species are large carnivores (e.g. gray wolves and tigers), not all large carnivores are well-recognized (Clucas et al. 2008). Conservation programs centered around flagship large carnivores that maintain adequate habitat, reduce trapping, and protect shared prey base may benefit some of the lesser known large carnivores like clouded leopards (Wolf & Ripple 2016). When assessing the coverage of intact carnivore guilds, we treated co-occurring large carnivores as forming a single guild. However, these species can also be divided into functional groups such as bone crushers, stalk and ambush carnivores, and pursuit carnivores based on their method of hunting and other characteristics (38). Our treatment of co-occurring large carnivores as forming a single guild allows for the possibility of complex emergent predator effects that span multiple functional groups (Sih et al. 1998). For example, co-occurring

62 wolves and brown bears have well-documented emergent effects despite being in different functional groups (Ripple & Beschta 2012) Model results The strong positive estimated effect of cattle density on the likelihood of range contraction (Figure B.4) is consistent with the literature on large carnivore conservation and livestock. There are several mechanisms by which cattle and other extensively grazed livestock can adversely impact large carnivores. Cattle compete with wild ungulates, potentially reducing the availability of the carnivores natural prey. This prey depletion leads to less food available for carnivores, reducing their abundances and possibly leading to increased humancarnivore conflict related to livestock depredation (Wolf & Ripple 2016). Similarly, loss of prey base was also likely a major driver of the Pleistocene large carnivore range contractions and extinctions as megaherbivores in many regions appear to have been primarily predator-limited prior to the arrival of human hunters (Ripple & Van Valkenburgh 2010). Regardless of prey availability issues, real or perceived risks to livestock may lead humans to persecute carnivores (Adams Knopff et al. 2016). The conversion of natural landscapes to cropland reduces the availability of wild prey for carnivores and brings them into closer contact with humans, helping to explain the observed positive association between cropland and range contractions. Higher rural population density may also put humans and carnivores in close contact, consistent with the positive estimated effect (Woodroffe 2000). Human tolerance of large carnivores, government policy, and other social factors are likely very important predictors of range contractions, but we lacked the data

63 45 to assess their effects. Even in areas with substantial livestock and cropland, carnivores may be able to persist depending on human attitudes. For example, leopards and spotted hyenas were found to persist in a cropland dominated region of western Maharashtra, India with more than 300 people per square kilometer (Athreya et al. 2016). Similarly, spotted hyenas have been observed in highly populated regions of Ethiopia despite a lack of natural prey as they are able to subsist on garbage and livestock (Yirga et al. 2015) Limitations There are several key limitations associated with our use of historic range maps. These maps tend to have low resolution, not showing holes in species historic ranges or small islands (Laliberté & Ripple 2004). We attempted to deal with this limitation by focusing on broad patterns and trends in species range contractions, potentially mitigating issues associated with fine scale range map accuracy. In addition to their coarse scale, the range maps do not include information on species abundances, which can vary greatly across species ranges. This means that we were unable to assess changes in regions with ecologically effective predator densities a key benchmark for conservation success (Soulé et al. 2003). There may also be variation in both historic and current range map accuracy from species to species, with particularly coarse historic range maps being associated with overestimates of percentage range contraction. The extents of range contractions may also be overestimated by the lack of range expansions in our core map set (Figure 3.1). Although large carnivore ranges may have expanded in some cases, we found no evidence of substantial range expansions (relative to the year 1500) in the literature. Most of the apparent range expansions in the raw range map set were very small and likely the result of mapping errors,

64 46 making potential range expansions a relatively minor source of error in our analysis. Extending the historic ranges to cover areas of apparent expansion resulted in a median increase in raw historic range area of 0.13% (maximum increase: 3.3%). Our range map set is also limited in that it does not show regions of hybridization (arguably a form of range contraction), which are important for canid species such as dingoes (Stephens et al. 2015) and red wolves (Bohling et al. 2016). The modeling portion of our analysis has an additional limitation in that model covariates (human and cattle density and cropland) are relatively current, while the range contraction process may have begun centuries ago. However, our results may still be interpretable as carnivore ranges have likely contracted the most within the last hundred years and current covariate values are likely strongly correlated with past values. That is, regions with high rural population density today likely had relatively high rural population density in the recent past, and so on. We have focused on models at the global scale (using all ranges together) to avoid the possibility of spurious correlations that could occur when fitting models at the level of individual species due to inaccuracies in individual range maps. The model (and other results) apply only to the species in our analysis and thus may not be relevant to semi-aquatic large carnivores, medium-sized carnivores, or other taxa Conservation implications This analysis provides several key insights into how best to conserve threatened large carnivore populations. The general lack of relationship between life history traits and range contraction means that most large carnivore species are

65 47 potentially at risk of range contraction and other associated drivers of extinction risk (e.g. population declines). As many carnivores were historically sympatric and are at high risk of future range contraction, conservation should be accomplished at the level of whole predator guilds when possible. Conservation of entire predator guilds has the added benefit of maintaining important species interactions and emergent ecological effects caused by co-occurring predators. Guild conservation can be accomplished, for example, by expanding and strengthening protected area networks or by increasing human tolerance of predators. Although increasing rural human population densities are linked to range contractions and significant future population increases are projected, many large carnivores are resilient, particularly when human attitudes and policy favor their conservation. This helps to explain the large carnivore recoveries observed in Europe and elsewhere (e.g. gray wolves in the continental United States). Similarly, although our results associate increasing cropland and cattle density with range contractions, this relationship may be limited when predator friendly agriculture methods are employed an area where more research and practice is needed. Ultimately, changes in species ranges are ongoing, dynamic processes and, in the face of newer threats like anthropogenic climate change, it is critical to continue to monitor large carnivore ranges to ensure the future of these species. Our analysis serves as a starting point for this by providing an accurate measure of the historic and current status of the world s largest carnivores. 3.6 Research ethics No ethical assessment was required prior to conducting this research. 3.7 Animal ethics

66 48 Does not apply. 3.8 Permission to carry out fieldwork Does not apply. 3.9 Data availability Historic range map sources and range contraction statistics are given in Tables B.1 and B Competing interests We have no competing interests Authors contributions CW carried out the data analysis and drafted the manuscript; WR conceived of the project and helped draft the manuscript. Both authors gave final approval for publication Acknowledgements We thank Bodil Elmhagen, Luke Hunter, Jan Kamler, Mike Letnic, Peter Lindsey, John Morrison, Thomas Newsome, Hugh Robinson, and Charles Yackulic for

67 providing species range maps, offering comments on our project, or reviewing a draft Funding We have no funding sources to report.

68 Figure 3.1. Range contraction maps for 25 large carnivores. Regions of persistence (i.e. inside both historic and current ranges) are shown in yelloworange, while regions of contraction (inside historic but not current range) are shown in dark red. Species are ordered by percentage range contraction with the greatest contractions shown in the upper most panels. 50

69 Figure 3.2. Percentage of historic range lost for each large carnivore. Carnivores names are colored by population trend (red decreasing, black italics stable, blue underlined increasing) and bar colors indicate carnivore endangerment status. 51

70 Figure 3.3. Composite range contractions maps based on all 25 large carnivores. Variables shown are historic species richness, current species richness, their difference (i.e. lost species richness), and the percentage of species lost. 52

71 Figure 3.4. Current and historic species richness histograms by region of the world. Asia excludes South-Eastern Asia, which is shown separately. Vertical lines indicate mean richness. Panels are sorted by difference in mean richness and indicate that the most extensive range contractions (by this metric) occurred in Africa, South-Eastern Asia, and the rest of Asia. Overlap between current and historic range histogram bars is shown in dark purple. 53

72 Figure 3.5. Regions of the world with intact or no longer intact large carnivore guilds (one or more species). Note that regions with high historic large carnivore richness (like Southeast Asia) seldom have intact guilds. All together, intact guilds make up 34% of the world s land area while 96% of land (excluding Antarctica) once contained one or more large carnivores. 54

73 55 4. Rewilding the World s Large Carnivores 4.1 Abstract Earth s terrestrial large carnivores form a highly-endangered group of species with unique conservation challenges. The majority of these species have experienced major geographic range contractions, which puts many of them at high risk of extinction or of becoming ecologically ineffective. As a result of these range contractions and the associated loss of intact predator guilds, the ecological effects of these species are now far less widespread and common, with inevitable consequences for ecosystem function. Rewilding which includes reintroducing species into portions of their former ranges is an important carnivore conservation tool and means for restoring top-down ecological regulation. We conducted a global analysis of potential reintroduction areas. We first considered protected areas where one of more large carnivores species have been extirpated, identifying a total of 130 protected areas that may be most suitable for carnivore reintroduction. These protected areas include sites in every major world region, and are most commonly found in Mongolia (n = 13), Canada (n = 11), Thailand (n = 9), Namibia (n = 6), Indonesia (n = 6), and Australia (n = 6). We considered the sizes of protected areas, their levels of protection, the extent of human impacts within and around the protected areas, and the status of prey species in the protected areas. Finally, we used the last of the wild approach to identify contiguous low human footprint regions within the former ranges of each species, identifying an additional 150 areas which could be the focus of conservation efforts to create conditions conducive to reintroductions. These low footprint regions were most commonly found in the United States (n = 14), Russia (n = 14), Canada (n = 10), China (n = 9), and Mauritania (n = 8).

74 56 Together, our results show the global-scale potential for carnivore rewilding projects to both conserve these species and provide critical ecological and social benefits. 4.2 Introduction Earth s terrestrial large carnivores are a charismatic, highly endangered group of species. In total, 64% of these species are threatened with extinction and 80% have declining population trends (Table 4.1, Figure 4.1). Major threats to large carnivore survival include habitat loss and fragmentation, persecution by humans (often due to livestock-related conflict), utilization of body parts for traditional medicine or trophies, and loss of prey base (Ripple et al. 2014; Wolf & Ripple 2016). These threats have together diminished the ranges of many species, often to the point where they are highly endangered. Sixty percent of these species have lost more than half of their historic ranges in the last 500 years (Wolf & Ripple 2017). As a result of these range contractions and associated population declines, the important ecological effects of large carnivores have been lost from much of the world (Svenning et al. 2016). For example, previous studies have documented the potential for large carnivores to trigger trophic cascades by limiting herbivore or mesopredator densities, indirectly benefitting a wide variety of plants and animals (Prugh et al. 2009; Ripple et al. 2014). While the loss of large carnivores from major portions of their historic ranges has altered the functioning of nearly all of earth s ecosystems, recent trends have not been entirely negative. The natural range expansions of the gray wolf, brown bear, and Eurasian lynx in parts of Europe and of the gray wolf in the United States suggest that it is possible for large carnivores and humans to coexist when

75 57 human tolerance and policy are favorable (i.e. when poverty is rare, people are educated, and reliance on subsistence agriculture and hunting is limited) (Carroll et al. 2012; Chapron et al. 2014; Bruskotter et al. 2017). Unfortunately, for some species like the endangered Ethiopian wolf (> 99% of historical range lost), relying on natural range expansions and conserving them where they currently reside may not be sufficient to ensure their survival. However, there is another option: rewilding planned reintroductions of large carnivores back into parts of their historic ranges from which they have been lost (Gittleman et al. 2001). Benefits of large carnivore reintroductions include reducing species extinction risk (Hayward et al. 2007a), providing opportunities for natural range expansions beyond the reintroduction area (e.g. the expansion of gray wolves into Washington, Oregon, and California following their reintroduction into Idaho), providing opportunities for wildlife viewing tourism (Lindsey et al. 2007), and potentially restoring ecosystem function by reestablishing predators ecological effects (Berger 2007). Such benefits must be weighed carefully against potential harm to animals being translocated, possibly lower human tolerance for reintroduced rather than naturally reuturning carnivores, and the risks that large carnivores can pose to humans, including potential loss of livestock or pets, direct attacks, and disease transmission (Bruskotter et al. 2017). In recent decades, there has been some research on the topic of carnivore reintroductions, which we summarize to provide context for our analysis. Most of this work relates to the question of what makes a carnivore reintroduction attempt successful. For example, protected area size has been found to be closely linked to the likelihood of large carnivore persistence, with one study reporting critical reserve sizes necessary for 50% probability of persistence ranging from 36 km 2 for the American black bear to 3,606 km 2 for the African wild dog (Woodroffe & Ginsberg 1998). Carnivores in smaller protected areas may be more vulnerable to

76 58 negative edge effects just outside reserve borders involving hunting or trapping by humans and conflict with humans over livestock and agriculture, particularly when efforts like fence construction are not taken to reduce conflict in surrounding buffer zones (Woodroffe & Ginsberg 1998; Lindsey et al. 2012). For example, in the Western United States, extensive grazing of livestock on public lands reduces the amount of food available for wild ungulates, leading to a reduction in prey base for carnivores (Fleischner 1994). Another important consideration for carnivore reintroductions is the availability of suitable prey, without which large carnivores cannot persist (Wolf & Ripple 2016; Stier et al. 2016). Food web-based modeling of reintroductions highlights the role of priority effects where established competitors can cause reintroductions to fail unless the size of the reintroduced population is sufficiently large (Stier et al. 2016). The life history traits of large carnivores relatively slow growth rates, a tendency to travel long distances, possibility for conflict with humans can make reintroducing these species exceptionally challenging (Stier et al. 2016). In a study of translocation success rates, carnivore and herbivore translocations had success rates of 48% (n = 40) and 77% (n = 145) respectively (Griffith et al. 1989). Motivated by the urgent need to address carnivore decline, we conducted the first comprehensive, global analysis of large carnivore reintroduction possibilities. Our primary goal was, for each large carnivore species, to identify specific protected areas and other areas where the likelihood of successful reintroduction may be high, providing data on likely predictors of reintroduction success for each region. To accomplish this broad goal, we defined the following objectives for our analysis (at the level of candidate reintroduction areas). Our first set of objectives was to determine geographic area, geographic region (e.g. continent), level of protection (protected areas only), mean human footprint (a spatial

77 59 measure of human impacts on the environment), and availability of suitable prey for each large carnivore species all likely predictors of reintroduction success (Woodroffe & Ginsberg 1998; Venter et al. 2016). Our second set of objectives was to determine which potential reintroduction efforts would lead to complete large carnivore guilds, which are associated with key ecological effects due to emergent impacts on prey, and to manually validate potential reintroduction sites using the literature to confirm extirpation (Sih et al. 1998). Taken as a whole, our analysis serves as a preliminary, data-driven assessment of global rewilding possibilities. 4.3 Methods To conduct our rewilding analysis, we considered the 25 large terrestrial ( 15 kg) carnivores (members of the mammalian order Carnivora) for which relatively accurate historic and current range maps were available (Wolf & Ripple 2017) (Table 4.1). We excluded semi-aquatic large carnivores like the polar bear (Ursus maritimus). The only exclusively terrestrial large carnivore species that we omitted was the maned wolf (Chrysocyon brachyurus), as we could not obtain a suitable historic range map for this species. Using the historic and current range map set from (Wolf & Ripple 2017), we constructed maps showing the lost range of each species the areas within its historic range that do not overlap its current range. These lost ranges are the foundation of our analysis as they indicate areas where reintroduction may be considered. For all spatial analysis, we used raster maps at 5 km resolution in Behrmann Equal Area Projection. Spatial analysis was carried out in R and ArcGIS 10.1 (ESRI 2012; R Core Team 2013).

78 60 After identifying the lost ranges of each species, we conducted parallel analyses using two different approaches. For the first approach, we focused on protected areas. We used the World Database on Protected Areas (WDPA) a global database of protected areas for this part (IUCN and UNEP-WCMC 2015). We considered only protected areas with polygon-type spatial data available and International Union for Conservation of Nature protected area category Ia (Strict Nature Reserve), Ib (Wilderness Area), II (National Park), or III (National Monument or Feature). These categories correspond to the highest levels of protection and are thus most suitable for large carnivore reintroductions. For each large carnivore species, we determined the set of such protected areas at least partially within its lost range. We excluded protected areas that overlap the species current range. We used reserve size as the primary criterion to determine the protected areas best suited for reintroduction. Working from largest to smallest, we consulted the literature to see if each reserve was known to contain the large carnivore species. We stopped this process after identifying the six largest reserves for each large carnivore species where its status in the reserve was either absent or unknown. To determine carnivore status within each reserve, we used a Google search consisting of carnivore species common name(s) and the protected area name(s) (exact matches only). To keep this task manageable, we looked only at the first page of search results, visiting any websites that appeared likely to contain the needed information. Admittedly, this approach could result in some inaccuracies, particularly for countries that lack English language literature on their protected areas. Our second approach to determining areas with high reintroduction potential was based on the 2009 global human footprint map (Venter et al. 2016). This map shows the impacts of humans on the environment based on source data including maps of roads, nighttime lights, land cover, and human population density.

79 61 Although the exact nature of large carnivore responses to each of these anthropogenic pressures varies, human footprint provides a reasonable starting point to assess where large carnivores are most likely to persist. We used the last of the wild methodology to determine large, relatively intact, regions within the lost ranges of each large carnivore species (Sanderson et al. 2002). Last of the wild regions are defined as contiguous regions within a bigger region that are in the bottom 10% in terms of human footprint over the bigger region. That is, we first identified the 10% of each lost range with the lowest human footprint. We then determined contiguous regions within this lowest 10% footprint portion of each range. When determining contiguous regions, we defined the neighborhood of each raster grid cell as the eight (rather than four) closest cells. For our primary analysis involving low footprint regions, we focused on the largest six regions for each carnivore species to match our protected area analysis. To provide context, we also constructed histograms of the human footprint across each large carnivores historic range split into separate categories for current range and lost range. After identifying protected areas and low footprint regions for each large carnivore, we conducted parallel analyses using these two datasets to explore where reintroductions may have the greatest likelihood of success. We present results for all category I-III protected areas and low footprint regions that we identified for each carnivore species, but emphasize results for the six largest protected areas and low footprint regions. For each large carnivore, in addition to looking at the geographic area and average human footprint of each area (protected area or low footprint region), using the historic range maps, we determined whether or not the large carnivore guild (set of species) becomes complete if that carnivore is reintroduced there. We also determined the country and broad-scale geographic region of the site (United Nations 2013). For low

80 62 footprint regions that cover multiple countries, we state only the country that contains the largest portion of the region. For low footprint regions only, we report the portion of the region that is protected (i.e. that overlaps category Ia, Ib, II, or III protected areas). Finally, for the hyper carnivores (large carnivores with diets containing at least 70% meat), when data are available, we report the preferred prey species, threatened preferred prey species, and estimated total number of preferred prey species available at each site (Wolf & Ripple 2016). We used the IUCN Red List to obtain range maps of the preferred prey species, considering only regions where each species is classified as Extant or Probably Extant. We present the results of our analysis using separate scatter plots and tables for each of the two approaches, along with maps showing site locations for all large carnivores together and separate maps for each large carnivore species. We used two approaches to assess the connectivity of the protected areas identified for each species. First, for each of these protected areas, we used the 5 km resolution protected area raster map to calculate the distance (accurate to ~5 km) to the nearest (other) category I-III protected area of any size. We summarized results for the six largest protected areas identified for each species. Second, pooling the sets of the six largest protected areas for each species together, we analyzed low cost corridors among these protected areas using the Linkage Mapper package (McRae & Kavanagh 2011). Linkage Mapper is designed to construct a map showing the value of each raster grid cell as a corridor for connecting protected (or other core ) areas. This map highlights the corridors that are most important to maintaining connectivity between these large protected areas. In short, this is accomplished by determining adjacent protected areas using least cost paths, building cost-weighted distance rasters for each protected area, and then normalizing and compositing the cost-weighted distance rasters to obtain a single map showing corridor value for each grid cell (McRae

81 63 & Kavanagh 2011). We treated protected areas separated by more than 500 km as non-adjacent, reflecting the dispersal distances possible for large carnivores (Linnell et al. 2005). To determine cost-weighted distances, we used human footprint (linearly rescaled to range from 1 to 100) as the resistance raster indicating the approximate difficulty for large carnivores to traverse a grid cell. Since cropland is a potential barrier to large carnivore movement, we masked out grid cells containing cropland from the resistance map using the Global Cropland Area Database (GCAD) (Teluguntla et al. 2015). For this analysis, we used the 25 largest protected areas in each species lost range in order to gain a more complete picture of connectivity. 4.4 Results We found dramatic variation in human footprint across the lost ranges of the large carnivores (Figure 4.2). On a scale from 0 to 50, the last of the wild (10% quantile thresholds) varied from 0.0 for the snow leopard and spotted hyena to 10.0 for the sloth bear (Figure 4.2). We identified the six largest protected areas for each large carnivore species (except the red wolf only three protected areas were identified for this species) where reintroduction may be successful following the implementation of conservation programs designed to limit ongoing threats to carnivores, possibly including the original causes of extirpation (Table 4.2, Figure 4.3). These form a set of 130 different protected areas globally, with areas ranging from 29 km 2 for Collier-Seminole (red wolf) to 99,331 km 2 for Parc Culturel du Tassili (Illizi) (lion) (Table 4.2). They cover all the major regions of the world: Africa (n = 34), the Americas (n = 28), Asia (excluding South-Eastern Asia) (n = 31), Europe (n =

82 64 10), Oceania (n = 6), and South-Eastern Asia (n = 28) and consist of Strict Nature Reserves (n = 20), Wilderness Areas (n = 14), National Parks (n = 94), and National Monuments or Features (n = 2) (Figure 4.3, Table C.2). These protected areas span 48 countries, and most commonly occur in Mongolia (n = 13), Canada (n = 11), Thailand (n = 9), Namibia (n = 6), Indonesia (n = 6), and Australia (n = 6) (Table C.2). Fifteen of these protected areas appeared in the top six largest protected areas for two different large carnivore species and one (Dakhla National Park in Morocco) appeared in the top six for three species (cheetah, lion, and leopard) (Table 4.2). Of the 147 protected area large carnivore combinations (six for each species except the red wolf), 59 (40.1%) would result in an intact carnivore guild following reintroduction of the large carnivore there (Figure 4.4, Table C.2). The average human footprint (across protected areas) was highest for the Eurasian lynx (13.2), sloth bear (12.5), and Asiatic black bear (10.0) and lowest for the puma (3.1), dingo (5.3), and brown hyena (5.8) (Figure 4.4, Table C.2). Fifteen of the 25 large carnivore species had known preferred prey species, and the carnivores with the greatest median (across protected areas) number of preferred prey species available were the jaguar (n = 8), gray wolf (n = 4), red wolf (n =3), dingo (n =3), and puma (n = 2) (Table C.2). Similarly, we identified the six largest low footprint regions for each large carnivore (Figure 4.3, Table C.3). These form a set of 150 regions (median area: 5,850 km 2 ), with areas ranging from 1,200 km 2 (sloth bear) to 1,222,925 km 2 (leopard) (Table C.3). As with the protected areas, these low footprint regions cover all the major regions of the world: Africa (n = 45), the Americas (n = 38), Asia (excluding South-Eastern Asia) (n = 18), Europe (n = 21), Oceania (n = 6), and South-Eastern Asia (n = 22) (Figure 4.3, Table C.3). The regions cover 40 countries, most commonly occurring in the United States of America (n = 14), Russia (n = 14), Canada (n = 10), China (n = 9), and Mauritania (n = 8) (Table

83 65 C.3). Of the 150 region large carnivore combinations (six per species; note that each region is specific to a different large carnivore species), 22 (14.7%) would result in an intact carnivore guild following reintroduction of the large carnivore species there (Figure C.1, Table C.3). On average, 8.0% of each low footprint region occurs within protected areas, with the lowest averages observed for the spotted hyena (0.0%), cheetah (0.0%), and lion (0.1%), and the highest averages for the dingo (26.8%), Andean black bear (23.6%), and Sunda clouded leopard (21.4%) (Table C.3). The average human footprint for these regions was highest for the sloth bear (7.1), clouded leopard (3.9), and Eurasian lynx (3.9) and lowest for the snow leopard, spotted hyena, and cheetah (all 0.0) (Figure C.1, Table C.3). The carnivores with the greatest median (across low footprint regions) numbers of preferred prey species available were the jaguar (n = 8), dingo (n = 2.5), red wolf (n = 2), gray wolf (n = 2), and Eurasian lynx (n = 2) (Table C.3). Species-specific maps of the six largest protected areas and low footprint regions reveal several spatial patterns (Figure C.2). Compared to protected areas, low footprint regions are often clustered together (e.g. for the lion and leopard) as human footprint is strongly spatially autocorrelated (Figure C.2). For species with lost ranges covering parts of Northern Africa, large low footprint regions nearly always occur there (as human footprint is low in this area of the world), while protected areas tend to be more evenly distributed (since there are relatively few large protected areas in Northern Africa) (Figure C.2). The species with candidate protected areas that have the greatest connectivity (as measured by mean distance to nearest protected area) were the clouded leopard (0 km 2 ), sun bear (0 km 2 ), dingo (2 km 2 ), and puma (2 km 2 ), while the species with the least protected area connectivity were the lion (223 km 2 ), cheetah (179 km 2 ), striped hyena (116 km 2 ), and leopard (115 km 2 ) (Table C.2). In terms of corridor

84 66 availability, large groups of connected protected areas were observed in much of the world, with regions of particularly high concentration including Mongolia, Central and Southern Africa, and Canada (Figure 4.5). 4.5 Discussion Protected area analysis The protected area analysis highlights protected areas for each large carnivore species where the likelihood of reintroduction success may be high. The smallest of the six largest protected areas is substantially larger than the estimated critical reserve size that is required for 50% probability of persistence for all ten of the large carnivore species with critical reserve size estimates (Woodroffe & Ginsberg 1998). Additionally, there are many other protected areas within the lost ranges of these species that exceed the species estimated critical reserve sizes (Figure C.3). Even relatively small protected areas may be viable options for reintroductions as part of broader-scale programs (e.g. systems of linked protected areas) or with active predator management techniques like fencing (Licht et al. 2010). Regardless of protected area size, excessive human activities within or near reserve boundaries can make it difficult for large carnivores to persist, although there are exceptions such as Asiatic lions in the Gir Forest National Park of India (Meena et al. 2014). Our finding of relatively high ( 10.0) average human footprint in protected areas for the Eurasian lynx, sloth bear, and Asiatic black bear suggests that this may be a particularly serious issue for these species, although recent large carnivore recoveries in Europe indicate that carnivore persistence in heavily modified landscapes is possible in certain cases provide prey are abundant and persecution is limited (Chapron et al. 2014). As the lynx

85 67 has had little range contraction in Asia, its lost range occurs nearly entirely within Europe, where human impacts have been relatively high (Wolf & Ripple 2017). Similarly, the sloth bear and Asiatic black bear have lost ranges in south Asia and south-eastern Asia where anthropogenic impacts are common. This relates to the problem posed by paper parks where human encroachment into the park (in the forms of, for example, bushmeat hunting and habitat loss) renders the protected area protected in name only (Wilkie et al. 2001; Lindsey et al. 2014). Thus, reintroduction attempts in protected areas must take into account the actual level of protection. This is particularly true in West and Central Africa, where subsistence and commercial hunting commonly occur in protected areas (Tranquilli et al. 2014). Given the sensitivity of large carnivores to both direct hunting and to loss of prey base, continued efforts to map bushmeat hunting pressure (using predictors like distance to roads and human population density) are vital to ensuring appropriate selection of reintroduction areas (Wolf & Ripple 2016; Ziegler et al. 2016). Such broad-scale mapping and modeling efforts would need to be followed up with local ground-truthing to either verify that reintroduction is a practical option or to determine what intermediate steps are required prior to reintroduction. Possible steps to reduce bushmeat hunting pressure include strengthening legal protections for wild mammals, providing alternative food sources to humans, and increasing access to education and family planning (Ripple et al. 2016). The focus of our analysis is on identifying broad spatial patterns in potential reintroduction areas, rather than making detailed arguments in support of any particular reintroduction effort. We now briefly discuss a few specific possibilities that are particularly intriguing. Following the extirpation of gray wolves from Olympic National Park in the early 1900s, elk have had strong negative impacts on riparian plant communities, which has been linked to erosion

86 68 of river banks (Beschta & Ripple 2008). This trophic cascade suggests that Olympic National Park, the fifth largest protected area that we identified for the gray wolf, should be considered as a candidate site for reintroducing this species. Another possible repatriation is the red wolf to Everglades National Park. This reintroduction was considered several decades ago by the Red Wolf Recovery Team (Parker et al. 1990). Additionally, it was recently the subject of an online petition, which noted that red wolves may help control the introduced Burmese python population in Everglades National Park as their diet includes snakes and snake eggs (North American Reintroduction Program 2015) Low footprint region analysis The low footprint regions in our analysis may be considered as candidate areas for reintroduction either immediately or following the establishment of additional protected areas there. Many other low footprint regions (beyond the six largest for each species) may also be well-suited for reintroduction (Figure C.4). By looking at regions with low human footprint, we partially avoid the issue of paper parks since the footprint map is based on more objective criteria. On the other hand, some of the most serious threats to large carnivores like bushmeat hunting (of both the carnivores and their prey) are difficult to map globally, and are likely not adequately reflected in the human footprint map or any other existing global map (Ripple et al. 2016). For example, many of the potential reintroduction sites in this portion of our analysis are located in the Sahara-Sahel region of North Africa (Figure C.2). Species with sites in this region include the African wild dog, cheetah, leopard, lion, and spotted hyena (Figure C.2). Although this region tends to have low human footprint, reintroduction may not be practical here. Threats to biodiversity in this area include climate change, the availability of

87 69 firearms used for hunting, overgrazing and other forms of habitat loss, widespread extraction of natural resources, water overexploitation, and extreme political instability (Brito et al. 2014). Connectivity must also be considered when interpreting the low footprint region results. We defined these regions as contiguous areas with low human footprint at 5 km grid cell resolution. Often, this resulted in adjacent regions separated by only a narrow band of grid cells, corresponding to a road. For example, see regions two and three for the African wild dog (Figure C.2). The extent to which such adjacent regions should be treated as separate depends on the nature of the road or other division as well as the biology of the large carnivore species. In general, it seems reasonable that roads often divide low footprint regions as they have well-documented negative effects on many large carnivores including being associated with vehicle collisions, aggressive carnivore-human encounters, hunting, and habitat loss and fragmentation (Kerley et al. 2002). Habitat fragmentation associated with roads (suggesting region isolation) has been documented for gray wolves, black bears, brown bears, Andean black bears, and pumas (Kerley et al. 2002). Further study of connectivity in this context could be useful to determine the likelihood of passive expansions, wherein carnivores naturally return to parts of their former ranges. When practical, passive expansions may be preferred to active reintroductions as they often require less human involvement and wildlife handling Limitations Our analysis has several key limitations. First, there is uncertainty associated with the data sources that we used. Reconstructing historic range maps is

88 70 difficult, and our historic map set only provides rough approximations to species historic ranges (Wolf & Ripple 2017). These correspond to roughly 1500 AD and thus our analysis reflects a relatively recent baseline time period (Lorimer et al. 2015). There is also uncertainty associated with the current range map set. Additionally, range maps do not provide information on species abundances, making it impractical to assess where translocations could bolster existing populations and to determine baseline predator densities required for ecological effectiveness, which could then be used to set targets for reintroduced populations (Soulé et al. 2003). The inaccuracies in our range map set imply that some of the proposed sites for each large carnivore species may either presently contain or have never contained the species. For example, several of the proposed sites for the African wild dog may be too dry to have supported this species and some of the northernmost proposed sites for the brown hyena may lie beyond the extent of its true historic range. Although we attempted to mitigate this issue by manually checking the status of the carnivore protected area combinations, this was not practical for the latter problem (determining whether or not the protected area ever contained the large carnivore). In many cases, we were also not able to conclusively determine whether or not the protected area currently contains the large carnivore. Another class of limitations is associated with our use of protected areas to explore candidate sites for rewilding. While we confined our search to strictly protected areas (IUCN categories I-III) to reduce the likelihood of mistakenly identifying insufficiently protected areas, in practice, the extent to which these areas are protected varies greatly and may not be fully reflected in the human footprint map (Wilkie et al. 2001). In some parts of the world, category I-III protected areas may not be suitable for reintroductions, while in other parts, even category IV ( Habitat/Species Management Area ), V ( Protected

89 71 Landscape/Seascape ), or VI ( Protected area with sustainable use of natural resources ) protected areas (which we did not consider) could be appropriate targets for reintroductions. Other protected-area specific variables that may be relevant include management budget, government versus private ownership, and whether or not hunting is allowed (Packer et al. 2013). Even when the actual level of protection is high, without appropriate buffer zones, policies in nearby areas can negatively affect carnivore populations. For instance, hunting and trapping of gray wolves in areas near Denali and Yellowstone National Parks may impact populations within these parks (Haber & Holleman 2013; Povilitis 2015, 2016). A closely related limitation applies to the map of protected area connectivity in that habitat quality may be inadequate along some of the mapped corridors (Figure 4.5). Although not necessarily a limitation, portions of our analysis are likely sensitive to our use of 5 km resolution. While higher resolution could be beneficial in certain cases, it might be inappropriate for identifying contiguous low footprint regions. In any case, the actual resolution of global range maps, especially those for historic ranges, is often on the order of several degrees or lower, making our choice of resolution adequate for our global analysis (Hurlbert & Jetz 2007). A final limitation of our analysis is that we were not able to explicitly order protected areas and low footprint regions by reintroduction potential. Although we present results ordered by protected area (or low footprint region) size, which is a key predictor of reintroduction success, we do not claim that this is the only predictor worth considering. Rather, we also include data on average human footprint, prey availability (when such data exist), protected area category (for protected areas), portion of the region protected (for low footprint regions), etc. (Tables C.2, C.3). Our hope is that these data and results can serve as both a

90 72 global view of rewilding possibilities and as a preliminary guide to more targeted carnivore reintroduction programs. All results that we present need to be more carefully validated when possible, especially if they are to be interpreted at local scales. This is critically important in the context of human tolerance for and policy toward large carnivores, which we could not quantify in our analysis, but are known to be vital to the survival of these species (Treves & Karanth 2003; Athreya et al. 2013). For example, control of dingoes is legally mandated throughout New South Wales, Australia, which means that dingo reintroductions are not practical there (Authority 2014). It is also important that managers quantify prey abundance and demographics prior to reintroduction, rather than simply looking at the number of prey species present (Hayward et al. 2007b). When preferred prey species are found to be absent in an area, reintroducing these species first can help to ensure predator reintroduction success, although some have argued that it is better for prey and predator reintroductions to occur together rather than sequentially (Samhouri et al. 2017). The potential for strong effects of predation on naive prey means that initial prey abundances may need to be relatively high in order to buffer prey declines while antipredator behavior is regained (Berger et al. 2001b; Gittleman & Gompper 2001) Conservation implications Our study is the first to provide a spatially explicit global assessment of future large carnivore rewilding possibilities. Although some have avoided using the term rewilding in situations where species are reintroduced to landscapes that have been modified by humans (Boitani & Linnell 2015), we embrace this term since rewilding need not require the exclusion of all human activity and large carnivores can help to maintain ecosystem processes, which are closely linked to

91 73 the idea of wildness (Seddon et al. 2014). Additionally, following predator reintroduction, formerly naive prey populations can exhibit increased vigilance and antipredator behavior within a single generation (Berger 2007). Other indicators of wildness include solitude and remoteness, both of which may be linked to protected areas and, especially, to regions with low human footprint (Aplet et al. 2000). Ultimately, predators like gray wolves are often seen as symbols of wildness, blurring the distinction between reintroduction and rewilding (Goble 1992; Wilson 1997). As mentioned in the limitations section, all protected areas and low footprint regions identified in our analysis must be thoroughly validated before any reintroduction attempts. This would need to include assessment of prey base in and around the region, connectivity with other reserves, hunting pressure, potential for human-carnivore conflict, funding available for reintroduction programs, relevant laws and regulations, extent of habitat loss, and other anthropogenic pressures (Ripple et al. 2016; Wolf & Ripple 2016). It is important that the original causes of extirpation be understood and, if necessary, mitigated prior to any reintroduction attempts. This is especially critical for sites near the current ranges of species, since the causes of extirpation may be preventing natural recoveries there. Our analysis is likely overly optimistic in that many threats to wildlife are difficult to quantify and may be severely underestimated at the global scale. It is possible that for some of the large carnivore species, none of the candidate sites that we identified are appropriate for reintroductions. For instance, regions with political instability and ongoing military conflicts can encompass large areas where reintroduction is not practical (Dudley et al. 2002). When planned reintroductions or natural recoveries in the near future are not realistic, broad-scale public-policy reforms can improve prospects for large carnivore conservation in the longer term. Not only can such transformative

92 74 policies and actions help to increase long term opportunities for successful large carnivore reintroductions, they can, in some cases, decrease the necessity of reintroductions by making natural returns more likely. While we focused on individual areas in our analysis, larger scale connectivity is also essential to large carnivore survival. This is particularly true in Africa where many protected areas are relatively isolated and quickly becoming more isolated in response to rapid human population growth (Newmark 2008). Large carnivores tend to have extensive home ranges, and may frequently roam outside even the largest protected areas (Boitani & Linnell 2015). Thus, ensuring that the areas around reintroduction sites have suitable habitat and high human tolerance for carnivores will help to promote reintroduced population survival. Many of the protected areas that we highlight are near other, smaller protected areas that could help sustain predator populations (Table C.2). Additionally, the numerous corridors that we mapped among the 25 largest protected areas in each species lost range (411 protected areas in total) suggest that reintroduced carnivores may be able to naturally traverse to other candidate reintroduction areas (Figure 4.5). This suggests that reintroduction into unfenced reserves may have the greatest long term likelihood of success, but there are possible drawbacks. For instance, African lion densities tend to be closer to estimated carrying capacities in fenced reserves than in unfenced reserves, likely due to fenced reserves having reduced human-lion conflict (e.g. over livestock depredation), habitat loss, and poaching (Packer et al. 2013). Fenced reserves can also benefit humans by reducing the risks posed by large carnivores. On the other hand, it has been argued that African lion populations in fenced reserves tend to be small and that fencing leads to fragmentation, limits dispersal routes, and leads to genetic isolation (Creel et al. 2013). This is especially problematic for reintroductions as they often begin with small founding populations that may lack genetic diversity (Hayward et al.

93 b). In any case, the extent to which fenced reserves should be prioritized for rewilding depends greatly on the nature of human activities in the surrounding habitat and should be considered on a case-by-case basis. This issue is less applicable in poorer countries where fencing large protected areas may be infeasible given management budgets. A less commonly considered benefit of reintroductions is derived from viewing reintroductions as landscape-scale natural experiments conducted through time. The ecological knowledge that can be gained from such broad scale interventions is invaluable, particularly given that the lack of documented trophic cascades for many large carnivore species could be due to their small current population sizes and a shortage of appropriate data (Ripple & Beschta 2011; Ripple et al. 2014). Predator reintroductions have already led to innovative work in the areas of community assembly, alternative stable states, and behavioral mediation in trophic cascades (Beschta & Ripple 2011; Stier et al. 2016). The potential for future work is rich, ranging from disentangling the ecological effects of top predators from other factors using causal modeling to further studying the effects of reintroduced predators on naive prey, which is important as many prey species are themselves endangered and predation on naive prey poses ethical and animal welfare challenges (Hayward et al. 2007a p. 200; Lorimer et al. 2015; Batavia & Nelson 2017). Together with the extensive literature on successful carnivore reintroduction efforts (see introduction), our analysis illustrates the potential for global rewilding of the earth s large carnivores across their former ranges. While care must be taken to mitigate risks to humans, reintroducing large carnivores can be a major part of carnivore conservation, promote functioning ecosystems, benefit numerous other species, and provide wildlife viewing opportunities for humans (Berger

94 ; Lindsey et al. 2007). The decision to promote large carnivore rewilding is consistent with a desire to strengthen ecosystem services that benefit humans. Moreover, it is a way of acknowledging the intrinsic value of these species, by helping them to once again flourish across their former ranges (Batavia & Nelson 2017). While the present endangerment of many large carnivore species has an array of complex multi-faceted causes, the ultimate driver is human-derived (anthropogenic) pressures. Similarly, conserving many of these species may require bold human intervention, without which, they may eventually be committed to extinction in the wild (Thomas et al. 2004). Thus, if carnivore conservation and all its associated benefits are a priority, carefully planned rewilding efforts will almost certainly be necessary as part of broader conservation programs. 4.6 Research ethics No ethical assessment was required prior to conducting this research. 4.7 Animal ethics Does not apply. 4.8 Permission to carry out fieldwork Does not apply. 4.9 Data availability

95 In addition to the publicly available data sources that we cite in the text, relevant data are given in Tables C.2 and C Competing interests We have no competing interests Authors contributions CW carried out the data analysis and drafted the manuscript; WR conceived of the project and helped draft the manuscript Acknowledgements We thank Laurence Frank, David Johns, Peter Lindsey, and Arian Wallach for reviewing an early draft of this paper Funding We have no funding sources to report.

96 Figure 4.1. The 25 terrestrial large carnivore species in our analysis (Table 4.1). From left to right, the species are: first row African wild dog, American black bear, Andean black bear, Asiatic black bear, brown bear; second row brown hyena, cheetah, clouded leopard, dhole, dingo; third row Ethiopian wolf, Eurasian lynx, gray wolf, jaguar, leopard; fourth row lion, puma, red wolf, sloth bear, snow leopard; fourth row spotted hyena, striped hyena, sun bear, Sunda clouded leopard, tiger. (photo credits are given in Table C.1) 78

97 Figure 4.2. Histograms for human footprint (a spatial measure of human impacts on the environment) across the historic ranges of each large carnivore. The historic range (both colors together) is split into Current range (regions where the carnivore is still present) and Lost range (regions where the carnivore has been extirpated). The vertical lines indicate thresholds for last of the wild regions within lost ranges (i.e. the bottom 10% threshold for human footprint in the lost range). 79

98 Figure 4.3. Potential sites for reintroducing large carnivores. The top panel shows the locations, areas, and mean human footprints of the six largest strictly protected areas within each of the 25 large carnivores lost ranges (i.e. where the species has been extirpated). The bottom panel shows the same data for the six largest low footprint regions within the lost range of each species. Low footprint regions were determined based on contiguous areas within the last of the wild regions of each large carnivore s lost range. Last of the wild regions are those in the bottom 10% for human footprint within each species lost range. 80

99 Figure 4.4. The six largest protected areas inside the lost (historic minus current) ranges of each large carnivore species (only three were identified for the red wolf). For each carnivore, variables shown are mean human footprint across the protected area, region of the world, and whether or not the large carnivore guild becomes complete following reintroduction of the carnivore. Only strictly protected (IUCN categories I-III) were considered for this analysis. 81

100 Figure 4.5. Corridors among the 411 protected areas that we identified as candidate sites for large carnivore reintroduction based on the 25 largest protected areas for each large carnivore species. The protected areas are shown in green. Corridors between protected areas were identified using Linkage Mapper and are colored according to their value based on compositing normalized cost-weighted distance rasters, with higher composite corridor values corresponding to greater potential contributions to connectivity. We used the human footprint map (linearly rescaled to range from 1 to 100) as the resistance raster for calculating cost distances, with areas containing cropland masked out. A 500 km Euclidean distance threshold was used to avoid mapping corridors between protected areas that are more than 500 km apart. Note that zooming can be used to view detail in this figure. 82

101 Table 4.1. The 25 large carnivore species in our analysis. From left to right, the variables shown are taxonomic family, species scientific name, species common name, IUCN Red List category (LC Least Concern, NT Near Threatened, VU Vulnerable, EN Endangered, CR Critically Endangered), IUCN Red List species population trend, percentage of species range lost, and whether a reintroduction of the species has been documented (with source if applicable). Family Scientific Name Common Name Category Trend Range lost Reintroduced? Canidae Canis rufus Red wolf CR Increasing > 99% Y (Gittleman et al. 2001) Canidae Canis simensis Ethiopian wolf EN Decreasing 99% N Felidae Panthera tigris Tiger EN Decreasing 95% N Felidae Panthera leo Lion VU Decreasing 94% Y (Hayward et al. 2007b) Canidae Lycaon pictus African wild dog EN Decreasing 93% Y (Hayward et al. 2007b) Felidae Acinonyx jubatus Cheetah VU Decreasing 92% Y (Hayward et al. 2007b) Canidae Cuon alpinus Dhole EN Decreasing 82% N Felidae Panthera pardus Leopard VU Decreasing 79% Y (Hayward et al. 2007b) Felidae Panthera uncia Snow leopard EN Decreasing 78% Y (Hayward & Somers 2009) Ursidae Tremarctos ornatus Andean black bear VU Decreasing 75% Y (Castellanos et al. 2005) Ursidae Ursus thibetanus Asiatic black bear VU Decreasing 64% Y (Kim et al. 2011) Felidae Neofelis nebulosa Clouded leopard VU Decreasing 64% N Felidae Neofelis diardi Sunda clouded leopard VU Decreasing 51% N Felidae Panthera onca Jaguar NT Decreasing 50% N Ursidae Helarctos malayanus Sun bear VU Decreasing 50% N Ursidae Ursus arctos Brown bear LC Stable 42% Y (Gittleman et al. 2001) Ursidae Ursus americanus American black bear LC Increasing 39% Y (Hayward & Somers 2009) Ursidae Melursus ursinus Sloth bear VU Decreasing 39% N Felidae Puma concolor Puma LC Decreasing 32% Y (Gittleman et al. 2001) Hyaenidae Hyaena brunnea Brown hyena NT Decreasing 27% Y (Hayward et al. 2007b) 83

102 Canidae Canis lupus Gray wolf LC Stable 26% Y (Bangs & Fritts 1996) Hyaenidae Crocuta crocuta Spotted hyena LC Decreasing 24% Y (Hayward et al. 2007b) Hyaenidae Hyaena hyaena Striped hyena NT Decreasing 15% N Felidae Lynx lynx Eurasian lynx LC Stable 12% Y (Hayward & Somers 2009) Canidae Canis dingo Dingo VU Decreasing 12% N 84

103 Table 4.2. For each large carnivore species, the six largest protected areas where it has been extirpated (i.e. where we found no evidence in the literature of its current presence). Carnivores species are listed in alphabetical order by common name. Numbers in parentheses are the range of areas for the six protected areas shown. Protected areas are grouped by country (countries sorted alphabetically). Within countries, protected areas are listed in order of decreasing area. In each case, the largest protected area is underlined and the smallest is italicized. Additional protected area data including information on potential inaccuracies is given in Table C.2. African wild dog (14,273-50,985 km 2 ): Angola (National Park Iona; National Park Cameia), Botswana (Gemsbok), Namibia (Namib-Naukluft; Etosha; Skeleton Coast Park) American black bear ( km 2 ): Canada (Grasslands National Park of Canada; Moose Mountain Provincial Park; Great Sand Hills; Spruce Woods Provincial Park; Bob Creek Wildland; Cypress Hills) Andean black bear (116-5,701 km 2 ): Colombia (Tinigua; La Tatacoa; Serrania De Minas), Panama (Darién), Peru (Pampa Hermosa), Venezuela, Bolivarian Republic of (Cerro Saroche) Asiatic black bear (1,276-23,358 km 2 ): India (Hemis), Malaysia (Taman Negara; Endau Rompin (Johor)), Pakistan (Khunjerab), Tajikistan (Tajik National Park), Thailand (Thung Salaeng Luang) Brown bear (5,029-9,049 km 2 ): Canada (Asatiwisipe Aki Traditional Use Planning Area), Mongolia (Khangai nuruu; Har Us Nuur; Tarvagatai nuruu; Eastern Mongolian Steppe), Turkmenistan (Kaplangurskiy) Brown hyena (146-10,494 km 2 ): Angola (National Park Luengue-Luiana; National Park Quiçama), Botswana (Kasane), Namibia (Mudumu; Nkasa Rupara), Zambia (Sioma Ngwezi) Cheetah (6,590-22,860 km 2 ): Angola (National Park Quiçama), Democratic Republic of the Congo (Bomu), Morocco (Dakhla National Park), Mozambique (Niassa), Saudi Arabia ('Uruq Bani Ma'arid; At-Tubayq) Clouded leopard (1,238-1,911 km 2 ): Thailand (Doi Phukha; Doi Luang; Khao Bantad; Tham Phathai; Mae Tuen; Huai Nam Dang) Dhole (11,724-53,465 km 2 ): Mongolia (Great Gobi; Gobi Gurvansaikhan range; Gobiin baga /A/, /B/; Khan Khentii; Khuvsgul), Tajikistan (Tajik National Park) Dingo (1,040-2,758 km 2 ): Australia (Cape Arid; Grampians; Mungo; Stirling Range; Yathong; Great Otway) Ethiopian wolf (2,213-19,887 km 2 ): Ethiopia (Gambella; Omo; Yangudi Rassa; Yabello), South Sudan (Boma; Boma Extension) Eurasian lynx (773-2,590 km 2 ): Bulgaria (Rila), Italy (Parco nazionale del Pollino; Parco nazionale del Cilento e Vallo di Diano; Parco nazionale del Gargano; Parco nazionale della Sila), Ukraine (Podolskie Tovtry) Gray wolf (3,665-5,527 km 2 ): Malaysia (Taman Negara), Myanmar (Lenya; Tanintharyi National Park), Sweden (Vindelfjällen), Thailand (Thungyai Naresuan), United States of America (Olympic) 85

104 Jaguar (5,416-17,884 km 2 ): Argentina (La Payunia), Brazil (Mapinguari; Campos Amazônicos; Pacaás Novos; Guaporé; Rio Novo) Leopard (3,399-16,404 km 2 ): Cambodia (Virachey), Egypt (Wadi El-Gemal - Hamata), Iran (Islamic Republic of) (Urumieh lake), Mauritania (Banc d'arguin), Morocco (Dakhla National Park), Myanmar (Khakaborazi) Lion (7,774-99,331 km 2 ): Algeria (Parc Culturel du Tassili (Illizi)), Angola (National Park Cameia), Congo (Odzala Kokoua), Morocco (Dakhla National Park), Namibia (Namib-Naukluft), South Sudan (Badingilo Extension) Puma (6,644-13,627 km 2 ): Canada (Wabakimi Provincial Park; Asatiwisipe Aki Traditional Use Planning Area; Algonquin Provincial Park; Spatsizi Plateau Wilderness Park; Northern Rocky Mountains Park), Peru (Cordillera Azul) Red wolf (29-4,187 km 2 ): United States of America (Everglades; Biscayne; Collier-Seminole) Sloth bear (115-1,740 km 2 ): Bhutan (Jigme Singye Wangchuck), India (Sundarban; Mouling), Sri Lanka (Knuckles; Peak Wilderness NR; Sinharaja National Heritage Wilderness Area) Snow leopard (2,977-18,315 km 2 ): Mongolia (Gobiin baga /A/, /B/; Khangai nuruu; Zed-Khantai-Buteeliin nuruu; Tarvagatai nuruu; Ulaan Taiga; Myangan-Ugalzat) Spotted hyena (632-11,042 km 2 ): Cameroon (Mpem et Djim; Takamanda), Democratic Republic of the Congo (Maiko; Bomu), Namibia (Ai- Ais Hot Springs), Nigeria (Cross River) Striped hyena (1,027-19,092 km 2 ): Central African Republic (Manovo-Gounda-Saint Floris), Democratic Republic of the Congo (Kahuzi- Biega), India (Kishtwar), Nepal (Langtang), Rwanda (Akagera), Saudi Arabia ('Uruq Bani Ma'arid) Sun bear (1,036-1,740 km 2 ): Bhutan (Jigme Singye Wangchuck; Royal Manas), Thailand (Sri Lanna; Thung Salaeng Luang; Khao Bantad; Tham Phathai) Sunda clouded leopard (192-1,486 km 2 ): Indonesia (Muara Kendawangan; Gunung Nyiut Penrissen; Teluk Kelumpang Selat Laut Selat Sebuku; Teluk Apar; Kepulauan Karimata; Teluk Pamukan) Tiger (6,315-12,599 km 2 ): Kyrgyzstan (Issyk-Kul), Mongolia (Altai Tavan range), Russian Federation (Sinyaya; Olekminsky; Dzhugdzhursky), Uzbekistan (Ugam-Chatkal) 86

105 5. BAYESIAN CHARACTERIZATION OF UNCERTAINTY IN SPECIES INTERACTION STRENGTHS Christopher Wolf, Mark Novak, and Alix I. Gitelman 87 Wolf, Christopher, Mark Novak, and Alix I. Gitelman. "Bayesian characterization of uncertainty in species interaction strengths." Oecologia (2017):

106 Introduction Quantifying the strength of species interactions is an important ecological challenge. Estimates can be used to identify keystone species whose impacts are disproportionate to their abundance (Power et al., 1996), help explain community structure (Wootton, 1994), are key to understanding food web stability (Allesina & Tang, 2012), and often underlie forecasts of community dynamics (Petchey et al., 2015; Novak et al., 2016b). Unfortunately, estimating interaction strengths in natural systems is difficult. In most food webs, the large number of pairwise interactions and the large number of weak interactions in particular makes the use of manipulative field experiments logistically prohibitive. Thus, many have resorted to indirect means of estimation, such as using energetic principles or allometric relationships from metabolic scaling theory (e.g., Neutel et al., 2002; Rall et al., 2012). More effort still has been devoted to estimating interaction strength parameters by characterizing predator functional responses, largely on a pairwise experimental basis or by tracking predator kills over time (Vucetich et al., 2002; Jeschke et al., 2004). As a consequence of the difficulty of estimating interaction strengths, most of the effort spent on characterizing species interactions has focused on obtaining point estimates and performing hypothesis tests (see also Poisot et al., 2016; Wells & O Hara, 2013; Melián et al., 2014). For example, Paine (1992) used a bootstrapping procedure only to quantify the uncertainty associated with the mean net strength of pairwise species interactions due to variation among experimental replicates. The focus has similarly been on obtaining point estimates and testing whether the associated parameters are different from zero in the use of functional response experi-

107 ments designed to determine the dependence of feeding rates on prey and/or predator densities (e.g., Jeschke et al., 2004; Ramos-Jiliberto et al., 2016). Thus only the deterministic core (i.e. systematic part) of alternative functional response formulations has generally been of interest. More specifically, functional responses have typically been fit to data using statistical models such as F = 89 1+ahN an +ε (the Holling type II response) whereby variation in a predator s feeding rate (F) is assumed to be controlled by a deterministic component governed by variation in variables such as abundances (N) or parameters such as attack rates (a) and handling times (h), and only a shell of stochastic variation (ε) is used to describe the variation left unexplained by the deterministic core. This is in contrast to the explicit modeling of the variation intrinsic to both the parameters and variables by describing each by a distribution that is itself governed by deterministic and stochastic sources of variation. As in many other contexts (e.g. Elderd & Miller, 2016), the distinction between these two approaches to considering variation in interaction strengths (i.e., using a single error term, ε, or using a more comprehensive consideration of uncertainty) is important when the uncertainty of the estimates itself is of interest. This is particularly true when forecasting the dynamics of species rich communities where indirect effects can rapidly compound even small amounts of uncertainty (Yodzis, 1988; Novak et al., 2011). In such applications, knowledge of the (co-)variation of parameter estimates is essential to assessing the sensitivity of predictions under plausible scenarios of estimation uncertainty. Of course, estimates of uncertainty are also important in comparing the utility and consistency of different interaction strength estimation methods (e.g. Wootton, 1997) and for the biological interpretation of the estimates themselves. Estimates derived from the allometric relationships underlying metabolic scaling theory, for example, are typically associated with several

108 90 orders of magnitude in variation left unexplained by species body sizes (Rall et al., 2012; Kalinoski & DeLong, 2016). In this paper we extend the observational method for estimating the per capita attack rates of predator-prey interactions presented by Novak & Wootton (2008) to characterize estimation uncertainty. Our interest in observational methods stems from their features of more easily accommodating instances of trophic omnivory than experimental and time-series methods (Novak, 2013); retaining the speciesspecific information lost in allometric and energetic approaches; and, given a sufficient number of feeding observations, estimating the species-specific attack rates for any subset (e.g., size class) of individuals within a focal predator population. Furthermore, with the method of Novak & Wootton (2008), attack rates may be estimated for all of a focal predator s prey species simultaneously while also accounting for an inherent nonlinearity of predator-prey interactions because a multispecies Holling type II functional response the most frequently observed functional response form among non-filter feeding consumers (Jeschke et al., 2004) is assumed in the method s derivation. The Bayesian formulation we develop here connects the deterministic multispecies type II functional response model with each of the sources of empirical data that contribute to the observational method s per capita attack rate estimator. We thereby account for variation due to both sampling effort and the environment. An issue with any Bayesian model is prior selection as posterior results may be sensitive to the choice of prior. This is a particularly sticky issue when data are sparse, wherein the prior weighs more heavily into results. Sparse data occur often in the context of species frequencies, particularly so in regard to species abundances and the diets of predators as these often range across many orders of magnitude (McGill et al., 2007; Novak, 2013). Therefore, as a key part of this work, we give

109 91 careful consideration to prior selection in attack rate estimation, and we assess the effects of alternative prior choices in estimating per capita attack rates. Because of the sensitivity we see to prior selection, we introduce to ecology a new prior that we show has appealing properties. To demonstrate the Bayesian method s utility and to explore the sensitivity of our results to prior choice, we apply it to data on the predator-prey interactions of a New Zealand intertidal whelk, contrasting these estimates with those obtained by nonparametric and parametric bootstrapping procedures. We show that posterior results using the sparse data typical of predator diet studies are sensitive to so-called noninformative priors commonly used in the Bayesian literature. We then show that our new neutral non-informative prior gives Bayesian posterior point estimates that are intunitively appealing and consistent with estimates obtained by bootstrapping approaches. Finally, we show how estimation uncertainty as described by 95% intervals is considerably more constrained and biologically realistic within the Bayesian framework; how the species-specific distribution of attack rates in whelks mirrors the skewed distribution of interaction strengths commonly seen at the community scale (Wootton & Emmerson, 2005); how a deterministic component of intraspecific predator variation relates to predator body size; and, how our approach provides posterior probability distributions on per capita attack rate estimates that lend themselves to a more useful and descriptive characterization of interaction strengths than do point estimates alone.

110 Materials and methods Model framework Novak & Wootton (2008) introduced an observational method for obtaining point estimates of a generalist predator s prey-specific per capita attack rates (a i ; where i indexes prey) using data on prey abundances (N i ), handling times (h i ), and snapshot feeding surveys in which the number of predator individuals feeding on each prey species is recorded. Assuming that a multispecies type II functional response F i = a i N i 1 + S, (5.1) a k h k N k k=1 describes the predator population s per predator feeding rate on the i th prey species, the estimator for the attack rate on the i th prey is equivalent to a i = A i A 0 1 h i N i (5.2) (see Appendix D.1). Here, A i is the number of observed predators feeding on prey i, and A 0 is the number of observed predators not feeding, during one or more snapshot surveys of the predator population. Both 5.1 and 5.2 are implicitly deterministic mathematical models that include no stochastic component, a deficiency we address below. The observational method capitalizes on the fact that handling times are more easily measured in laboratory experiments than in the field by using a smaller number of longtitudinally-followed

111 93 individuals than may be surveyed during a snapshot survey. Thus, even if handling time data are based on field observations, these will typically not be measured on the individuals observed during the snapshot feeding survey, hence the lengths of time those predators had been feeding are unknown and must be estimated. The feeding counts and species abundances similarly reflect estimates. In acknowledgement of this, we develop a parameter-based version of 5.2 a statistical formulation of the attack rate estimator that can incorporate sampling and environmental variation explicitly. We describe this next in the context of a specific case study. In Appendix D.2, we provide a more general introduction to the principles of the Bayesian framework, as well as more specific details of our implementation than presented in the following main text Case study dataset Our case study dataset pertains to the predatory whelk Haustrum scobina of the New Zealand marine intertidal. Haustrum feeds primarily on barnacles and mussels but also limpets and snails, often by first drilling through the shells of its prey. Handling times, which can be hours to days, are the times needed to drill and ingest a prey individual. The dataset we use contains information from replicate feeding surveys and quadrat-based prey species abundance surveys from a single site (Tauranga Head), and laboratory-based handling time experiments. We summarize the relevant attributes of these data below, referring to Novak (2010, 2013) for further details. Fifteen feeding surveys were conducted during low tides over two years. In each survey, the number of whelks not feeding (x 0 ) or feeding on each prey species

112 94 (x i ) was recorded, amounting to a total of 2,089 whelks observed. All but two of the eight recorded prey species were observed very rarely (Table 5.1). The sizes of the predator individuals (both feeding and not feeding) and of the prey being fed upon were also recorded (±1mm), along with the average temperature of the month in which each survey was conducted. These three covariates contribute to the deterministic variation in per capita attack rate estimates. Prey abundance surveys used 5 replicate quadrats randomly distributed along 2 transects, each repeated 3 times over the same time periods in which the feeding surveys were conducted. As is typical of community abundance surveys, numerous zeros exist in these data as many species did not occur in every quadrat (Table 5.1). The presence of such zeroes reflects both deterministic variation associated with real variation in species abundances (i.e., no individuals may be present in the area), as well as stochastic variation associated with sampling effort (i.e., no individuals happened to be found in the quadrat). Aside from these zeroes, the abundance measurements are not integer counts but rather reflect densities derived on the basis of counts (for mobile prey) or percent cover-count relationships (for sessile prey) and the effective area of each quadrat as overlaid on an irregular substrate. The dataset also contains data on laboratory experiments that Novak (2010) used to build a statisitcal model for the relationship between handling times and predator size; prey identity and size; and temperature. These experiments housed individual whelks in separate aquaria with different prey and entailed hourly checks to determine handling time durations. As a result, handling time measurements are interval censored, equally so for prey species with short (hour-long) and long (multi-day) handling times. The uncertainty associated with the interval censoring, along with estimation uncertainty associated with the experimental trials that were performed for each prey species (Table 5.1), reflect sources of variation that are modeled in the

113 95 error term of the statistical model for handling times Bayesian model formulation Treating the prey abundances, handling times, and feeding surveys data as independent, we now specify likelihood and prior models for each of these components. Following standard statistical practice for notation, we use uppercase letters to denote random variables, lowercase letters for realizations of random variables (the observed data), bold letters for vectors, and bold uppercase letters for matrices of random variables. We use f to represent the density function of an arbitrary distribution, using the function s argument(s) to indicate the specific distribution being referenced. For example, the density of a random variable X is indicated by f (x), and that of θ by f (θ), even though these are not necessarily density functions of the same form. A table of notation is given in the Appendix (Table D.1). Modeling the feeding surveys We model the combined feeding survey data of feeding and not feeding individuals using a multinomial likelihood and a Dirichlet prior having concentration parameters c. The resulting posterior distribution is also Dirichlet (eqn D.10), for which we focus on the posterior medians (rather than means) as our point estimates of interest because medians are generally the more appropriate measure of a skewed distribution s central tendency. Four concentration parameter values have been used in the past to make Dirichlet priors non-informative: Laplace s prior (c = 1), Jeffreys prior (c = 1 2 ), Perks prior (c = S+1 1 where S+1 is the length of the multinomial vector see Appendix D.2) and Haldane s prior (c = 0) (Hutter, 2013). However, our preliminary investigations

114 96 indicate that these priors result in posterior medians that differ substantially from the sample proportions, x i /x 0, particularly for rarely-observed prey. This leads to attack rate point estimates that, for rarely observed prey species, are entirely driven by the choice of the prior (i.e., the priors are not non-informative in this case, Fig. 5.1). Because of the deficiency of the existing non-informative priors, we introduce to ecology a neutral prior, c = 1 3, for modeling the ratios of multinomial parameters (i.e., the ratio of α i feeding and α 0 not-feeding indiduals). This prior extends the insight in Kerman et al. (2011) that when c = 1 3, the multinomial parameter posterior medians closely match the maximum likelihood estimates (MLE), which in this setting correspond to the sample proportions. We derive the prior by letting γ i = α i α 0 and noting that the posterior distribution of γ i is the ratio of Dirichlet components, which is the ratio of independent gamma random variables. This may be written as: f (γ i x i,x 0 ) = x ( ) 0 + c x i + c g x0 + c x i + c γ i;2(x i + c),2(x 0 + c), (5.3) where x i and x 0 are the observed counts of feeding and non-feeding individuals and g(y;d 1,d 2 ) is an F-distribution probability density function with d 1 and d 2 degrees of freedom. Using the approximation for the median of an F-distribution med(f m n ) x i x 0, yields the solution c = 1 3 3n 2 n 3m 2 m and setting it equal to the MLE of α i α 0, (Appendix D.5). Thus, the neutral prior leads to posterior medians that closely match the MLEs for both multinomial parameters, as shown by (Kerman et al., 2011), and for the ratios of multinomial parameters. Modeling the abundance surveys We use a zero-inflated gamma (ZIG) model to accommodate the numerous zeros in the prey abundance data. By condition-

115 ing on whether or not a zero occurs, the likelihood density of the ZIG distribution can be expressed in terms of ρ (the probability of a zero) and f (y;α,β) (the usual gamma density with shape α, rate β, and mean α β ). The ZIG density is separable in ρ and (α,β), which means that the zero-inflation parameter can be treated separately, provided a separable prior is used. Thus, for each prey species, we 97 model the number of observed zeros using a binomial distribution with a uniform prior on ρ. For the gamma part, we use log(α) Uni f ( 100,100) and log(β) Uni f ( 100, 100) priors to approximate the independent scale-invariant non-informative prior f (α,β) = f (α) f (β) 1 α 1 β (Syversveen, 1998). Modeling the handling time experiments We use regression to model the relationship between handling times and the predator size, prey size and temperature covariates of the laboratory experiments. We obtain average field-estimated handling times for use in the attack rate estimation by combining these regression coefficients with the same covariate information obtained during feeding surveys. Specifically, we consider the i th handling time observation for a given prey species to be associated with a covariate vector, X i, consisting of temperature, predator size, and prey size (all log transformed, and a 1 for the intercept term). We then model the likelihood of the i th handling time using a normal distribution (mean: e XT i β, variance: σ 2 ) plus a uniform (minimum: l i 2, maximum: l i 2 ) error corresponding to the interval censoring with which handling times were observed. The exponential link of the normal distribution mean avoids negative mean handling time estimates. Treating the field covariates (predator size, prey size, and temperature) as random to account for sampling variability, we model the distributions of the (log-

116 98 transformed) covariate observations X 1,...,X N, where N is the total number of field observations, as independent, identically distributed, and drawn from a multivariate normal distribution with mean vector µ and covariance matrix Σ. We use non-informative multivariate normal and inverse Wishart priors for µ and Σ respectively (Fink, 1997). Letting X follow the posterior predictive distribution (our estimate of the distribution of the covariates), the mean handling time is E(e βt X ) (Appendix D.3). We estimate this expectation by sampling from the posterior distribution of the regression parameters, sampling new covariates from their posterior predictive distribution, computing e βt X for each sample, and averaging across all samples. The weak law of large numbers ensures convergence to E(e βt X ) as sample size increases (Petrov, 1995) Accounting for spatio-temporal variation As the feeding survey, prey abundance, and handling time data all have multiple levels of spatial and temporal structure (e.g. structured variation across replicate quadrats, transects, seasons, and years), we consider several hierarchical models seeking to account for such possible dependencies (Cressie et al., 2009). Unfortunately, insufficient data at the larger scales made fitting such models impractical in the case of the whelk data, with models either failing to converge or resulting in inference similar to that from the non-hierarchical models. We provide an example of how to implement a hierarchical model to incorporate spatial and temporal variation in Appendix D.6. The data of our case study are sufficient to illustrate the utility of the observational approach for assessing the deterministic influence of intraspecific predator varia-

117 99 tion (in the form of individual body size) on attack rate estimates. To accomplish this we divide all predator observations made during the feeding surveys into eight groups based on predator body size, with approximately equal numbers of predator individuals per group (Table D.2). To draw inferences relevant to theory on the allometric scaling between predator size and attack rates (Rall et al., 2012; Kalinoski & DeLong, 2016), we convert predator lengths (shell length, L, in mm) to masses (total wet weight, w, in grams) using W = L (Novak, 2013). Our analysis here focuses on the two most common prey species (C. columna and X. pulex, Table 5.1) to ensure that sufficient data are available for each predator size group Estimating per capita attack rates Using the likelihoods and priors given above for the feeding surveys, abundances and handling times, we draw samples from the posterior distribution of the parameters using Markov Chain Monte Carlo (MCMC). We use JAGS with the R package rjags (Plummer & Stukalov, 2014) for the MCMC sampling. We then combine posterior samples using eqn D.6 to produce samples from the posterior distribution of attack rates for each prey species. We also plot the individual attack rate components posterior distributions separately to show how each part contributes to the attack rates posterior distributions. In our approach, we treat handling times, H, as being independent of the predator feeding surveys, F, even though we use covariate observations of predator size, prey size and temperature from the feeding surveys informing F to inform H by combining them with the laboratory-based handling time regression coefficients associated with these covariates. We establish the va-

118 100 lidity of this assumption by examining the relationship between feeding proportions and covariate averages between the individual surveys (Appendix D.7). We verify Markov chain convergence using trace plots and the Gelman and Rubin convergence diagnostic (Gelman & Rubin, 1992), remove samples obtained before the chains had converged (i.e., burn-in samples), and thin each chain to ensure independence among the remaining samples. We compute scale reduction factors a convergence diagnostic that compares within versus between chain variability using 250 independent chains with random initial values. With the help of trace plots we determine burn-in lengths separately for feeding survey, prey abundance, and handling time models. We base our final inferences on 1,000 samples after confirming that independent sets of 1,000 samples led to the same conclusions Comparison of Bayesian and bootstrapping procedures We assess the utility and performance of our Bayesian approach by contrasting point and 95% interval estimates from (i) the model with Laplace s prior (c = 1) on the Dirichlet feeding proportions; (ii) the model with Haldane s prior (c = 0); and (iii) the model with the neutral prior (c = 1 3 ) to estimates obtained using (iv) non-parametric and (v) parametric bootstrapping procedures. For the non-parametric bootstrap, we sample with replacement from each of the feeding survey, prey abundance, and handling time datasets until we draw the same number of samples as was present in each dataset (Efron & Tibshirani, 1994). We calculate per capita attack rates for 1,000 sets of such resampled data to estimate the mean and 95% confidence intervals of the corresponding bootstrapped distribu-

119 101 tions. We implement the parametric bootstrap using the likelihood function that we assume in our Bayesian method. That is, we use the data to estimate the parameters of the three likelihood functions (eqn D.9, eqn D.11 and eqn D.12) by maximum likelihood, use these fit likelihood functions to simulate new datasets, and combine samples from the three distributions to estimate per capita attack rates. We then determine the medians and 95% confidence intervals of the resulting bootstrapped attack rate distributions. In contrast to the Bayesian 95% credible intervals, which reflect the range of values within which a parameter will occur with 95% probability, the 95% confidence intervals associated with bootstrapping do not have a simple, empirically useful interpretation. Rather, if 95% confidence intervals were repeatedly constructed using newly collected equivalent datasets, 95% of them would contain the true value of the parameter. To highlight this difference, we use our Bayesian results to estimate the probability that the prey species with the highest posterior median attack rate has an attack rate greater than the species with the next highest posterior median attack rate, and so on. This type of inference is not possible within the frequentist framework (i.e., using the bootstrapped samples). 5.3 Results The comparison of the log differences in the MLE relative to the posterior medians of the Bayesian model for several values of the concentration parameter c of the Dirichlet prior evidenced that our non-informative neutral prior, c = 1 3, is indeed

120 102 the most appropriate prior to use on the feeding proportions when the median is the preferered point estimate of the attack attack rate posterior distribution (Fig. 5.1). All other non-informative priors result in median point estimates that are either considerably greater or less than the MLE at small sample sizes, converging only after significantly more observations are assumed than in fact had been made for most of the prey species in our case study data set. Concentration parameter values greater than 1/3 result in median point estimates that are inflated relative to the MLE, whereas values less than 1/3 result in estimates that are less than the MLE. Similarly, the comparison of the Bayesian and bootstrapping approaches applied to the entire case study data set also indicates that the model with the neutral prior (c = 1 3 ) was both sufficient for, and performs best in, describing the variation inherent in the estimated rates with which Haustrum scobina attacked its prey species (Fig. 5.2). With the neutral prior, the model exhibits median point estimates most closely matching the point estimates of the two bootstrapping approaches regardless of the number of feeding observations per prey species. The two bootstrap distributions, in contrast, frequently exhibit lower 95% confidence interval end points of zero; a nonsensical result given that the consumption of these species was in fact observed. Consistent with Fig. 5.1, the models using Laplace s (c = 1) or Haldane s (c = 0) priors result in inflated and depressed attack rate point estimates respectively, particularly for prey species that were observed infrequently in the feeding surveys. Fig. 5.3 shows the posterior probability distributions of Haustrum s per capita attack rates on each of its prey species as estimated using the neutral prior (c = 1 3 ). The distributions are roughly symmetric on the logarithmic scale, indicating right skew and justifying the use of the median as the point estimate of their central tendency.

121 103 Using the posterior distribution of the attack rate, we estimate the probability of the attack rate on Mytilus galloprovincialis being greater than on Xenostrobus pulex to be 0.68 (relative to the null expectation of 0.5 given no difference in probabilities), even though the 95% posterior interval for X. pulex is completely contained within the 95% interval for Mytilus galloprovincialis (Fig. 5.3). In addition, we estimate the probability of the attack rate on X. pulex being greater than on Austrolittorina antipodum to be Probabiity estimates such as these are unavailable from the bootstrap samples. Fig. 5.3 also illustrates an additional utility of modeling the three components of the attack rates estimator the abundances, handling times, and feeding ratios explicitly, permitting the decomposition of their contributions to the variation of inferred attack rate estimates. For example, while the interspecific variation observed in handling times spans less than two orders of magnitude, the interspecific variation in feeding ratios and prey abundances each span more than four orders of magnitude (Fig. 5.3). Hence the latter two components contributed more to the interspecific variation seen in the estimated attack rates than did variation in handling times. That said, nearly all of the interspecific variation in feeding ratios was driven by the two most commonly observed species, Xenostrobus pulex and Chamaesipho columna (Fig. 5.3). Thus, for most prey species, interspecific variation in the attack rates may be inferred to have been driven primarily by variation in their abundances. The partitioning of the predator observations into eight body size groups reveals a generally positive relationships between a whelk s body size and its attack rate on both of Haustrum s two primary prey species (Fig. 5.4). The point estimates for the allometric slopes of these intraspecific relationships were and for C. columna and X. pulex respectively. These slopes belie substantial variation

122 104 surrounding each size group s median attack rates on the two prey species. Thus, while the probability that the attack rate of the largest whelk group (17-28 mm) was greater than the corresponding attack rate of the smallest group (6-10 mm) on X. pulex was 0.89, it was only 0.60 for their attack rates on C. columna (versus the null expectation of 0.5). 5.4 Discussion Effort devoted to estimating the strengths of species interactions has centered on obtaining point estimates, leaving the characterization of estimation uncertainty largely unconsidered. This shortcoming reflects not only the logistical difficulty of quantifying interaction strengths in nature s species-rich communities, but is also a consequence of the still nascent integration of the mathematical and statistical methods available to food web ecologists. The fitting of deterministic mathematical models to data requires that they be formulated as stochastic statistical models whose constants like the per capita attack rates considered here be treated as unknown parameters to be estimated. For the observational estimator of Novak & Wootton (2008) the unknown attack rate parameters of interest are functions of other unknown parameters that must themselves be estimated. Uncertainty in attack rate estimates thus reflects the contributions of both the deterministic and stochastic variation of these component parameters. The propagation of both such forms of variation is inherent to all other experimental and observational approaches as well. Our case study serves to illustrate how the explicit modeling of the components that go into estimating attack rates using the observational approach (i.e. feeding ratios,

123 105 handling times, and prey abundances) provides insight into the drivers of variation in the attack rates among prey species. It is worth highlighting, however, that the attack rate posterior distributions that we estimate here represent population-level uncertainty (i.e. uncertainty in the overall attack rates) rather than intraspecific variation in the diets of individuals. Thus the wide posterior interval for Mytilus galloprovincialis, for example, means that there is a high degree of overall uncertainty about the attack rate on this species, rather than being a reflection of the individual specialization that many generalist predators, including whelk species, are known to exhibit (Bolnick et al., 2003). Nevertheless, just as for interspecific comparisons of variation, insight into the species-specific uncertainty is also possible by the partitioning of its components (which combine additively on the logarithmic scale). Thus for prey species like Mytilus that occur infrequently in feeding surveys (all prey species except Chamaesipho columna and Xenostrobus pulex, Table 5.1), the largest source of uncertainty comes from the estimation of the feeding ratios (Fig. 5.3). Additional feeding surveys would therefore provide the most important data for better constraining this stochastic source of uncertainty. In contrast, a simple way to obtain further insight into potential additional deterministic drivers of species-specific variation is to apply the estimation approach to subsets of the data as in Fig In our case study, the point estimates for the allometric slopes of the intraspecific relationships between body size and attack rate are both far lower than predicted by theory for the dependence of a specialist predator s interspecific attack rates on predator body size (Rall et al., 2012), possibly suggesting size-dependent changes in prey preferences.

124 Advantages of the Bayesian approach Unlike frequentist methods, Bayesian methods offer a relatively straightforward way to estimate parameters that are functions of other parameters using multiple sources of information. Bayesian methods also permit a more natural interpretation of the uncertainty that accompanies parameter estimates and provide a complete characterization of this uncertainty in the form of posterior probability distributions; frequentist methods provide the moments and intervals of distributions whose interpretation is arguably less intuitive (Clark, 2005). In our case study, we are able to infer the probability of the attack rate on Mytilus galloprovincialis being greater than on Xenostrobus pulex, and so on. In the context of food webs and predator-prey interactions, this complete probabilistic characterization of uncertainty regarding observational interaction strength estimates opens the door for probabilistic predictions of species effects and population dynamics (Calder et al., 2003; Yeakel et al., 2011; Koslicki & Novak, 2016). This stands in contrast to the typical use of arbitrarily chosen interaction strength ranges in stochastic simulations and numerical sensitivity analyses (Yodzis, 1988; Novak et al., 2011). An alternative choice to use bootstrapped (frequentist) confidence intervals to inform predictions could lead to additional problems when lower interval bounds extend to zero for prey species that are rarely found in a predator s diet. First, draws of zeros would amount to the outright removal of the predatorprey interaction and could lead to biased predictions through the underestimation of food web complexity (Poisot et al., 2016). Second, as evidenced by Haustrum scobina s feeding on Mytilus galloprovincialis (Fig. 5.2), prey species whose attack rate confidence intervals extend to zero may in fact experience very high per capita

125 107 attack rates on average. Treating these interactions as potentially absent would fail to identify strong interactions that are rarely observed only because of strong topdown control of the prey populations sizes, for example. Such issues do not occur in the Bayesian framework where the Dirichlet prior distribution is conjugate for the multinomial likelihood, thereby producing a Dirichlet posterior from which MCMC samples of zero cannot occur Considerations and implications Bayesian methods offer a powerful tool, but they should not be applied without careful consideration of the prior distribution. The choice of non-informative (objective) priors is particularly important when data are sparse (Van Dongen, 2006). It follows that, for rarely observed prey species, different prior specifications lead to different point estimates of the per capita attack rates (Figs. 5.1 and 5.2). That is, while priors with concentration parameters c > 1 3 (e.g., Laplace s prior) will produce higher attack rate point estimates the less frequently a prey species is observed in the predator s diet, priors with concentration parameters c < 1 3 (e.g., Haldane s prior) will produce lower attack rate point estimates the less frequently a prey species is observed in the predator s diet (see also Fig. D.2). The biological implication of choosing to use one such prior over another is that this choice can alter the relative frequency of weak and strong interactions. Thus, the choice of priors can alter inferences of population dynamics and food web stability (Allesina & Tang, 2012). These considerations are avoided only when all prey occur frequently in a predator s diet (see Xenostrobus pulex and Chaemaesipho columna in Fig. 5.2). In such cases, the large sample sizes mean that the likelihood overwhelms the prior

126 108 regardless of its information content such that Bayesian and frequentist estimates are similar. The use of the neutral prior produces posterior distribution median point estimates that are least influenced by the prior and thus most like the point estimates of the frequentist bootstrap methods (Figs. 5.1, 5.2, D.2). We therefore suggest that this be the preferred objective prior to use. Tuyl et al. (2008) argue against the use of such sparse (c < 1) priors for binomial parameters as they put more weight on extreme outcomes. For example, if Y Bin(n, p) and Y {0,n}, the use of sparse priors leads to inappropriately narrow credible intervals. Fortunately, this problem is avoided in our application because all considered prey species (and not feeding ) are observed at least once (i.e. Y {1,...,n 1}). It is true that in hierarchical models, to which our framework is naturally extended (Appendix D.6), Y {0, n} is more likely for any individual survey, but this is not an issue as inference at the survey level is typically not desired in the absence of additional covariates. An influence of Bayesian prior choice also occurs in the estimation of prey abundances by means of a zero-inflated gamma likelihood model. Here the assumption that a zero-inflated gamma is descriptive of the abundance structure of all prey species can lead to the inflation of per capita attack rate estimates for species that are ubiquitous. When species occur in all but a few sampled quadrats, relatively little data are available to estimate the probability of obtaining a count of zero. In such situations the influence of even an uninformative uniform prior will be increased, resulting in an inflated estimate of the proportion of zeros and thus a reduced estimate of a species abundance. Attack rate estimates are thereby inflated because a species abundance occurs in the denominator of the estimator (5.2). For our dataset, where many species were present in all sampled quadrats (Table 5.1), this inflation effect appears to have been weak as seen by comparing the results

127 109 of the Bayesian models to the frequentist bootstrapping procedures for which such inflation does not occur (Fig. 5.2); the probability of obtaining a value of zero during bootstrapping is equal to the sample proportion of zeros in the data, which is zero for species that are always observed. Arguably, however, this inflation effect of the prior that is inherent to the use of the zero-inflated gamma in a Bayesian framework is appropriate because observations of species absences at the spatial scale of quadrats are fundamentally different from observations of species presences when no prior knowledge about the patchiness of prey species abundances is available. Issues of prior choice aside, Bayesian methods offer a more complete characterization of the estimated uncertainty of parameter estimates in the form of posterior probability distributions. Several metrics may be chosen to summarize the shapes of these distributions. For example, means, medians and modes are all commonly used as point estimates to reflect a distribution s typical and most likely value. For strongly skewed distributions such as those observed here (Fig. 5.3) medians are a more representative metric of a distribution s central tendency. Furthermore, a distribution s median, unlike its mean, will always fall within the equal-tailed interval that is typically used to describe the variation surrounding the distribution s estimated central tendency. Of course, point estimates provide little information on a distribution s shape. Confidence or credible intervals provide more such information with which to characterize parameter variation. The typical metrics for these intervals are equal-tailed, but for posterior distributions the highest posterior density (HPD) interval may also be useful (Gelman et al., 2013). While intervals characterized by highest posterior density are more resistant to distribution skew and will always include the distribution s mode, equal-tailed intervals are invariant under monotone transformations, making them easier to interpret after log-

128 110 transformation. Log-transformation is frequently necessary in the context of interaction strengths given the wide range of values that the community-wide strengths of species interactions typically exhibit (Wootton & Emmerson, 2005). Ultimately, the entire joint posterior distribution should be presented whenever possible Conclusion While many ecological processes can be described in purely mathematical terms, mathematical models are often most useful when they are linked with real data (Codling & Dumbrell, 2012). Linking models with data is necessary to validate and compare models, and to parameterize them for real-world use in predicting future system dynamics (Bolker, 2008). This has been a challenging task in the study of species rich food webs, not least because of the difficulty of parameter estimation in typical food web models and challenges with integrating data collected across multiple spatial and temporal scales. Statistical models of predator-prey interactions that consider both the deterministic and stochastic variation in data are needed to accompany the numerous mathematical models that have been proposed (Poisot et al., 2015). Our work represents a step in this direction, and has the potential to be extended in several directions to address questions of optimal foraging theory, prey profitability, and functional response formulations other than the multispecies type II response considered here (Pyke, 1984; Berger & Pericchi, 1996; Novak et al., 2016a).

129 Acknowledgments This work was supported by NSF DEB and DEB We thank the editor and two anonymous reviewers whose comments substantially improved the manuscript. 5.6 Conflict of Interest The authors declare that they have no conflict of interest. 5.7 Data accessibility Data and R scripts are available on the Dryad Digital Repository (doi: / dryad.6k144) and on GitHub ( Interaction-Strength).

130 Sparsity (c) log 10 θ^bayes X i X Predators Feeding Figure 5.1. Comparison of alternative non-informative priors in estimating the ratio of the proportions of feeding versus not feeding predator individuals. The x-axis reflects the number of predators observed in the process of feeding on a given prey species, with a total of 1,629 individuals assumed to have been not feeding, corresponding to the number not feeding in our case study dataset (Table 5.1). The y-axis shows the difference in logarithms of the posterior median using a Dirich(c,..., c) prior and the maximum likelihood estimate of the ratio (sample proportion). From top to bottom in the graph, the values of c are 1 (Laplace), 1 2 (Jeffreys ), 3 1 (neutral), 1 S+1 = 1 9 (Perks ), and 0 (Haldane s). Our neutral prior (c = 1 3 ) leads to estimates that most closely match the maximum likelihood estimates

131 113 Mytilus galloprovincialis Xenostrobus pulex Austrolittorina antipodum Notoacmea Radial Risellopsis varia Chamaesipho columna Austrolittorina cincta Epopella plicata Attack Rate ( ξ i ) Nonparametric Bootstrap Parametric Bootstrap Bayes (c=0) Bayes (c=0.333) Bayes (c=1) Figure 5.2. Comparison of the frequentist and Bayesian approaches to estimating the per capita attack rates with which Haustrum scobina consumed its 8 prey species. Variation in attack rate estimates is illustrated for each by the medians and 95% equal-tailed intervals of their distributions. The approaches are organized the same for each prey species as, from top to bottom: (i) non-parametric bootstrap (filled square), (ii) parametric bootstrap (circle), (iii-v) Bayesian procedure with sparsity parameters c = 0 (Haldane s prior; triangle), 1 3 (neutral prior; diamond), and 1 (Laplace s prior; open square) respectively. Unlike the 95% confidence intervals for the bootstrap procedures which often span zero (= 10 7 for graphical convenience), the 95% posterior posterior intervals of the Bayesian method indicate the regions where attack rates lie with 95% probability. A color version of this figure is available online

132 114 Density Feeding Ratio α i α 0 H.time η i Abundance ν i Attack Rate ξ i Mytilus galloprovincialis Xenostrobus pulex Austrolittorina antipodum Notoacmea Radial Risellopsis varia Chamaesipho columna Austrolittorina cincta Epopella plicata Figure 5.3. Posterior distributions for Haustrum scobina s per capita attack rate parameters (prey predator 1 prey 1 m 2 day 1 ) and their components (ξ i = α i α 0 1ν i 1η i ) using neutral (c = 3 1 ) Dirichlet prior on feeding proportions

133 115 Chamaesipho columna Xenostrobus pulex Attack Rate ( ξ i ) Median predator mass (g) Figure 5.4. Deterministic variation in per capita attack rates due to predator body size for the two prey species consumed by Haustrum scobina most frequently. Points indicate posterior medians and violin widths reflect posterior probabilities of the attack rate magnitudes. Predator individuals were split into body mass size classes of roughly equally-numbered counts (Table D.2) with class median body weights (W, total wet weight in grams) estimated on the basis of each whelk s shell length (L, in mm) (W = L 3.210, from Novak (2013))

134 116 Table 5.1. Summary statistics for the datasets we use to estimate the per capita attack rates with which the intertidal predator Haustrum scobina fed on its eight prey species. Feeding observations indicates the total frequency with which predator individuals were observed to be feeding on each prey species across all feeding surveys. Abundance zeros indicates the number of zeros recorded in the 30 quadrat-based community surveys of prey species abundances. Handling-time experiments indicates the number of laboratory experiment trials that were used to estimate handling time regression coefficients for each prey species Feeding Abundance Handling-time Prey Species Observations Zeros Experiments Chamaesipho columna Xenostrobus pulex Austrolittorina antipodum Austrolittorina cincta Epopella plicata Mytilus galloprovincialis Notoacmea Radialspokes Risellopsis varia Not Feeding 1,629 Total Surveyed 2,089

135 117 6 A unification of priors for modeling rare events in nonlinear regression 6.1 Introduction Binary data where events are rare relative to non-events occur frequently in many situations. Examples include data related to species occurrence (presence may be much less common than absence), international conflict (peace between countries is often more common than war), fraud or anomaly detection, and natural disasters (King & Zeng, 2001b). While other types of rare events are also possible (e.g., outliers among continuous data), we consider only the binary case here. A key feature of these data is that the number of observations may be quite large, unlike in small sample size problems. For such data, standard logistic regression is known to perform poorly (King & Zeng, 2001a,b). The ordinary maximum likelihood estimates (MLE) either do not exist or have substantial bias. Assessing their performance is challenging since MLE frequently do not exist when simulating rare events data and tests for MLE convergence vary (van Smeden et al., 2016). King & Zeng (2001a,b) discuss methods for modeling rare events in this framework, including alternative data collection procedures (selecting on the dependent variable with adjustment), correcting estimates using prior information on the prevalence of events in the population, and finite sample corrections. Other possible methods that may be used here are exact logistic regression and Firth s logistic regression where the score function is modified by a penalty term equivalent to using Jeffreys prior (Mehta & Patel, 1995; Firth, 1993). Firth s logistic regression reduces the bias of parameter estimates, always

136 118 produces estimates, and is computationally straightforward. It works well when samples sizes are small, and may be suitable for modeling rare events (van Smeden et al., 2016; Van der Paal, 2014). Scientific models often involve nonlinear relationships among variables. While linear models are frequently assumed in statistics, it is also possible to fit nonlinear models that may be more realistic (Wakefield, 2004). In a typical nonlinear model, the mean response is linked to covariates through a function that is nonlinear with respect to the parameters (Wakefield, 2004). Nonlinear models may have greater predictive power than ordinary linear models due to being able to represent nonlinear relationships. However, a primary motivation for such mechanistic models is the interpretability of the parameters, which often have clear scientific interpretations (Domijan et al., 2006). Although there has been little work on nonlinear modeling of rare events data, Kosmidis & Firth (2009) have shown how the method of Firth (1993) can be used to reduce bias in nonlinear regression parameter estimates. Here, we consider the problem of fitting nonlinear models to rare events data. We use a Bayesian approach since this framework allows for parameters to be described with a complete (posterior) distribution, simple probability statements to be made about parameters, and is common in the scientific literature (Gelman et al., 2013). A challenge of Bayesian statistics is the specification of an appropriate prior distribution for the model parameters. We will assume that no prior information is available. Although common non-informative priors generally perform well when there are sufficient data, this does not apply to rare events modeling. Even rare events datasets with thousands of observations may contain only a few events, leading to high sensitivity to the prior distribution. This is further compounded by nonlinearity since the probability of an event may vary little with respect to one or

137 119 more of the parameters for certain covariate values. We focus on three families of univariate nonlinear functions: Type I, Type II, and Type III (Figure 6.1). Each function (defined on x > 0) describes the probability of an event p(x) and has the properties that p(0) = 0, p(x) 1 as x, and p (x) 0. The Type II function family is closely related to the Michaelis-Mentin functions used to model enzyme kinetics, and all three functions have been used to model predator feeding rates as functions of prey abundance (Michaelis & Menten, 2007; Jeschke et al., 2004). Although the assumption that p(x) 1 as x, which we term saturation, may seem unrealistically simple, it is plausible in many cases for binary data. For example, in medical studies to determine the lethality of a compound, the probability of death may approach 1 as the dose increases. Similarly, in simple models of predator feeding behavior the likelihood of a predator feeding approaches 1 as prey abundance approaches infinity. We present an analysis of non-informative prior distributions for these three families of functions. We consider common non-informative priors: uniform, log uniform, functional uniform, and Jeffreys (Kass & Wasserman, 1996; Bornkamp, 2012). Additionally, we present new prior distributions for the Type I and Type II functions that are designed to minimize the frequentist-sense bias of the posterior point estimates and are suitable for use when events are exceptionally rare. By frequentistsense bias, we simply mean the usual frequentist bias of a point estimate (i.e. the bias as a function of the true parameter value). For the Type II function, we show that all of these prior distributions are special cases of a more general distribution. We use this unifying result to determine when the posterior distribution and posterior mean exist. For each function family, we then evaluate the performance of all of these prior distributions using a simulation study. Variables in the simulation are chosen to cover a wide range of rarity, covariate distributions, and so on.

138 120 Throughout, our primary focus is on the (frequentist-sense) bias of the posterior mean, although we also consider the coverage of credible intervals when assessing our results. Finally, we fit all three functions with each prior distribution to ecological data collected on predator feeding behavior, showing that the posterior point estimates can vary substantially depending on the non-informative prior used. Specifically, we model the probability of a predator being observed feeding on a prey individual. This is closely linked to functional response (per capita kill rate) estimation, which has applications to the study of species population dynamics (Novak et al., 2017b). Throughout, we use bias to describe the frequentist-sense bias of Bayesian point estimates. Although it is somewhat counter-intuitive (since parameters in Bayesian statistics are often viewed as random), this quantity is of interest in many practical applications, and has been considered in other Bayesian analyses (e.g. Park et al., 2010). We denote the probability density function of a random variable X as f (x) (i.e., f is generic), we use g to represent the nonlinear function being considered, and we use subscripts 1,2, and 3, to reference the Type I, II, and III settings respectively. We use non-informative to describe priors that are designed for use when no prior information is available and are intended to have minimal effect on inference (Syversveen, 1998).

139 Methods Function families and likelihoods We consider three families of functions for nonlinear regression (Figure 6.1). We denote the three functions as Type I, Type II, and Type III respectively: g 1 (x;β) = min(βx,1), x > 0,β > 0 (6.1) g 2 (x;β) = g 3 (x;α,β) = βx, x > 0,β > 0 (6.2) 1 + βx βxα, x > 0,β > 0,α > 1. (6.3) 1 + βxα For these functions, half-saturation (g = ) occurs at x = 2β, x = 1 β, and x = ( 1 β ) α 1, respectively. For the Type I function, saturation (g = 1) first occurs at x = 1 β. For the Type III function, increasing α causes the function to be more convex for small x. In each case, we assume that the response is binary and that the data are independent. We treat the covariate values as constant and denote the data (x i,y i ) for i = 1,...,n. For convenience, we let p i = P(Y i = 1) and S = n Y i. Noting that, in the Type I case, the likelihood for a single observation (x,y ) is i=1 (βx) y (1 βx) 1 y x < 1 β f (y β) =,β > 0 I(y = 1) x 1 β,β > 0, (6.4)

140 122 the likelihood functions for the Type I, II, and III families respectively are: f 1 (y β) = f 2 (s β) f 3 (y α,β) {i:x i < 1 β } (βx i ) yi (1 βx i ) 1 yi, 0 < β < min β s {i:y i =0} 1, (6.5) x i n, β > 0, (6.6) (1 + βx i ) i=1 n (βxi α)y i i=1 n i=1 (1 + βx α i ), α > 1,β > 0, (6.7) where the latter two likelihoods are only given up to a scaling factor that does not involve the parameters. Note that the Type I likelihood is not identifiable when x i β 1 for all x i as the likelihood is either zero or one there. In the next sections, we consider low-impact prior distributions to use in each of these cases. In general, we denote these priors as f 1 (β), f 2 (β), and f 3 (α,β). In each case, we are primarily interested in identifying priors that have low frequentistsense bias when we use the posterior mean as a point estimate. We look at a set of common non-informative prior distributions: (1) uniform (uniformly distributed over the parameter space), (2) log uniform (uniformly distributed on the log scale), (3) functional uniform (uniformly distributed with respect to the corresponding non-linear functions), and (4) Jeffreys (invariant to reparameterization) (de Laplace, 1820; Kass & Wasserman, 1996; Bornkamp, 2012). Additionally, we derive new priors that we develop by considering the simplified case where all covariate values are equal. We then unify the Type II function priors by showing that they are special cases of a more general family of prior distributions.

141 Uniform prior Many common non-informative priors are designed to be uniform in some sense. Laplace s prior is uniform over the parameter space (de Laplace, 1820). This is often a reasonable choice as models may be parameterized in such a way that a lack of information corresponds to all parameter values being equally likely Log uniform prior Since β > 0, we can also consider the prior f 1 (β) = f 2 (β) 1 β. This is equivalent to using a uniform prior on log(β) and was initially recommended by Jeffreys due to its invariance under power transformations of the parameter (Kass & Wasserman, 1996). In the Type III case, we can use independent log uniform prior distributions on each parameter: f 3 (α,β) 1 α 1 β Functional uniform prior Bornkamp (2012) considers prior choice for nonlinear regression (among other cases). He develops the idea of a functional uniform prior a uniform prior on the space of functions. It is derived by embedding the functions (indexed by parameter vectors) in a metric space and then back-transforming the uniform prior on that metric space to the parameter space. An advantage of this approach is that since we are often interested in estimating the shape of a nonlinear function, using a

142 124 uniform prior in the space of shapes can be easier to justify than using a uniform prior with respect to an arbitrary parameterization (Bornkamp, 2012). When the distance function, d, for the metric space is given by the L 2 distance between functions, d(u(x),v(x)) = (u(x) v(x)) 2 dx, (6.8) the functional uniform distribution for the parameters θ (defined on a compact set) is given by: f (θ) ( θ g(x;θ))( θ g(x;θ)) T dx, (6.9) where g(x; θ) is the nonlinear function of interest (indexed by parameter vector θ) and θ g(x;θ) is the column vector of first partial derivatives of g(x;θ) taken with respect to the components of θ. In the Type I setting, It follows that β g 1(x;β) = β min(βx,1) = x, x < 1 β. (6.10) f 1 (β) 1 β 0 x 2 1 dx = 3β 3 β 1.5. (6.11) Although functional uniform priors are normally defined over compact sets to ensure that the prior is proper (Bornkamp, 2012), we simply let β > 0 since there is no prior information with which to restrict the support.

143 125 Similarly, in the Type II setting, which implies that β g x 2(x;β) = (1 + βx) 2, (6.12) [ ] x 2 1 f (β) 0 (1 + βx) 2 dx = 3β 3 β 1.5, (6.13) where the integral can be solved by making the substitution u = 1 + βx. Again, we let β > 0. Finally, in the Type III setting, g 3 (x;α,β) = show that for α > 1 and β > 0, f 3 (α,β) βxα 1+βx α. In sections E.3 and E.4, we β 2 α 1 α 5 sin( α π ) (α 2 1) 2 π 2 sin 2 ( α π ) α2 (α 4 + 3). (6.14) Jeffreys prior Jeffreys prior is proportional to the square root of the determinant of the Fisher information matrix, and it is partly motivated by its invariance to reparameterization (Kass & Wasserman, 1996). In the Type I setting, we have that I 1 (β) = {i:x i < 1 β } x i β(1 βx i ) (6.15)

144 126 (details in section E.4), which means that Jeffreys prior is f 1 (β) {i:x i < 1 β } x i, β > 0. (6.16) β(1 βx i ) This prior is 0 if βx i 1 for all x i, since the model is not identifiable in this region, which means that the log likelihood is flat, and thus its derivative (the score function) is 0. In the Type II setting, so Jeffreys prior is f 2 (β) I 2 (β) = n i=1 n i=1 x i β(1 + βx i ) 2, (6.17) x i, β > 0. (6.18) β(1 + βx i ) 2 Lastly, in the Type III setting, β n I 3 (α,β) = i=1 n i=1 x α i ln 2 x i (1+βx α i )2 xi α lnx i 1 (1+βxi α)2 β n x i α lnx (1+βx i=1 i α)2 n i=1 x α i (1+βx α i )2 (6.19) (details in section E.4), and Jeffreys prior is thus f 3 (α,β) I 3 (α,β). (6.20)

145 Information prior So far, none of the priors that we have discussed have been explicitly designed to minimize the frequentist-sense bias of the posterior mean. With this goal in mind, we propose priors proportional to the Fisher information matrices for the Type I and Type II settings: f 1 (β) f 2 (β) {i:x i < 1 β } n i=1 x i β(1 βx i ), β > 0 (6.21) x i, β > 0. (6.22) β(1 + βx i ) 2 In the rare events case, P(Y i = 1) 0, so the βx i terms tend to be small (that is, the likelihood tends to be highest in regions where β corresponds to small βx i ), which means that f 1 (β) f 2 (β) 1 β. To see why the posterior mean is expected to have low bias in the Type I setting, consider the case when x 1 =... = x n = x. Here, S = n i=1 Y i Binomial(n, p = min(βx,1)). (6.23) In the rare events setting, the likelihood is nearly always zero when βx 1 (since the probability of observing S = n is negligible), so we may approximate it with a binomial likelihood with p = βx (0 < βx < 1), and thus the general form of the posterior distribution is f 1 (β s) (βx) s (1 βx) n s f 1 (β), 0 < βx < 1, (6.24)

146 128 which is a beta distribution in β x. βx Taking Haldane s prior (Haldane, 1948) on f 1 (β) 1, 0 < βx < 1, (6.25) βx(1 βx) f 1 (β s) (βx) s 1 (1 βx) n s 1, 0 < βx < 1. (6.26) So, βx S = s. Beta(s,n s) (6.27) and, treating P(βx = 0 S = 0) and P(βx = n S = n) as 1, [ β ] E = E[E(β S)] E [ 1 x S n ] nxβ xn = β. (6.28) In the more general case, suppose x 1,...,x n are not necessarily equal. Since the equal covariate values case prior that we just considered is proportional to the Fisher information, by analogy with Jeffreys prior, we again use the Fisher information in this more general case: f 1 (β) {i:x i < 1 β } x i β(1 βx i ). (6.29) This incorporates all of the x i terms and reduces to equation 6.25 when the covariate values are equal. For the Type II setting, we similarly begin from the simplifying assumption that

147 129 x 1 =... = x n = x, in which case S = n i=1 ( Y i Binomial n, p = βx ) 1 + βx (6.30) and f 2 (β s) ( ) βx s ( ) 1 n s f 2 (β) (6.31) 1 + βx 1 + βx β s (1 + βx) n f 2 (β). (6.32) Consider the conjugate prior p Beta(a,b) with a,b > 0. Note that this is equivalent to In this case, the posterior distribution is ( 2a p Beta 2, 2b ) 2 (6.33) 2bp F(2a,2b) 2a(1 p) (6.34) β = p 1 1 p x 1 a F(2a,2b) x b (6.35) ( 2(a + s) p s Beta, 2 2(b + n s)p ) 2(b + n s) 2 (6.36) F(2(a + s),2(b + n s)) (6.37) 2(a + s)(1 p) β s = p 1 s 1 a + s F(2(a + s),2(b + n s)) (6.38) 1 p x x b + n s Using the result that Y = cx implies f Y (y) = 1 c f X ( 1c y ), we can write out the prob-

148 130 ability density functions explicitly: f (β) β a 1 (1 + xβ) a b (6.39) f (β s) β s+a 1 (1 + xβ) n a b (6.40) From equation 6.38, it follows that, when it s defined, the posterior mean is the posterior mode is β mean = E(β S) = 1 a + S x b + n S 1, (6.41) β mode = 1 a + S 1 x b + n S + 1, (6.42) and, using an approximation for the median of an F-distribution (Kerman, 2011), the posterior median is approximately β median = median(β S) 1 x a + S 1 3 b + n S 1. (6.43) 3 Thus, we may take a = 0 and b = 2 when working with the posterior mean, a = 1 3 and b = 4 3 when working with the posterior median, or a = 1 and b = 0 when working with the posterior mode to obtain the Bayesian point estimate β = 1 S x n S + 1. (6.44) When using a = 0, the posterior distribution does not exist when S = 0 (since we are integrating over roughly 1 β when β is near 0). However, we can still use the estimator as defined above in this case since this is the limit as a 0. This is

149 131 similar to what is typically done with Haldane s prior for a binomial proportion when S = 0 or S = n is observed. We provide a more detailed and careful discussion of the posterior distribution s properness in section The advantage of using these prior(s) is that the resulting Baysian point estimate (equation 6.44) has very low bias (in the frequentist sense). Moreover, we can evaluate its bias explicitly (details in section E): ( β ) [ ] 1 S E = E x n S + 1 =... = β(1 p n ) (6.45) ( β ) This shows that the absolute bias is E β = β p n and the absolute relative bias is ( β ) E β β = p n. So, the bias decays geometrically with n, which is often fairly large in rare events problems (unlike the number of events). In contrast, for other similar values of a and b, the bias appears to be much more substantial (Figure E.1). Since this prior (i.e. the one focused on the posterior mean) is proportional to the Fisher information, we again use the Fisher information when covariate values are not all equal: f 2 (β) n i=1 x i β(1 + βx i ) 2. (6.46) As in the Type II setting, this incorporates all of the x i and reduces to the corresponding equal covariates prior when x 1 =... = x n = x. Although analytical results for these priors are not available in the unequal covariate values cases, we further justify their use through a simulation study. For the Type III function, we were unable to develop an analogous prior using the same approach since setting

150 132 x 1 =... = x n = x results in a likelihood that is not identifiable with respect to the parameters, so useful estimators cannot be derived in that case Properness of priors (Type II) Here, we determine the properness of the resulting posterior distributions for each of the Type II function priors. All of these priors have the form f (β) [ n i=1 ] t x i β u (1 + βx i ) v (6.47) where t, u, and v are nonnegative. To see when the posterior distributions are proper, first note that for x > 0, 0 β a (1 + βx) b dβ = = β a (1 + βx) b dβ + 1 (1 + βx) b β a dβ + 1 β a dβ (6.48) (1 + βx) b 1 ( ) β b β a b dβ (6.49) 1 + βx The first terms in each integrand are bounded by positive constants (over the ranges of integration), so they can be ignored for checking convergence. It follows that the sum converges if and only if a > 1 (first integral) and a b < 1 (second integral; i.e. b > a 1). To use this result, note that the integral of the unnormalized posterior distribution

151 133 is 0 and 0 n i=1 n i=1 β s (1 + βx i ) [ n i=1 β s (1 + βx i ) [ n i=1 ] t x i β u (1 + βx i ) v dβ 0 = c 1 ] t x i β u (1 + βx i ) v dβ 0 β s (1 + βx min ) n [ n i=1 0 = c 2 β s ut ] t x max β u (1 + βx min ) v dβ (6.50) dβ (6.51) (1 + βx min ) n+vt β s (1 + βx max ) n [ n i=1 0 β s ut ] t x min β u (1 + βx max ) v dβ (6.52) dβ (6.53) (1 + βx max ) n+vt for positive constants c 1,c 2. Since the integral of the unnormalized posterior is bounded between these integrals, the posterior is proper if and only if ut 1 < s < n + vt + ut 1. This allows us to list the values of s for which each prior produces a proper posterior distribution (Table 6.1). For the expected value to exist, we also require this constraint to hold when ut is replaced with ut 1 (corresponding to multiplying the integrand by β) (Table 6.1). As noted in section 6.2, for improper posterior distributions with s = 0 or s = n, we use the MLEs ˆβ = 0 and ˆβ = respectively. This is similar to the common approach to handling s = 0 and s = n when estimating a binomial proportion using Haldane s prior. A consequence of this is that the uniform and log uniform priors will have infinite bias, although this may not be apparent in rare events simulations

152 134 as s = n is very unlikely. In the case of the (posterior mean-based) information prior for the Type II function, we could alternatively take f (β) n i=1 x i β 1 ε (1 + βx i ) 2 (6.54) for some small ε. When the covariates are all equal, the resulting posterior mean is β = 1 S + ε x n S + 1, (6.55) which approaches 0 as ε 0 when S = 0. Similarly, we can that show that the posterior mean approaches 0 when the covariates are not all equal Simulation study To compare the performance of these priors, we conduct a simulation study. This approach allows us to assess the performance of these priors from a frequentist perspective. Assessing the frequentist properties of Bayesian point estimates and credible intervals provides one way to compare the performance of different priors (e.g. Datta & Sweeting, 2005). It is particularly well-suited to cases in which no prior information is available and accurate parameter estimates are desired (rather than focusing on out-of-sample prediction ability). As the posterior distributions and resulting point estimates are not straightforward to calculate analytically, we use the Hamiltonian Markov chain Monte Carlo (MCMC) software Stan (Stan De-

153 135 velopment Team, 2016). For each simulation, we compute 500 samples in each of two separate chain, with inference based on the second half of samples. We assess convergence using the Gelman-Rubin convergence statistic ˆR, which compares within and between chain variation (Brooks & Gelman, 1998). In this simulation study, we choose a range of settings intended to be representative of real rare events datasets. For the distribution of covariate values, we use a lognormal distribution with log mean equal to and log standard deviation chosen to yield coefficients of variation (CV = σ/µ) equal to 0.1, 1, or 10 (CV was fixed at 1 for the Type III function). This is in line with King & Zeng (2001b), who define rare events data as consisting of dozens to thousands of times more events than non-events. Rather than specify β directly, we consider the following levels of rarity p, which we define as the unconditional probability of an event: 0.1, 0.01, For each value of p and covariate distribution, we calculate β using p = E(Y ) = E[E(Y X)]. For the Type III function, we let α {1.25, 2}. For sample sizes, we use n = 100,500,1000,5000 (except for the Type III function where we fix n = 1000). Values in the upper portion of this range are typical for intertidal predator feeding surveys the subject of our case study (Wolf et al., 2017). More generally, this range covers all but one of the rare events datasets analyzed in Maalouf & Trafalis (2011). For prior distributions, we use the information priors, along with the uniform, log uniform, functional uniform, and Jeffreys priors (Table 6.1). For the Type II function, when posterior means do not exist, we treat the posterior distributions as point masses at 0 (s = 0) or (otherwise). A summary of the simulation variables and their values is given in Table 6.2. For each parameter configuration, we conduct 1,000 separate simulations (5,000 for the Type II function). For each simulation and parameter, we estimate the posterior

154 136 mean θ mean and whether or not the marginal 90% equal-tailed credible interval covers the parameter, I( θ L < θ < θ U ) (Burton et al., 2006; van Smeden et al., 2016). Since we compute these quantities for each independent simulation, for each parameter configuration, we estimate their expected values (representing the true posterior mean and 90% coverage probability respectively) by taking averages and compute approximate 95% confidence intervals for their expected values using the central limit theorem Case study We conduct a case study, fitting each type of function to the same dataset, using each of the priors from the simulation study. Our case study data are derived from the manipulated patch dataset given in (Novak et al., 2017a,b). These data were collected in 2013 in Yachats, Oregon (44.3 N, W). The data contain observations of the intertidal predator whelks Nucella ostrina and Nucella canaliculata and whether or not individuals were feeding when observed. For feeding predators, the species of the prey individuals being fed upon were recorded. Prey were most commonly barnacles or mussels. The predator feeding surveys were performed at low tide using 10 haphazardly selected, naturally formed patches, ranging in size from 0.8m 2 to 5.8m 2. Concurrently, prey species abundances were estimated using three cm 2 quadrats randomly placed within each patch. Additional feeding survey data including predator and prey size were also recorded, but we do not use these data. For more detail on the data collection procedures, see (Novak et al., 2017a,b). For our primary example, we use the feeding survey data for the predator Nucella

155 137 ostrina and whether it was feeding on the prey species Lottia asmi or not feeding (Table E.1). The total number of observations is 5,917 and the proportion of predators feeding is (Table E.1). As a secondary example, we also separately model the feeding behavior of this predator on the prey species Balanus glandula a substantially more common event (total observations: 6,399; proportion feeding: 0.077). Within each of the 10 patches, we estimate prey abundances (individuals per m 2 ) using the averages of the three quadrat-level abundance estimates. This estimated prey abundance is then used as the continuous predictor variable in our models. As with the simulation study, we conducted the MCMC sampling in Stan. For each function and prior, we used four separate chains with 2,000 samples each (first half discarded). Convergence was verified by checking that the Gelman-Rubin convergence statistic ( ˆR) was at most Results Simulation study Here we report the results of our simulation study. As our information prior distributions are designed to have low frequentist-sense bias, we focus on the relative bias (of the posterior means) when comparing priors. For certain parameter configurations with the Jeffreys and information priors (Type I function) and functional uniform prior (Type III function), chains failed to converge (average ˆR 1.1). In such cases, we exclude these settings when summarizing our results.

156 138 For the Type I and Type II functions, the uniform and Jeffreys priors tended to overestimate the parameter β, while the functional uniform prior tended to underestimate β (Figure 6.2). The log uniform and information priors showed substantially lower bias in these settings. However, for the Type I function, using the log uniform prior appears to have resulted in underestimating the parameter when p = 0.1 and CV = 1 (Figure 6.2). For the Type II function, the log uniform prior frequently resulted in overestimating the parameter, especially when CV = 10 (Figure 6.3). Overall, we found the lowest relative bias occurred when using our information prior (Figures 6.2, 6.3). For the Type I function, 83% of the confidence intervals for the relative bias (where average ˆR < 1.1) overlapped zero. The percentages overlapping zero for the other priors were: log uniform (81%), functional uniform (17%), uniform (14%), and Jeffreys (13%) (Figure 6.2). For the Type II function, 92% of information prior relative bias confidence intervals overlapped zero, compared to 56% for the log uniform prior, 17% for the functional uniform prior, 3% for Jeffreys prior, and 0% for the uniform prior (Figure 6.3). Generally, relative bias decreased as the sample size (n) increased, and as the rarity decreased (i.e. as p increased) (Figures 6.2, 6.3). The effect of the CV on relative bias was less clear, but at least in the Type II setting, decreasing the CV appeared to decrease the relative bias (Figure 6.3). In terms of credible interval coverage, for the Type I function, the percentage of 95% confidence intervals for 90% credible interval coverage that covered 0.9 was 81% for the uniform prior, 52% for Jeffreys prior, 44% for the log uniform prior, 36% for the functional uniform prior, and 30% for the information prior (Figure E.2). For the Type II function, the percentages were 55% for Jeffreys prior, 44% for the uniform prior, 17% for the information prior, 14% for the log uniform prior, and 11% for the functional uniform prior (Figure E.3). Overall, estimated coverage

157 139 probability tended to monotonically approach 0.9 as n increased, however this was not the case for the log uniform and information priors in the Type I setting when p = (Figure E.2). Results for the Type III function were more mixed (Figures 6.4, E.4). None of the priors considered appeared to perform strictly better than the others in terms of relative bias. Often, high estimates of one parameter were accompanied by low estimates of the other parameter (Figure 6.4). Patterns in the relative bias estimates tended to vary greatly depending on α, although increasing p from 0.01 to 0.1 consistently reduced the relative bias (Figure 6.4). In terms of credible interval coverage, when p = 0.01, performance tended to be best when α = 2. Credible intervals tended to perform the worst when p = 0.01 and α = 1.25, particularly for α, where the coverage probability 95% confidence interval lower limit was always greater than 0.9 (Figure E.4) Case study When fitting the Type I, II, and III functions to our primary case study dataset involving the prey species Lottia asmi, we found that estimates and credible intervals for β for the Type I and II functions tended to be quite similar to each other (for each prior distribution) (Figure 6.5, Table E.2). For example, using Jeffreys prior led to an estimate of for β in both the Type I and Type II functions (Table E.2). Across priors, the difference between the highest and lowest point estimates was 15% for the Type I and 14% for the Type II functions (Table E.2). In both cases, the highest point estimate was for the uniform prior, followed by the Jeffreys prior, the information prior, the log uniform priors, and the functional uni-

158 140 form prior (Table E.2). For the Type III function, convergence was only obtained for the uniform and Jeffreys priors. Although ˆR was less than 1.1 for the functional uniform prior, posterior distribution summaries varied substantially from chain to chain, so we omit results for this prior. Of these priors, Jeffreys prior produced the higher point estimate (posterior mean) of α (28% higher) and the lower point estimate of β (64% lower) (Figure 6.5, Table E.2). Both Type III priors produced lower interval estimates for alpha of approximately 1. For each function and prior, the point estimate of each parameter was within the 95% credible interval for that parameter using the other priors, with the exception of the Type III Jeffreys prior point estimate of α, which was outside the corresponding credible interval based on the uniform prior (Table E.2). For the more commonly observed prey species Balanus glandula, all HMC chains converged. Prior sensitivity was substantially lower here. Specifically, the ranges of parameter point estimates across priors were much narrower: Type I β ( , ), Type II β ( , ), Type III β ( , ), and Type III α (1.00, 1.00). 6.4 Discussion Simulation study Our results show that for the Type I and II functions, the information prior generally performs better than other non-informative priors in terms of relative bias (Figures 6.2, 6.3). However, the performance of the information and log uniform priors is

159 141 similar in many cases, especially for the Type I function. Notably, for the Type II function, the information prior performs well across the different values of rarity (p) and coefficient of variation (CV) used in the simulation. This suggests that the generalization from the constant covariate values case is reasonable. For reference, the coefficients of variation of all the predator-prey pairs in our dataset ranged from (Nucella ostrina feeding on Lottia asmi) to (Nucella ostrina feeding on Balanus glandula) well below the value of 10 used as the upper limit in our simulations. In several cases, simulation results could not be obtained due to the failure of MCMC chains to converge. This was particularly common in the cases of the information and Jeffreys priors for the Type I function (Figure 6.2). These sampling issues are likely due to the priors involving summation over {i : x i < 1 β }. This introduces spikes in the posterior distribution at 1 x i where Y i = 1 (Figure E.5). When 1 x {i:y i =0} i Y i = 0, these spikes are not seen as the likelihood is only nonzero when β < min (equation 6.5). Even for other priors in the Type I setting, sampling was slow, possibly due to the posterior distribution being non-differentiable at these points. Direct numerical integration could be used for inference here, but must be employed carefully in simulations to ensure accuracy. Alternatively, sampling performance was improved when using the log uniform prior and this is very similar for rare events modeling since when βx i 0, the log uniform prior and information priors are approximately equivalent (Figure E.5). This can be seen by comparing the Type I and Type II point estimates in Table E.2. Moreover, the Type I and Type II likelihoods look similar in this case, so the Type II posterior distribution could be used instead as it has continuous first derivative, making it easier to sample from. While both Jeffreys prior and the functional uniform prior tended to produce substantially biased point estimates, it should be noted that neither were developed with

160 142 bias reduction in mind. For the Type I and II functions, they tended to over- and under-estimate the true parameter β respectively. The functional uniform prior has been applied to nonlinear regression before, and is considered to be well-suited to this problem as the resulting prior is not a function of the covariate values (Bornkamp, 2012). In practice, we found the functional uniform prior somewhat tricky to implement as without requiring the parameter support set to be compact, the prior may be improper and lead to an undefined posterior distribution (for example, see Table 6.1). Determining an appropriate support set for the parameter(s) is difficult since the true value of the parameter may be quite extreme, particularly in the rare events setting where the nonlinear function is likely to lie close to 0. A further complication is that while the functional uniform prior does not depend on the covariate values (by design), the distances between functions can look very different depending on how they are weighted. For example, in the Type II case, if we let x max be the maximum possible value of x, then the functional uniform prior becomes f (β) ( 1 x max + β) 1.5. Depending on xmax, the resulting distribution over the set of functions can look very different (Figure E.6). We chose to use the posterior mean rather than the posterior median as our point estimate of interest since it is more mathematically tractable to work with in these settings. However, in the Type I and Type II cases, by using an approximation for the median of a beta distribution, similar priors can be developed with the posterior median in mind (Type II case shown in Table 6.1). The median is often the preferred univariate summary for skewed distributions, and has the advantage that it always lies between equal-tailed credible interval endpoints. When working with the posterior mean, it may be useful to instead focus on highest posterior density (HPD) intervals (Hyndman, 1996). This could improve credible interval coverage probabilities in some cases. Similarly, for the Type II function, the uniform and Jef-

161 143 freys priors show very positively biased posterior means but relatively good credible interval coverage (Figure 6.3, E.3). As the posterior distributions are likely rightskewed in these cases, the posterior medians may perform better in terms of relative bias Case study Our case study analysis shows that for these data (Table E.1), the choice of prior distribution has a major effect on parameter point estimates and credible intervals (Figure 6.5, Table E.2). This means that an inappropriate prior distribution could ultimately lead to the magnitudes of species interaction strengths being incorrectly estimated, which has consequences for determining food web dynamics (Iles & Novak, 2016; Koslicki & Novak, 2016). This issue is even more likely when converting models for the proportion of predators feeding to functional response models, as uncertainty in covariates (species abundances) and handling times must also be taken into account (Wolf et al., 2017; Novak et al., 2017b). This can be done by treating proportions of predators feeding as feeding rates multiplied by handling times a connection that we have not explicitly made in our case study analysis here (Novak et al., 2017b). However, prior sensitivity declines rapidly as the number of events (e.g. proportion of predators feeding) increases. This is apparent in the results for the more commonly observed prey species Balanus glandula. Specifically, the low variability in parameter point estimates illustrates how prior sensitivity is strongly linked to the level of rarity of events.

162 Conclusion In summary, rare events nonlinear regression presents additional challenges compared to linear regression, since the mapping between parameter values and functions can be quite complicated. Here, we have conducted a systematic analysis of non-informative priors for three nonlinear function families. By considering the resulting bias of the posterior mean, we have derived two new priors that are proportional to the Fisher information and have reduced bias. For the Type II function, we have developed a general prior distribution form that unifies common noninformative priors (i.e. they are special cases of this general form). We have used this unification of prior distributions to determine the circumstances under which posterior distributions are well-defined and under which posterior means exist (Table 6.1). Our findings show that when reducing relative bias is of primary interest and events are hundreds or thousands of times less likely than non-events, conventional non-informative priors can actual encode substantial information relative to the likelihood. Possible future work includes developing low-bias prior(s) for the Type III function and multivariate functions of multiple variables and deriving approximate probability-matching priors to improve frequentist-sense performance of credible intervals (Datta & Sweeting, 2005). Low bias estimation of multivariate function parameters is relevant to our case study since predators can select from multiple prey species to consume. Thus, multi-species functional responses are substantially more realistic and do not require discarding feeding data for all but one of the prey species (Wolf et al., 2017).

163 Type I Type II Type III p(x, β) = Min(β x, 1) p(x, β) = β x 1 + β x β xα p(x, α, β) = 1 + β x α 0.75 p x Figure 6.1. Nonlinear functions that we consider in our analysis. Each function is defined on x > 0. The response p represents the proportion parameter for Bernoulli or binomial data. Parameter constraints are: β > 0 and α > 1. For each function, p(0) = 0 and p(x) 1 as x. For the Type I function, 1 β is the smallest value of x such that p(x) = 1; for the Type II function, p( 1 β ) = 1 2 ; for the Type III function, p(β α 1 ) = 1 2 and p(x) I(x > 1) as α. In our example, we consider the use of this set of functions to model predator feeding behavior (as a function of prey abundance).

164 146 p: p: p: p: 0.01 p: 0.01 p: 0.01 p: 0.1 p: 0.1 p: % CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% Information Jeffreys Uniform Log uniform Functional uniform Relative bias Sample size Figure 6.2. Type I function simulation results based on 1,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen based on the desired coefficient of variation (standard deviation divided by mean). Coefficients of variation are shown in the second row of the panel column labels. The first row shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). Within each panel, the( x-axis shows the sample size β β ) and the y-axis shows the estimated relative bias E of the posterior mean β. Error bars indicate approximate 95% confidence intervals for the mean relative bias. Open circles show cases where the average value of ˆR (across simulations) exceeded 1.1 (suggesting frequent failure of chains to converge). Each row corresponds to a different prior distribution. Points that are outside the range of the y-axis are not shown. β

165 147 p: p: p: p: 0.01 p: 0.01 p: 0.01 p: 0.1 p: 0.1 p: % CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 Relative bias 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% 20% 10% 0% 10% 20% Sample size Information Jeffreys Uniform Log uniform Functional uniform Figure 6.3. Type II function simulation results based on 5,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen based on the desired coefficient of variation (standard deviation divided by mean). Coefficients of variation are shown in the second row of the panel column labels. The first row shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). Within each panel, the( x-axis shows the sample size β β ) and the y-axis shows the estimated relative bias E of the posterior mean β. Error bars indicate approximate 95% confidence intervals for the mean relative bias. Each row corresponds to a different prior distribution. Points that are outside the range of the y-axis are not shown. β

166 148 p : 0.01 p : 0.01 p : 0.1 p : 0.1 α : 1.25 α : 2 α : 1.25 α : 2 40% Relative bias 20% 0% 20% 40% 20% 0% 20% 40% 20% 0% 20% 40% 20% 0% 20% α β α β α β α β Jeffreys Uniform Log uniform Functional uniform Figure 6.4. Type III function simulation results based on 1,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen such that the coefficient of variation equals 1. The first row of column labels shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). The second row of column labels shows( the value of α. Within each θ θ ) panel, the y-axis shows the estimated relative bias E of the posterior mean θ (where θ is α or β, as shown on the x-axis). Error bars indicate approximate 95% confidence intervals for the mean relative bias. Open circles show cases where the average value of ˆR (across simulations) exceeded 1.1 (suggesting frequent failure of chains to converge). Throughout, a sample size of n = 1,000 is used. Each row corresponds to a different prior distribution. θ

167 149 Type 1 : β Type 2 : β Functional uniform Functional uniform Log uniform Log uniform Uniform Uniform Jeffreys Jeffreys Information Information Type 3 : α Type 3 : β Uniform Uniform Jeffreys Jeffreys Posterior mean Figure 6.5. Parameter point estimates (posterior means) for the nonlinear function parameters of the Type I, Type II, and Type III functions fit to our example dataset of the proportion of Nucella ostrina individuals feeding on Lottia asmi (Table E.1). The bottom row of panels corresponds to a single function (Type III) with two parameters (α and β).

168 150 Table 6.1. Values of n y i = s for which the posterior distribution is proper (Type II i=1 function). As shown in section 6.2.7, the posterior is proper if and only if ut 1 < s < n+vt +ut 1. Values of t,u,v are not always unique. For the posterior mean to exist when the posterior is proper, we replace ut with ut 1. So, the mean exists if and only if ut 1 < s < n + vt + ut 2. The final three versions of the information prior are designed to ensure the posterior mean is proper, minimize the bias of the posterior median, and minimize the bias of the posterior mode respectively. Prior Form t u v Proper Mean Uniform s n 1 s n 2 Log uniform 1 β s n 1 s n 2 Functional uniform β s 1 s n 1 n x Jeffreys i 1 β(1+βx i ) always s n 1 Information Information - epsilon Information - median Information - mode i=1 n i=1 n i=1 n i=1 x i β(1+βx i ) s 1 s 1 x i β 1 ε (1+βx i ) ε 2 always always n i=1 x i β 2 3 (1+βx i ) always always x i (1+βx i ) s n 1 s n 2

169 151 Table 6.2. Simulation parameters for our simulations to assess the performance of sparse priors in estimating Type I, Type II, and Type III function parameters (Figure 6.1). The sample sizes, rarities (probabilities of an event), and covariate coefficients of variation (CV = σ/µ) cover a wide range, including the sample size, estimated CV, and estimated rarity for our primary example dataset (4,235, 0.358, and respectively; Table E.1). For the distribution of the covariate, we selected σlog 2 to obtain the desired CV. The parameter α applies to the Type III function only. For the Type III function, no information prior was considered, n was restricted to 1,000, p to {0.01,0.1}, and the CV to 1. Variable Value(s)/Explanation sample size (n) {100, 500, 1000, 5000} distribution of covariate lognormal with µ log = and CV = {0.1,1,10} true parameter (β) Chosen such that the rarity p = P(Y = 1) = {0.1, 0.01, 0.001} true parameter (α) prior {1.25, 2}; Type III only Information, Jeffreys, Uniform, Log uniform, Functional uniform

170 152 7 Conclusion This dissertation has considered a number of topics in predator conservation and ecology. In Chapter 2, I assessed the status of large carnivores prey, finding that a substantial portion of prey species were in decline. This analysis evidences the value of a holistic approach to carnivore conservation, wherein tools like protected areas are used to conserve both predators directly as well as the prey upon which they depend. Chapter 3 shows how the geographic ranges of large carnivore species have contracted in recent centuries. My results show that large carnivore species range contractions have been a common occurrence and that, at the global scale, cattle density, rural population density, and cropland are all associated with predator range contractions. Next, in Chapter 4, I explored potential sites for large carnivore reintroductions, identifying 130 protected areas and 150 low footprint regions where large carnivore reintroductions should be most likely to succeed. Transitioning to the development of new statistical methodology for modeling predator functional responses and feeding behavior, in Chapter 5, I showed how Type II functional response attack rate parameters can be estimated in a biologically realistic way using Bayesian statistics. Finally, in Chapter 6, I developed new prior distributions for nonlinear regression model parameter estimation that have desirable frequentist-sense relative bias, which is particularly important when modeling sparse predator feeding survey data. 7.1 Future work

171 153 The global analyses in large carnivore conservation that I have conducted (Chapters 3-5) suggest a number of possibilities for future work. The global scope of these analyses means that, when possible, they should be supported by future local-scale research. For example, the prey lists that we have presented in Chapter 4, should be validated at the scale of individual carnivore populations. A benefit of such local-scale research is that predator and prey abundances could be estimated, allowing for greater insight into the status of large carnivores prey. Local-scale research is especially badly needed for the less well-studied large carnivores species like the Clouded leopard (Neofelis nebulosa) and the Sunda clouded leopard (Neofelis diardi). Additionally, further validation of potential large carnivore reintroduction sites is needed to ensure that they are suitable. In terms of estimating functional response parameters, important future work includes generalizing the methodology that I presented for deriving low bias estimators to the Type III function and multi-species Type II function cases and unifying the Type I and Type III function priors in the same manner as the Type II function priors. Although much future work remains, I hope that the analyses presented here will contribute to both large carnivore conservation science and to efforts to understand the basic ecology of predation and food webs.

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206 APPENDICES 188

207 189 A. Supplementary Material for: Prey Depletion as a Threat to the World s Large Carnivores

208 Figure A.1. Prey endangerment maps (complete set). 190

209 191

210 Figure A.2. Prey decreasing trend maps (complete set). 192

211 Figure A.3. Prey status by continent. Status is the IUCN Red List endangerment status: DD (data deficient), LC (least concern), NT (near threatened), VU (vulnerable), EN (endangered), CR (critically endangered). 193

212 Figure A.4. Prey population trends by continent. 194

213 195 Figure A.5. Status of large carnivores preferred prey. Carnivores are ordered by decreasing percentage threatened (VU/EN/CR) prey from the top down. The numbers of preferred prey species are shown after the large carnivore names. Status is the IUCN Red List endangerment status: DD (data deficient), LC (least concern), NT (near threatened), VU (vulnerable), EN (endangered), CR (critically endangered).

214 196 Figure A.6. Population trends of large carnivores preferred prey. Carnivores are sorted by percentage of preferred prey with decreasing population trends. The numbers of preferred prey species are shown after the large carnivore names.

215 197 Figure A.7. Percentages of all 114 preferred prey species that are threatened (top) or have decreasing population trends (bottom).

216 198

217 Figure A.8. Preferred prey endangerment maps (complete set). 199

218 200

219 Figure A.9. Preferred prey decreasing trend maps (complete set). 201

220 202 Figure A.10. Major threats faced by large carnivores threatened prey. The percentages are out of all prey, including non-threatened prey. The red wolf is omitted as none of its prey are threatened.

221 203 Figure A.11. Mass and order information for each large carnivore s prey species. Results for all prey species together are shown in the bottom right panel. Masses were obtained for 360 (73%) of the 494 total prey species from Jones et al. (2009). Only orders with more than five prey species appearing in large carnivore prey lists are labeled. Carnivores are sorted top to bottom, left to right by median prey mass (indicated by vertical lines). Jones KE, Bielby J, Cardillo M, Fritz SA, O Dell J, Orme CDL, et al. PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals. Ecology Aug 17;90(9):

222 204 Figure A.12. References to prey depletion in the literature. Results shown are for the top six most cited conservation articles for each large carnivore. Each article was categorized based on whether the term prey was not mentioned ( Not mentioned ), mentioned without reference to prey status or depletion ( Prey ), or mentioned in the context of prey status/depletion ( Prey status ).

223 205 Figure A.13. Mass and order information for each large carnivore s preferred prey species. Results for all preferred prey species together are shown in the bottom right panel. Masses were obtained for 101 (89%) of the 114 total preferred prey species from Jones et al. (2009). Only orders with more than five preferred prey species appearing in large carnivore preferred prey lists are labeled. Carnivores are sorted top to bottom, left to right by median preferred prey mass (indicated by vertical lines). Jones KE, Bielby J, Cardillo M, Fritz SA, O Dell J, Orme CDL, et al. PanTHERIA: a species-level database of life history, ecology, and geography of extant and recently extinct mammals. Ecology Aug 17;90(9):

224 206 Table A.1. Diet study sources for the large carnivores. Full references are listed below the table. Whenever possible, we referenced diet meta-analyses that synthesized diet studies throughout a carnivore s range. Additional details are given in the methods section of the paper. Common Name Diet Reference(s) Cheetah (1) Gray wolf (2) Dingo (3 8) Red wolf (9) Ethiopian wolf (10) Spotted hyena (11) Dhole (12) African wild dog (13) Eurasian lynx (14 16) Sunda clouded leopard (17 21) Clouded leopard (22,23) Lion (24) Jaguar (25) Leopard (26) Tiger (27) Snow leopard (28) Puma (29) Diet references 1. Hayward MW, Hofmeyr M, O brien J, Kerley GIH. Prey preferences of the cheetah (Acinonyx jubatus)(felidae: Carnivora): morphological limitations or the need to capture rapidly consumable prey before kleptoparasites arrive? J Zool. 2006;270(4): Mech LD, Boitani L, editors. Wolves: Behavior, Ecology, and Conservation. University Of Chicago Press; p. 3. Newsome AE, Corbett LK, Catling PC, Burt RJ. The Feeding Ecology of the Dingo. 1. Stomach Contents From Trapping in South-Eastern Australia, and the Non-Target Wildlife Also Caught in Dingo Traps. Wildl Res. 1983;10(3):

225 4. Newsome TM, Ballard G-A, Fleming PJS, van de Ven R, Story GL, Dickman CR. Human-resource subsidies alter the dietary preferences of a mammalian top predator. Oecologia May;175(1): Robertshaw JD, Harden RH. The Ecology of the Dingo in North-Eastern New South Wales. 2. Diet. Wildl Res. 1985;12(1): Corbett LK, Newsome AE. The Feeding Ecology of the Dingo. III. Dietary Relationships with Widely Fluctuating Prey Populations in Arid Australia: An Hypothesis of Alternation of Predation. Oecologia Jan 1;74(2): Thomson PC. The behavioural ecology of dingoes in north-western Australia. III. Hunting and feeding behaviour, and diet. Wildl Res. 1992;19(5): Allen BL, Leung LK-P. Assessing Predation Risk to Threatened Fauna from their Prevalence in Predator Scats: Dingoes and Rodents in Arid Australia. Hayward M, editor. PLoS ONE May 1;7(5):e Dellinger J. Foraging and Spatial Ecology of Red Wolves (Canis rufus) in Northeastern North Carolina [Internet] [thesis] [cited 2014 Aug 8]. Available from: Sillero-Zubiri C, Gottelli D. Diet and Feeding Behavior of Ethiopian Wolves (Canis simensis). J Mammal May 1;76(2): Hayward MW. Prey preferences of the spotted hyaena (Crocuta crocuta) and degree of dietary overlap with the lion (Panthera leo). J Zool. 2006;270(4): Selvan KM, Veeraswami GG, Hussain SA. Dietary preference of the Asiatic wild dog (Cuon alpinus). Mamm Biol - Z Für Säugetierkd Nov;78(6): Hayward MW, O Brien J, Hofmeyr M, Kerley GI. Prey preferences of the African wild dog Lycaon pictus (Canidae: Carnivora): ecological requirements for conservation. J Mammal. 2006;87(6):

226 Nowicki P. Food habits and diet of the lynx (Lynx lynx) in Europe. J Wildl Res. 1997;2(2): Herfindal I, Linnell JDC, Odden J, Nilsen EB, Andersen R. Prey density, environmental productivity and home-range size in the Eurasian lynx (Lynx lynx). J Zool Jan;265(1): Krofel M, Huber D, Kos I. Diet of Eurasian lynx Lynx lynx in the northern Dinaric Mountains (Slovenia and Croatia): Importance of edible dormouse Glis glis as alternative prey. Acta Theriol (Warsz) Oct;56(4): Rabinowitz A, Andau P, Chai PP. The clouded leopard in Malaysian Borneo. Oryx. 1987;21(2): Gordon CH, Stewart A-ME, Meijaard E. Correspondence regarding Clouded leopards, the secretive top-carnivore of South-East Asian rainforests: their distribution, status and conservation needs in Sabah, Malaysia. BMC Ecol. 2007;7(1): Matsuda I, Tuuga A, Higashi S. Clouded leopard (Neofelis diardi) predation on proboscis monkeys (Nasalis larvatus) in Sabah, Malaysia. Primates Jul;49(3): Mohamed A, Samejima H, Wilting A. Records of five Bornean cat species from Deramakot Forest Reserve in Sabah, Malaysia. Cat News. 2009;51: Ross J, Hearn AJ, Johnson PJ, Macdonald DW. Activity patterns and temporal avoidance by prey in response to Sunda clouded leopard predation risk: Activity of Sunda clouded leopards and their prey. J Zool Jun;290(2): Grassman Jr LI, Tewes ME, Silvy NJ, Kreetiyutanont K. Ecology of three sympatric felids in a mixed evergreen forest in north-central Thailand. J Mammal. 2005;86(1): Ngoprasert D, Lynam AJ, Sukmasuang R, Tantipisanuh N, Chutipong W, Steinmetz R, et al. Occurrence of Three Felids across a Network of

227 Protected Areas in Thailand: Prey, Intraguild, and Habitat Associations. Biotropica Nov;44(6): Hayward MW, Kerley GIH. Prey preferences of the lion (Panthera leo). J Zool Nov 1;267(3): Seymour KL. Panthera onca. Mamm Species Oct 26;(340): Hayward MW, Henschel P, O brien J, Hofmeyr M, Balme G, Kerley GIH. Prey preferences of the leopard (Panthera pardus). J Zool. 2006;270(2): Hayward MW, Jędrzejewski W, Jêdrzejewska B. Prey preferences of the tiger Panthera tigris. J Zool Mar 1;286(3): Lyngdoh S, Shrotriya S, Goyal SP, Clements H, Hayward MW, Habib B. Prey Preferences of the Snow Leopard (Panthera uncia): Regional Diet Specificity Holds Global Significance for Conservation. PLoS ONE Feb 12;9(2):e Iriarte JA, Franklin WL, Johnson WE, Redford KH. Biogeographic variation of food habits and body size of the America puma. Oecologia. 1990;85(2):

228 210 Table A.2. Information on the 494 prey species in our analysis. Predators lists the predators of each prey species (using the first 2 letters of each word of the predator s common name), RLS and Trend are the IUCN Red List status (2008 or later) and population trend respectively, Mass is the mass in kg, and % in PAs is the percentage of the prey s range within protected areas. Predators for which a prey species is preferred are marked with an asterisk. Prey species Common Name Predators RLS Trend Mass % in PAs Cetartiodactyla (even-toed ungulates) Elaphodus cephalophus Tufted deer GrWo* NT Dec % Muntiacus crinifrons Black muntjac Dh*,Le VU Dec % Moschus berezovskii Chinese forest musk deer SnLe,Ti EN Dec % Cephalophus adersi Aders' duiker Le CR Dec % Bos mutus Wild yak SnLe VU Dec 0% Muntiacus puhoatensis Puhoat muntjac Dh*,Le,Ti DD Unk 0% Tragulus versicolor Silver-backed chevrotain Dh DD Dec 0% Tragulus williamsoni Williamson's chevrotain Dh DD Dec 0% Connochaetes gnou Black wildebeest Ch,SpHy LC Inc % Damaliscus pygargus Blesbok AfWiDo,Ch*,Le LC Stable % Hydropotes inermis Chinese water deer GrWo* VU Dec % Raphicerus melanotis Cape grysbok Ch LC Stable % Muntiacus reevesi Chinese muntjak Dh*,GrWo*,Le LC Dec % Boselaphus tragocamelus Nilgai Le,Ti LC Stable % Tetracerus quadricornis Chousingha Ti VU Dec % Mazama pandora Yucatan brown brocket Ja VU Dec 1% Gazella bennettii Chinkara Ti LC Stable % Moschiola indica Indian chevrotain Dh LC Unk 1% Pseudois nayaur Bharal SnLe* LC Unk % Muntiacus rooseveltorum Roosevelts' barking deer Dh*,Le,Ti DD Dec % Mazama gouazoubira Brown brocket Ja LC Dec % Capra falconeri Markhor SnLe EN Dec % Moschus chrysogaster Alpine musk deer SnLe,Ti EN Dec % Ovis orientalis Cyprian wild sheep EuLy*,GrWo*,SnLe VU Dec 1% Mazama nana Brazilian dwarf brocket Ja DD Unk % Axis axis Axis deer Dh*,GrWo*,Le,Li,Ti LC Unk %

229 Prey species Common Name Predators RLS Trend Mass % in PAs Muntiacus truongsonensis Annam black muntjac Dh*,Le,Ti DD Dec 1% Dama dama Fallow deer GrWo* LC Unk % Gazella subgutturosa Goitered gazelle SnLe VU Dec % Capreolus pygargus Eastern roe deer GrWo* LC Dec % Sus scrofa Eurasian wild pig ClLe,Dh*,GrWo*,Le,SnLe,Ti* LC Unk % Axis porcinus Hog deer ClLe,GrWo*,Ti EN Dec % Moschus cupreus Kashmir muskdeer SnLe EN Dec 2% Capreolus capreolus European roe deer EuLy*,GrWo* LC Inc % Muntiacus vaginalis Barking deer Dh*,GrWo*,Le,Ti LC Dec 2% Tragulus javanicus Java mousedeer Dh DD Unk % Philantomba maxwellii Maxwell's duiker Le LC Dec % Catagonus wagneri Chacoan peccary Pu EN Dec % Kobus megaceros Nile lechwe Ch EN Dec % Cephalophus ogilbyi Ogilby's duiker Le LC Dec % Cephalophus natalensis Natal duiker Le,SpHy LC Dec % Cephalophus niger Black duiker Le LC Dec % Muntiacus putaoensis Leaf deer Dh*,GrWo*,Le,Ti DD Dec 3% Ovis ammon Argali SnLe NT Dec % Cervus elaphus Bactrian deer EuLy*,GrWo*,Ti* LC Inc % Rusa unicolor Sambar ClLe,Dh*,GrWo*,Le,Li,SuClLe,Ti* VU Dec % Redunca fulvorufula Mountain reedbuck AfWiDo,Ch,Le,Li,SpHy LC Stable % Tragelaphus angasii Nyala AfWiDo,Ch,Le,Li,SpHy LC Stable % Cephalophus nigrifrons Black-fronted duiker Le LC Dec % Moschus moschiferus Siberian musk deer SnLe,Ti VU Dec % Cephalophus dorsalis Bay duiker Le LC Dec % Cephalophus zebra Banded duiker Le VU Dec % Alces alces Elk GrWo* LC Inc % Cephalophus silvicultor Yellow-backed duiker Le LC Dec % Tragelaphus imberbis Lesser kudu AfWiDo*,Ch,Le,Li,SpHy NT Dec % Blastocerus dichotomus Marsh deer Ja VU Dec % Tragelaphus scriptus Bushbuck AfWiDo*,Ch,Le*,Li,SpHy LC Stable % Odocoileus virginianus Key deer GrWo*,Pu*,ReWo* LC Stable % Cephalophus harveyi Harvey's duiker Le LC Dec 4% 211

230 Prey species Common Name Predators RLS Trend Mass % in PAs Philantomba monticola Blue duiker Ch,Le LC Stable % Redunca arundinum Common reedbuck AfWiDo,Ch,Le,Li,SpHy LC Stable % Rucervus duvaucelii Barasingha GrWo*,Ti* VU Dec % Cephalophus callipygus Peter's duiker Le LC Dec % Mazama temama Central american red brocket Ja DD Dec 5% Oreotragus oreotragus Klipspringer AfWiDo,Ch,Le,Li,SpHy LC Stable % Cephalophus jentinki Jentink's duiker Le EN Dec % Cephalophus rufilatus Red-flanked duiker Le LC Dec % Pudu mephistophiles Northern pudu Pu VU Dec % Sylvicapra grimmia Common duiker AfWiDo,Ch,Le*,Li,SpHy LC Stable % Redunca redunca Bohar reedbuck AfWiDo,Ch,Le,Li,SpHy LC Dec % Hyemoschus aquaticus Water chevrotain Le LC Dec % Ourebia ourebi Oribi AfWiDo,Ch,Le,Li LC Dec % Cervus nippon Shansi sika GrWo*,Ti LC Inc % Tragelaphus spekii Marshbuck Le LC Dec % Bos gaurus Gaur Dh,Ti VU Dec 5% Kobus ellipsiprymnus Waterbuck AfWiDo,Ch,Le,Li,SpHy LC Dec % Cephalophus leucogaster White-bellied duiker Le LC Dec % Phacochoerus africanus Common warthog AfWiDo,Ch,Le,Li,SpHy LC Stable % Pecari tajacu Collared peccary Ja*,Pu LC Stable % Potamochoerus larvatus Bushpig Ch,Le,Li,SpHy LC Stable % Tragelaphus strepsiceros Greater kudu AfWiDo*,Ch,Le,Li,SpHy LC Stable % Muntiacus vuquangensis Giant muntjac Dh*,Le,Ti EN Dec % Tragelaphus eurycerus Bongo Le NT Dec % Raphicerus sharpei Sharpe's grysbok AfWiDo,Ch,Le,Li,SpHy LC Stable % Cephalophus weynsi Weyn's duiker Le LC Dec 6% Muntiacus muntjak Barking deer ClLe,Dh*,Le,SuClLe,Ti LC Dec % Tragelaphus oryx Common eland AfWiDo,Ch,Le,Li,SpHy LC Stable 6% Rangifer tarandus Caribou EuLy*,GrWo* LC Stable % Alces americanus Moose GrWo* LC Stable % Rupicapra rupicapra Alpine chamois EuLy*,GrWo* LC Unk % Kobus kob Kob Li LC Dec % Odocoileus hemionus Black-tailed deer GrWo*,Pu* LC Stable % 212

231 Prey species Common Name Predators RLS Trend Mass % in PAs Mazama americana Red brocket Ja DD Unk % Syncerus caffer African buffalo AfWiDo,Ch,Le,Li*,SpHy LC Dec % Tayassu pecari White-lipped peccary Ja*,Pu VU Dec % Aepyceros melampus Black-faced impala AfWiDo*,Ch*,Le*,Li,SpHy LC Stable % Nanger granti Grant's gazelle AfWiDo,Ch*,Le,Li,SpHy LC Dec % Moschus fuscus Black musk deer SnLe,Ti EN Dec % Alcelaphus buselaphus Hartebeest AfWiDo,Ch,Le,Li,SpHy LC Dec % Hippotragus equinus Roan antelope Ch,Le,Li,SpHy LC Dec % Raphicerus campestris Steenbok AfWiDo,Ch,Le,Li,SpHy LC Stable % Muntiacus gongshanensis Gongshan muntjac Dh*,GrWo*,Le,Ti DD Dec % Naemorhedus goral Goral SnLe,Ti NT Dec % Mazama rufina Dwarf red brocket Ja VU Dec % Tragulus napu Balabac chevrotain Dh,SuClLe LC Dec % Neotragus batesi Bates' pygmy antelope Le LC Stable % Sus barbatus Bearded pig SuClLe VU Dec % Mazama bororo Small red brocket Ja VU Dec 8% Capra sibirica Asiatic ibex SnLe* LC Unk % Tragulus kanchil Lesser malay chevrotain Dh,SuClLe LC Unk 8% Mazama nemorivaga Amazonian brown brocket Ja LC Dec 9% Connochaetes taurinus Blue & white-bearded wildebeest AfWiDo,Ch,Le,Li*,SpHy LC Stable % Hemitragus jemlahicus Himalayan tahr SnLe NT Dec % Antidorcas marsupialis Springbok AfWiDo,Ch*,Le,Li,SpHy LC Inc % Moschus leucogaster Himalayan muskdeer SnLe,Ti EN Dec 10% Hippopotamus amphibius Common hippopotamus Ch,Le,Li,SpHy VU Dec % Damaliscus lunatus Tiang AfWiDo,Ch,Le,Li,SpHy LC Dec % Oryx gazella Gemsbok Ch,Le,Li*,SpHy* LC Stable % Pudu puda Chilean pudu Pu VU Dec % Eudorcas thomsonii Thomson's gazelle AfWiDo*,Ch*,Le,Li,SpHy NT Dec % Giraffa camelopardalis Giraffe Ch,Le,Li*,SpHy LC Dec % Bos javanicus Banteng Ti EN Dec % Ovis canadensis Bighorn sheep GrWo* LC Stable % Mazama chunyi Chunyi Ja VU Dec % Muntiacus montanus Sumatran mountain muntjac Dh*,Ti DD Unk 20% 213

232 Prey species Common Name Predators RLS Trend Mass % in PAs Mazama bricenii Mérida brocket Ja VU Dec % Ovibos moschatus Muskox GrWo* LC Stable % Kobus leche Southern lechwe Ch LC Stable % Oreamnos americanus Mountain goat GrWo* LC Stable % Muntiacus feae Fea's muntjac Dh*,Le,Ti DD Unk % Bison bison American bison GrWo* NT Stable % Dama mesopotamica Mesopotamian fallow deer GrWo* EN Inc 49% Cephalophus spadix Abbott's duiker Le EN Dec % Chiroptera (bats) Nyctophilus geoffroyi Lesser long-eared bat Di LC Stable 7% Cingulata (armadillos) Dasypus hybridus Southern long-nosed armadillo Ja*,Pu NT Dec % Chaetophractus vellerosus Screaming hairy armadillo Ja*,Pu LC Stable % Tolypeutes matacus Southern three-banded armadillo Ja*,Pu NT Dec % Cabassous tatouay Greater naked-tailed armadillo Ja*,Pu LC Unk % Calyptophractus retusus Burmeister's armadillo Ja*,Pu DD Unk % Chaetophractus nationi Andean hairy armadillo Ja*,Pu VU Dec % Chlamyphorus truncatus Lesser fairy armadillo Pu DD Unk % Chaetophractus villosus Large hairy armadillo Ja*,Pu LC Inc % Cabassous chacoensis Chacoan naked-tailed armadillo Ja*,Pu NT Unk % Zaedyus pichiy Pichi Pu NT Dec % Dasypus septemcinctus Brazilian lesser long-nosed armadillo Ja*,Pu LC Unk % Euphractus sexcinctus Six-banded armadillo Ja*,Pu LC Stable % Dasypus yepesi Yepes s mulita Ja*,Pu DD Unk 3% Tolypeutes tricinctus Brazilian three-banded armadillo Ja*,Pu VU Dec % Dasypus sabanicola Llanos long-nosed armadillo Ja*,Pu LC Unk % Dasypus novemcinctus Common long-nosed armadillo Ja*,Pu LC Inc % Dasypus pilosus Hairy long-nosed armadillo Ja*,Pu VU Unk % Cabassous centralis Northern naked-tailed armadillo Ja*,Pu DD Unk % Cabassous unicinctus Southern naked-tailed armadillo Ja*,Pu LC Unk % Priodontes maximus Giant armadillo Ja*,Pu VU Dec % Dasypus kappleri Greater long-nosed armadillo Ja*,Pu LC Unk % 214

233 Prey species Common Name Predators RLS Trend Mass % in PAs Dasyuromorphia (quolls and dunnarts) Sminthopsis macroura Stripe-faced dunnart Di LC Unk % Sminthopsis crassicaudata Fat-tailed dunnart Di LC Stable % Antechinus stuartii Brown antechinus Di LC Stable % Antechinus swainsonii Dusky antechinus Di LC Unk % Didelphimorphia (opossums) Marmosops handleyi Handley's slender mouse opossum Ja CR Dec % Marmosops cracens Slim-faced slender mouse opossum Ja DD Unk % Cryptonanus unduaviensis Ja DD Unk 0% Marmosops creightoni Ja DD Unk 0% Marmosops ocellatus Ja LC Stable 0% Monodelphis handleyi Handley's short-tailed opossum Ja NT Unk 0% Monodelphis maraxina Marajó short-tailed opossum Ja DD Dec 0% Philander olrogi Olrog`s four-eyed opossum Ja DD Unk 0% Tlacuatzin canescens Grayish mouse opossum Ja LC Stable % Chacodelphys formosa Ja VU Dec 0% Thylamys macrurus Long-tailed fat-tailed opossum Ja NT Dec % Thylamys pulchellus Ja LC Unk 0% Monodelphis rubida Chestnut-striped opossum Ja DD Dec % Thylamys pusillus Small fat-tailed opossum Ja LC Dec % Thylamys venustus Buff-bellied fat-tailed mouse opossum Ja DD Unk 1% Monodelphis americana Northern three-striped opossum Ja LC Dec % Monodelphis dimidiata Eastern short-tailed opossum Ja LC Stable % Monodelphis kunsi Pygmy short-tailed opossum Ja LC Stable % Thylamys velutinus Dwarf fat-tailed mouse opossum Ja LC Unk % Thylamys sponsorius Ja LC Unk 1% Monodelphis theresa Southern three-striped opossum Ja DD Dec % Didelphis virginiana Virginia opossum Ja LC Inc % Cryptonanus chacoensis Chacoan mouse opossum Ja LC Stable 1% Cryptonanus agricolai Agricola's gracile opossum Ja DD Unk 1% Didelphis albiventris White-eared opossum Ja LC Stable % Didelphis aurita Big-eared opossum Ja LC Stable % 215

234 Prey species Common Name Predators RLS Trend Mass % in PAs Marmosa constantiae Bay-colored mouse opossum Ja LC Unk 2% Philander frenatus Southeastern four-eyed opossum Ja LC Unk 2% Monodelphis domestica Gray short-tailed opossum Ja LC Stable % Marmosa paraguayanus Tate's woolly mouse opossum Ja LC Stable 2% Gracilinanus microtarsus Brazilian gracile mouse opossum Ja LC Unk % Marmosops incanus Gray slender mouse opossum Ja LC Unk % Monodelphis scalops Long-nosed short-tailed opossum Ja LC Dec % Monodelphis iheringi Ihering's short-tailed opossum Ja DD Dec % Thylamys cinderella Cinderella fat-tailed mouse opossum Ja LC Unk 2% Lutreolina crassicaudata Little water opossum Ja LC Unk % Thylamys karimii Karimi's fat-tailed mouse opossum Ja VU Dec 3% Marmosa xerophila Dryland mouse opossum Ja VU Dec % Gracilinanus agilis Agile gracile mouse opossum Ja LC Unk % Marmosa mexicana Mexican mouse opossum Ja LC Stable % Monodelphis emiliae Emilia's short-tailed opossum Ja LC Unk % Philander mcilhennyi Mcilhenny's four-eyed opossum Ja LC Unk 4% Didelphis pernigra Ja LC Stable 5% Gracilinanus marica Northern gracile mouse opossum Ja LC Dec % Marmosops bishopi Ja LC Unk 5% Caluromys philander Bare-tailed woolly opossum Ja LC Dec % Caluromys derbianus Central american woolly opossum Ja LC Dec % Philander mondolfii Mondolfi's four-eyed opossum Ja LC Unk 5% Gracilinanus emiliae Emilia's gracile mouse opossum Ja DD Unk % Marmosops paulensis Brazilian slender opossum Ja LC Unk % Gracilinanus aceramarcae Aceramarca gracile mouse opossum Ja LC Unk % Marmosa robinsoni Robinson's mouse opossum Ja LC Stable % Glironia venusta Bushy-tailed opossum Ja LC Unk % Caluromys lanatus Brown-eared wooly opossum Ja LC Dec % Marmosops juninensis Ja VU Dec 7% Chironectes minimus Water opossum Ja LC Dec % Marmosops noctivagus White-bellied slender mouse opossum Ja LC Stable % Marmosa regina Short-furred woolly mouse opossum Ja LC Stable 7% Metachirus nudicaudatus Brown four-eyed opossum Ja LC Stable % 216

235 Prey species Common Name Predators RLS Trend Mass % in PAs Marmosa rubra Red mouse opossum Ja DD Unk % Marmosops fuscatus Gray-bellied slender mouse opossum Ja DD Unk % Monodelphis adusta Sepia short-tailed opossum Ja LC Stable % Marmosa demerarae Long-furred woolly mouse opossum Ja LC Stable 8% Didelphis marsupialis Black-eared opossum Ja LC Stable % Monodelphis palliolata Hooded red-sided opossum Ja LC Unk 8% Marmosops neblina Ja LC Stable 9% Marmosops impavidus Andean slender mouse opossum Ja LC Stable % Marmosa murina Linnaeus's mouse opossum Ja LC Stable % Philander opossum Gray four-eyed opossum Ja LC Stable % Philander deltae Deltaic four-eyed opossum Ja LC Unk 10% Monodelphis glirina Amazonian red-sided opossum Ja LC Unk 10% Hyladelphys kalinowskii Kalinowski's mouse opossum Ja LC Unk 11% Marmosa lepida Little rufous mouse opossum Ja LC Stable % Monodelphis osgoodi Osgood's short-tailed opossum Ja LC Unk % Marmosa alstoni Alston's woolly mouse opossum Ja LC Stable 12% Marmosops invictus Slaty slender mouse opossum Ja LC Stable % Marmosops parvidens Delicate slender mouse opossum Ja LC Unk % Philander andersoni Anderson's four-eyed opossum Ja LC Stable % Gracilinanus dryas Wood sprite gracile mouse opossum Ja NT Dec % Marmosops pinheiroi Pinheiro's slender opossum Ja LC Unk 14% Monodelphis brevicaudata Northern red-sided opossum Ja LC Unk % Marmosa quichua Quechuan mouse opossum Ja LC Dec 20% Caluromysiops irrupta Black-shouldered opossum Ja LC Dec % Didelphis imperfecta Guianan white-eared opossum Ja LC Stable 22% Marmosa andersoni Anderson's mouse opossum Ja DD Unk % Monodelphis reigi Reig's opossum Ja VU Unk 48% Marmosa tyleriana Tyler's mouse opossum Ja DD Unk % Monodelphis ronaldi Ronald's opossum Ja LC Stable 100% Diprotodontia (diprotodonts) Macropus giganteus Eastern grey kangaroo Di LC Stable % Macropus rufus Red kangaroo Di* LC Stable % 217

236 Prey species Common Name Predators RLS Trend Mass % in PAs Macropus robustus Barrow island euro Di* LC Stable % Trichosurus vulpecula Common brushtail possum Di LC Dec % Wallabia bicolor Swamp wallaby Di* LC Inc % Petrogale rothschildi Rothschild's rock wallaby Di LC Unk % Petauroides volans Greater glider Di LC Dec % Macropus rufogriseus Bennett's wallaby Di* LC Stable % Pseudocheirus peregrinus Common ring-tailed possum Di LC Stable % Thylogale thetis Red-necked pademelon Di LC Stable % Potorous tridactylus Long-nosed potoroo Di LC Dec % Vombatus ursinus Coarse-haired wombat Di LC Stable % Macropus parma Parma wallaby Di NT Unk % Trichosurus cunninghami Mountain brushtail possum Di LC Stable NA 25% Burramys parvus Broom's pygmy-possum Di CR Dec % Lagomorpha (rabbits, hares and pikas) Lepus comus Yunnan hare GrWo*,Le,SnLe LC Unk % Lepus yarkandensis Yarkand hare GrWo*,SnLe NT Dec % Ochotona huangensis Tsing-ling pika SnLe LC Unk % Ochotona cansus Gansu pika SnLe LC Unk % Ochotona erythrotis Chinese red pika SnLe LC Unk 0% Ochotona gloveri Glover's pika SnLe LC Unk 0% Ochotona iliensis Ili pika SnLe EN Dec 0% Ochotona koslowi Koslov's pika SnLe EN Dec 0% Ochotona muliensis Muli pika SnLe DD Unk 0% Ochotona thomasi Thomas's pika SnLe LC Unk 0% Lepus tibetanus Desert hare GrWo*,SnLe LC Unk 0% Lepus sinensis Chinese hare GrWo*,Le LC Unk % Lepus oiostolus Woolly hare GrWo*,Le,SnLe LC Unk % Ochotona ladacensis Ladak pika SnLe LC Unk 0% Ochotona curzoniae Black-lipped pika SnLe LC Dec % Ochotona rufescens Afghan pika SnLe LC Stable % Ochotona himalayana Himalayan pika SnLe LC Unk 0% Ochotona pusilla Little pika SnLe LC Dec % 218

237 Prey species Common Name Predators RLS Trend Mass % in PAs Lepus coreanus Korean hare GrWo*,Le LC Unk 1% Lepus saxatilis Savannah hare Ch,Le LC Dec % Lepus habessinicus Abyssinian hare Ch,Le LC Unk % Lepus alleni Antelope jackrabbit GrWo* LC Stable % Lepus mandshuricus Manchurian hare GrWo*,Le LC Unk % Ochotona nubrica Nubra pika SnLe LC Unk 1% Lepus nigricollis Black-napped hare GrWo*,Le,SnLe LC Unk % Sylvilagus floridanus Eastern cottontail ReWo* LC Inc % Lepus granatensis Granada hare GrWo* LC Stable % Ochotona thibetana Moupin pika SnLe LC Unk 2% Sylvilagus palustris Key rabbit ReWo* LC Unk % Ochotona macrotis Large-eared pika SnLe LC Unk % Lepus capensis Arabian hare Ch,EuLy,GrWo*,Le,SnLe LC Dec % Ochotona hyperborea Northern pika SnLe LC Unk % Lepus starcki Ethiopian highland hare Ch,EtWo,Le LC Unk % Lepus europaeus Brown hare GrWo*,Le,Pu,SnLe LC Dec % Lepus timidus Arctic hare EuLy,GrWo*,Le,SnLe LC Unk % Lepus californicus Black-tailed jackrabbit GrWo* LC Stable % Lepus tolai Tolai hare Ch,GrWo*,Le,SnLe LC Unk % Lepus fagani Ethiopian hare Ch,Le DD Unk 4% Ochotona dauurica Daurian pika SnLe LC Unk % Lepus townsendii White-tailed jackrabbit GrWo* LC Dec % Lepus microtis African savanna hare Ch,Le LC Unk % Ochotona roylei Royle's pika SnLe LC Stable % Oryctolagus cuniculus European rabbit Di* NT Dec % Ochotona forresti Forrest's pika SnLe LC Dec 6% Ochotona rutila Turkestan red pika SnLe LC Stable 6% Lepus othus Alaskan hare GrWo* LC Unk % Lepus peguensis Burmese hare GrWo*,Le LC Stable % Ochotona alpina Alpine pika SnLe LC Unk % Ochotona pallasi Mongolian pika SnLe LC Dec 9% Lepus americanus Snowshoe hare GrWo* LC Stable % Lepus corsicanus Apennine hare GrWo* VU Dec 11% 219

238 Prey species Common Name Predators RLS Trend Mass % in PAs Lepus arcticus Arctic hare GrWo* LC Unk % Lepus castroviejoi Broom hare GrWo* VU Dec % Monotremata (platypus and echidnas) Tachyglossus aculeatus Kangaroo island echidna Di LC Stable % Peramelemorphia (bilbies and bandicoots) Perameles nasuta Long-nosed bandicoot Di LC Unk % Isoodon obesulus Nuyts southern brown bandicoot Di LC Dec % Perissodactyla (odd-toed ungulates) Equus grevyi Grevy's zebra AfWiDo,Ch,Li*,SpHy EN Stable % Tapirus bairdii Baird's tapir Ja EN Dec % Diceros bicornis Black rhinoceros Ch,Le,Li CR Inc % Ceratotherium simum Northern white rhinoceros Ch,Le,Li NT Inc % Tapirus terrestris Brazilian tapir Ja VU Dec % Equus zebra Hartmann's mountain zebra AfWiDo,Ch,Le,Li*,SpHy VU Unk % Equus quagga Burchell's zebra AfWiDo,Ch,Le,Li*,SpHy LC Stable % Tapirus pinchaque Andean tapir Ja EN Dec % Rhinoceros unicornis Greater one-horned rhino Ti VU Inc % Pholidota (pangolins) Manis javanica Malayan pangolin ClLe EN Dec % Primates (primates) Macaca thibetana Milne-edwards macaque Ti NT Dec % Trachypithecus francoisi Francois's langur Dh,Le EN Dec % Cercopithecus solatus Sun-tailed guenon Le VU Unk % Cercopithecus dryas Dryad monkey Le CR Unk % Macaca munzala Arunachal macaque Ti EN Dec 0% Rungwecebus kipunji Kipunji Le CR Dec 0% Semnopithecus ajax Chamba sacred langur Le EN Dec 0% Trachypithecus laotum Lao langur Dh,Le,Ti VU Dec 0% Semnopithecus dussumieri Dussumier's malabar langur Dh,Le,Ti LC Stable 0% Macaca radiata Bonnet macaque Ti LC Dec % Procolobus pennantii Bouvier's red colobus Le CR Dec 1% Papio hamadryas Hamadryas baboon Ch,Le,Li,SpHy LC Inc % 220

239 Prey species Common Name Predators RLS Trend Mass % in PAs Semnopithecus entellus Bengal hanuman langur Dh,Le,Ti LC Dec % Trachypithecus pileatus Bonneted langur Dh,Le,Ti VU Dec % Macaca mulatta Rhesus macaque SnLe,Ti LC Unk % Cercopithecus erythrogaster Red-bellied guenon Le VU Dec % Nycticebus pygmaeus Lesser slow loris ClLe VU Dec % Colobus polykomos King colobus Le VU Unk % Cercopithecus diana Diana guenon Le VU Dec % Papio papio Guinea baboon Le,Li,SpHy NT Unk % Colobus satanas Black colobus Le VU Dec % Cercopithecus mona Mona guenon Le LC Unk % Trachypithecus auratus Ebony leaf monkey Dh,Le VU Dec % Cercopithecus petaurista Lesser spot-nosed guenon Le LC Unk % Procolobus badius Bay colobus Le EN Dec 3% Trachypithecus delacouri Delacour's langur Dh,Le,Ti CR Dec 3% Macaca assamensis Assamese macaque Ti NT Dec % Semnopithecus hector Gray langur Dh,Le,Ti NT Dec 3% Cercocebus atys Red-capped monkey Le VU Dec % Trachypithecus poliocephalus Cat ba langur Dh,Le CR Dec 3% Colobus angolensis Angola colobus Le LC Unk % Cercocebus torquatus Collared mangabey Le VU Dec % Trachypithecus shortridgei Shortridge s capped langur Dh,Le,Ti EN Dec 4% Cercopithecus nictitans Greater spot-nosed guenon Le LC Dec % Cercopithecus campbelli Campbell's guenon Le LC Unk % Papio anubis Anubis baboon Ch,Le,Li,SpHy LC Inc % Cercopithecus ascanius Black-cheeked white-nosed monkey Le LC Unk % Cercopithecus cephus Moustached guenon Le LC Unk % Presbytis siamensis Pale-thighed langur Dh,Le,Ti NT Dec % Macaca silenus Lion-tailed macaque Ti EN Dec % Cercopithecus neglectus De brazza's monkey Le LC Unk % Semnopithecus schistaceus Central himalayan langur Dh,Le,Ti LC Dec 4% Papio ursinus Chacma baboon Ch,Le,Li,SpHy LC Stable % Lophocebus aterrimus Black crested mangabey Le NT Dec % Papio cynocephalus Yellow baboon Ch,Le,Li,SpHy LC Stable % 221

240 Prey species Common Name Predators RLS Trend Mass % in PAs Trachypithecus phayrei Phayre's langur Dh,Le,Ti EN Dec % Semnopithecus priam Coromandel sacred langur Dh,Le,Ti NT Dec 5% Gorilla gorilla Lowland gorilla Le CR Dec % Macaca arctoides Bear macaque Ti VU Dec % Colobus vellerosus Geoffroy's black-and-white colobus Le VU Unk % Nycticebus bengalensis Bengal loris ClLe VU Dec % Pan troglodytes Chimpanzee Le EN Dec % Lophocebus albigena Gray-cheeked mangabey Le LC Dec % Trachypithecus johnii Black leaf monkey Dh,Le,Ti VU Dec % Cercopithecus mitis Blue monkey Le LC Dec % Chlorocebus aethiops Green monkey Ch,Le LC Stable % Trachypithecus germaini Germain s langur Dh,Le,Ti EN Dec 6% Trachypithecus hatinhensis Hatinh langur Dh,Le,Ti EN Dec 6% Colobus guereza Eastern black-and-white colobus Le LC Unk % Cercopithecus pogonias Crowned guenon Le LC Unk % Nasalis larvatus Long-nosed monkey SuClLe EN Dec % Cercocebus agilis Agile mangabey Le LC Stable % Macaca fascicularis Crab-eating macaque Ti LC Dec % Presbytis comata Grizzled leaf monkey Dh,Le EN Dec % Macaca leonina Northern pig-tailed macaque Ti VU Dec 6% Trachypithecus cristatus Silvered langur Dh,Le,Ti NT Dec % Procolobus rufomitratus Eastern red colobus Le LC Dec 7% Macaca nemestrina Pig-tailed macaque Ti VU Dec % Cercocebus chrysogaster Golden-bellied mangabey Le DD Dec 7% Nycticebus coucang Greater slow loris ClLe VU Dec % Semnopithecus hypoleucos Black-footed gray langur Dh,Le,Ti VU Dec % Presbytis hosei Gray leaf monkey SuClLe VU Dec % Presbytis melalophos Mitred leaf monkey Dh,Ti EN Dec % Cercopithecus erythrotis Red-eared guenon Le VU Dec % Cercopithecus preussi Preuss's guenon Le EN Dec % Trachypithecus obscurus Dusky langur Dh,Le,Ti NT Dec % Presbytis thomasi North sumatran leaf monkey Dh,Ti VU Dec % Cercopithecus hamlyni Hamlyn s monkey Le VU Dec 13% 222

241 Prey species Common Name Predators RLS Trend Mass % in PAs Cercopithecus lhoesti L'hoest's guenon Le VU Dec % Presbytis femoralis Banded langur Dh,Le,Ti NT Dec % Cercocebus galeritus Tana river crested mangabey Le EN Dec % Trachypithecus vetulus Purple-faced langur Le EN Dec % Trachypithecus geei Gee's golden langur Dh,Le,Ti EN Dec % Procolobus gordonorum Udzungwa red colobus Le EN Dec 30% Procolobus preussi Preuss's red colobus Le CR Dec 35% Trachypithecus barbei Barbe's langur Dh,Le,Ti DD Dec 41% Cercocebus sanjei Sanje crested mangabey Le EN Dec 53% Proboscidea (elephants) Elephas maximus Asian elephant Ti EN Dec % Loxodonta africana African elephant Ch,Le,Li,SpHy VU Inc % Rodentia (rodents) Notomys aquilo Northern hopping mouse Di EN Dec % Aeretes melanopterus Groove-toothed flying squirrel SnLe NT Dec 0% Biswamoyopterus biswasi Namdapha flying squirrel SnLe CR Dec 0% Eupetaurus cinereus Woolly flying squirrel SnLe EN Unk 0% Sciurotamias davidianus Pére david's rock squirrel Le,SnLe LC Unk 0% Sciurotamias forresti Forrest's rock squirrel Le LC Unk 0% Spermophilus taurensis Le LC Unk 0% Spermophilus xanthoprymnus Asia minor ground squirrel Le NT Dec 0% Trogopterus xanthipes Complex-toothed flying squirrel SnLe NT Dec 0% Petaurista xanthotis Chinese giant flying squirrel SnLe LC Unk 0% Spermophilus ralli Tien shan ground squirrel SnLe LC Unk 0% Petaurista alborufus Red and white giant flying squirrel SnLe LC Unk % Spermophilus fulvus Yellow ground squirrel Le,SnLe LC Unk % Dremomys pernyi Perny's long-nosed squirrel SnLe LC Stable % Spermophilus pygmaeus Little ground squirrel Le LC Dec % Tamiops swinhoei Swinhoe's striped squirrel SnLe LC Stable 1% Sigmodon hispidus Hispid cotton rat ReWo LC Inc % Funambulus pennantii Five-striped palm squirrel SnLe LC Unk % Spermophilus dauricus Daurian ground squirrel Le LC Unk 1% 223

242 Prey species Common Name Predators RLS Trend Mass % in PAs Marmota himalayana Himalayan marmot Le,SnLe LC Unk 1% Callosciurus pygerythrus Hoary-bellied squirrel SnLe LC Unk 1% Spermophilopsis leptodactylus Long-clawed ground squirrel SnLe LC Unk 1% Spermophilus brevicauda Brandt's ground squirrel SnLe LC Unk 1% Spermophilus major Russet ground squirrel SnLe LC Unk 1% Spermophilus erythrogenys Red-cheeked ground squirrel SnLe LC Stable 1% Otomys typus Typical vlei rat EtWo* LC Dec 1% Spermophilus alashanicus Alashan ground squirrel Le,SnLe LC Dec 2% Pseudomys australis Plains mouse Di VU Dec % Myocastor coypus Coypu Ja LC Dec % Tamias sibiricus Siberian chipmunk Le,SnLe LC Stable % Pteromys volans Russian flying squirrel SnLe LC Dec % Callosciurus erythraeus Pallas's squirrel SnLe LC Stable % Sciurus vulgaris Eurasian red squirrel SnLe LC Dec % Dremomys lokriah Orange-bellied himalayan squirrel SnLe LC Dec % Leggadina forresti Central short-tailed mouse Di LC Unk % Petaurista philippensis Indian giant flying squirrel SnLe LC Dec % Mus musculus House mouse Di,ReWo LC Stable % Hylopetes alboniger Particolored flying squirrel SnLe LC Dec % Hystrix brachyura Himalayan crestless porcupine SuClLe LC Dec % Rattus villosissimus Long-haired rat Di LC Unk % Eoglaucomys fimbriatus Small kashmir flying squirrel SnLe LC Unk % Marmota baibacina Altai marmot SnLe LC Unk 4% Spermophilus pallidicauda Pallid ground squirrel SnLe LC Unk 4% Atherurus macrourus Asiatic brush-tailed porcupine ClLe LC Dec % Pseudomys desertor Brown desert mouse Di* LC Dec % Petaurista elegans Grey-headed flying squirrel SnLe LC Stable % Petaurista petaurista Common giant flying squirrel SnLe LC Dec % Marmota caudata Long-tailed marmot Le,SnLe LC Unk % Dremomys rufigenis Asian red-cheeked squirrel SnLe LC Stable % Belomys pearsonii Hairy-footed flying squirrel SnLe DD Unk 6% Spermophilus undulatus Long-tailed ground squirrel SnLe LC Stable % Pseudomys hermannsburgensis Sandy inland mouse Di LC Stable % 224

243 Prey species Common Name Predators RLS Trend Mass % in PAs Hydrochoerus hydrochaeris Capybara Ja*,Pu LC Unk % Ratufa bicolor Black giant squirrel SnLe NT Dec % Ondatra zibethicus Muskrat ReWo LC Stable % Castor canadensis American beaver GrWo* LC Stable % Cuniculus paca Spotted paca Ja* LC Stable % Petaurista magnificus Hodgson's giant flying squirrel SnLe LC Dec % Pedetes capensis Springhaas Ch,Le LC Unk % Marmota sibirica Mongolian marmot SnLe EN Dec 7% Alticola roylei Royle's mountain vole SnLe NT Dec % Tamiops macclellandii Himalayan striped squirrel SnLe LC Stable 7% Spermophilus relictus Tien shan ground squirrel SnLe LC Unk % Menetes berdmorei Indochinese ground squirrel ClLe LC Stable 8% Erethizon dorsatum North american porcupine Pu* LC Stable % Arvicanthis blicki Blick's grass rat EtWo* NT Unk % Petaurista nobilis Bhutan giant flying squirrel SnLe NT Dec 14% Rattus fuscipes Bush rat Di LC Stable % Spermophilus musicus Caucasian mountain ground squirrel Le NT Unk 26% Lophuromys melanonyx Black-clawed brush-furred rat EtWo* VU Unk % Marmota menzbieri Menzbier's marmot SnLe VU Dec 35% Mastacomys fuscus Broad-toothed mouse Di NT Dec % Tachyoryctes macrocephalus Giant mole rat EtWo* EN Dec % Tubulidentata (aardvark) Orycteropus afer Aardvark Le LC Unk % 225

244 Table A.3. Analysis of the six most cited conservation-related articles for each large carnivore. Articles are classified according to whether the term prey was mentioned ( Prey ) and whether prey endangerment, status or depletion was mentioned ( Status ). Only four articles were available for the Sunda clouded leopard. Species Article title Prey Status Laurenson, M. Karen. "High juvenile mortality in cheetahs (Acinonyx jubatus) and its consequences for maternal care." Journal of Zoology (1994): Y N Merola, Michele. "A reassessment of homozygosity and the case for inbreeding depression in the cheetah, Acinonyx jubatus: implications for conservation." Conservation biology 8.4 (1994): 961- Y Y 971. Hayward, M. W., et al. "Prey preferences of the cheetah (Acinonyx jubatus)(felidae: Carnivora): Cheetah morphological limitations or the need to capture rapidly consumable prey before kleptoparasites Y Y arrive?." Journal of Zoology (2006): Kelly, Marcella J., et al. "Demography of the Serengeti cheetah (Acinonyx jubatus) population: the first 25 years." Journal of Zoology (1998): Y Y Crooks, Kevin R., M. A. Sanjayan, and Daniel F. Doak. "New insights on cheetah conservation through demographic modeling." Conservation Biology 12.4 (1998): Y Y Durant, Sarah M. "Predator avoidance, breeding experience and reproductive success in endangered cheetahs, Acinonyx jubatus." Animal behaviour 60.1 (2000): Y N Mladenoff, David J., et al. "A regional landscape analysis and prediction of favorable gray wolf habitat in the northern Great Lakes region." Conservation Biology 9.2 (1995): Y Y Vilà, Carles, et al. "Rescue of a severely bottlenecked wolf (Canis lupus) population by a single immigrant." Proceedings of the Royal Society of London B: Biological Sciences (2003): 91- Y N 97. Gray wolf Vilà, Carles, et al. "Mitochondrial DNA phylogeography and population history of the grey wolf N N Canis lupus." Molecular Ecology 8.12 (1999): Mladenoff, David J., Theodore A. Sickley, and Adrian P. Wydeven. "Predicting gray wolf landscape recolonization: logistic regression models vs. new field data." Ecological Applications 9.1 (1999): Y Y 226

245 227 Species Article title Prey Status Wayne, R. K., et al. "Conservation genetics of the endangered Isle Royale gray wolf." Conservation Biology 5.1 (1991): N N Liberg, Olof, et al. "Severe inbreeding depression in a wild wolf Canis lupus population." Biology letters 1.1 (2005): Y N Glen, Al S., et al. "Evaluating the role of the dingo as a trophic regulator in Australian ecosystems." Austral Ecology 32.5 (2007): Y N Letnic, Mike, Euan G. Ritchie, and Christopher R. Dickman. "Top predators as biodiversity regulators: the dingo Canis lupus dingo as a case study." Biological Reviews 87.2 (2012): Y N Daniels, Mike J., and Laurie Corbett. "Redefining introgressed protected mammals: when is a wildcat a wild cat and a dingo a wild dog?." Wildlife Research 30.3 (2003): Y N Dingo Dickman, Chris R., Alistair S. Glen, and Mike Letnic. "Reintroducing the dingo: can Australia s conservation wastelands be restored." Reintroduction of top-order predators 7 (2009): 238. Y N Allen, Benjamin L., Richard M. Engeman, and Lee R. Allen. "Wild Dogma: An Examination Of Recent" Evidence" For Dingo Regulation Of Invasive Mesopredator Release In Australia." (2011). Y N Elledge, Amanda E., et al. "An evaluation of genetic analyses, skull morphology and visual appearance for assessing dingo purity: implications for dingo conservation." Wildlife Research 35.8 (2009): N N Kalinowski, Steven T., Philip W. Hedrick, and Philip S. Miller. "No inbreeding depression observed in Mexican and red wolf captive breeding programs." Conservation biology 13.6 (1999): N N Miller, Craig R., Jennifer R. Adams, and Lisette P. Waits. "Pedigree based assignment tests for reversing coyote (Canis latrans) introgression into the wild red wolf (Canis rufus) population." Molecular Ecology (2003): N N Red wolf Phillips, Michael K., V. Gary Henry, and Brian T. Kelly. "Restoration of the red wolf." (2003). Y Y Bohling, Justin H., and Lisette P. Waits. "Assessing the prevalence of hybridization between sympatric Canis species surrounding the red wolf (Canis rufus) recovery area in North Carolina." Y N Molecular Ecology (2011): Brownlow, C. Alexander. "Molecular taxonomy and the conservation of the red wolf and other endangered carnivores." Conservation Biology 10.2 (1996): N N

246 228 Species Article title Prey Status Kennerly, Erin, et al. "A gene expression signature of confinement in peripheral blood of red wolves (Canis rufus)." Molecular Ecology (2008): N N Gottelli, Dada, et al. "Molecular genetics of the most endangered canid: the Ethiopian wolf Canis simensis." Molecular Ecology 3.4 (1994): Y N Sillero-Zubiri, C., A. A. King, and D. W. Macdonald. "Rabies and mortality in Ethiopian wolves (Canis simensis)." Journal of Wildlife Diseases 32.1 (1996): N N Haydon, D. T., M. K. Laurenson, and C. Sillero Zubiri. "Integrating epidemiology into population viability analysis: managing the risk posed by rabies and canine distemper to the Ethiopian wolf." N N Conservation Biology 16.5 (2002): Ethiopian Gottelli, Dada, et al. "The effect of the last glacial age on speciation and population genetic wolf structure of the endangered Ethiopian wolf (Canis simensis)." Molecular Ecology 13.8 (2004): Y Y Marino, J., C. Sillero Zubiri, and D. W. Macdonald. "Trends, dynamics and resilience of an Ethiopian wolf population." Animal Conservation 9.1 (2006): Y Y Sillero-Zubiri, C., F. H. Tattersall, and D. W. Macdonald. "Habitat selection and daily activity of giant molerats Tachyoryctes macrocephalus: significance to the Ethiopian wolf Canis simensis in the Afroalpine ecosystem." Biological Conservation 72.1 (1995): Y Y Hayward, Matt W., and Gina J. Hayward. "Activity patterns of reintroduced lion Panthera leo and spotted hyaena Crocuta crocuta in the Addo Elephant National Park, South Africa." African journal Y N of ecology 45.2 (2007): Spotted hyena Yirga, Gidey, et al. "Adaptability of large carnivores to changing anthropogenic food sources: diet change of spotted hyena (Crocuta crocuta) during Christian fasting period in northern Ethiopia." Journal of Animal Ecology 81.5 (2012): Holekamp, Kay E., and Stephanie M. Dloniak. "Intraspecific variation in the behavioral ecology of a tropical carnivore, the spotted hyena." Advances in the Study of Behavior 42 (2010): Abay, Gidey Yirga, et al. "Peri-urban spotted hyena (Crocuta crocuta) in northern Ethiopia: diet, economic impact, and abundance." European Journal of Wildlife Research 57.4 (2011): Y Y Y Y Y Y

247 229 Species Article title Prey Status Yirga, Gidey, et al. "Spotted hyena (Crocuta crocuta) coexisting at high density with people in Wukro district, northern Ethiopia." Mammalian Biology-Zeitschrift für Säugetierkunde 78.3 (2013): Y Y Bout, Nicolas, Céline Born, and Colin Spohr. "Evidence that the spotted hyena is present in the rainforest-savannah mosaic of south-east Gabon." Mammalian Biology-Zeitschrift für Säugetierkunde 75.2 (2010): Y Y Iyengar, Ararti, et al. "Phylogeography, genetic structure, and diversity in the dhole (Cuon alpinus)." Molecular Ecology 14.8 (2005): Y Y Volodina, Elena V., et al. "Biphonation may function to enhance individual recognition in the dhole, Cuon alpinus." Ethology (2006): Y N Dhole Borah, Jimmy, et al. "Food habits of dholes (Cuon alpinus) in Satpura Tiger Reserve, Madhya Pradesh, India." Mammalia 73.2 (2009): Y Y Kamler, Jan F., et al. "The diet, prey selection, and activity of dholes (Cuon alpinus) in northern Laos." Journal of Mammalogy 93.3 (2012): Y Y Jenks, Kate E., et al. "Mapping the distribution of dholes, Cuon alpinus (Canidae, Carnivora), in Thailand." mammalia 76.2 (2012): Y Y Srivathsa, Arjun, et al. "On a dhole trail: examining ecological and anthropogenic correlates of dhole habitat occupancy in the Western Ghats of India." PloS one 9.6 (2014): e Y Y Girman, Derek J., et al. "A molecular genetic analysis of social structure, dispersal, and interpack relationships of the African wild dog (Lycaon pictus)." Behavioral Ecology and Sociobiology 40.3 N N (1997): Courchamp, Franck, and David W. Macdonald. "Crucial importance of pack size in the African wild African wild dog Lycaon pictus." Animal Conservation 4.02 (2001): Y N dog Monfort, S. L., et al. "Evaluating adrenal activity in African wild dogs (Lycaon pictus) by fecal corticosteroid analysis." Journal of Zoo and Wildlife Medicine (1998): N N Lindsey, Peter A., Johan T. Du Toit, and M. G. L. Mills. "Attitudes of ranchers towards African wild dogs Lycaon pictus: conservation implications on private land." Biological Conservation (2005): Y Y

248 230 Species Article title Prey Status Gusset, M., et al. "Human wildlife conflict in northern Botswana: livestock predation by Endangered African wild dog Lycaon pictus and other carnivores." Oryx (2009): Y N Creel, Scott, and Nancy Marusha Creel. "Six ecological factors that may limit African wild dogs, Lycaon pictus." Animal Conservation 1.01 (1998): 1-9. Y N KRAMER SCHADT, S. T. E. P. H. A. N. I. E., et al. "Fragmented landscapes, road mortality and patch connectivity: modelling influences on the dispersal of Eurasian lynx." Journal of Applied Ecology Y N 41.4 (2004): Schadt, Stephanie, et al. "Assessing the suitability of central European landscapes for the reintroduction of Eurasian lynx." Journal of Applied Ecology 39.2 (2002): Y N Herfindal, Ivar, et al. "Prey density, environmental productivity and home-range size in the Eurasian Eurasian Y N lynx (Lynx lynx)." Journal of Zoology (2005): lynx Schadt, Stephanie, et al. "Rule-based assessment of suitable habitat and patch connectivity for the Y N Eurasian lynx." Ecological Applications 12.5 (2002): Gaona, Pilar, Pablo Ferreras, and Miguel Delibes. "Dynamics and viability of a metapopulation of the endangered Iberian lynx (Lynx pardinus)." Ecological monographs 68.3 (1998): Y N Breitenmoser, Urs, et al. "Spatial organization and recruitment of lynx (Lynx lynx) in a re introduced population in the Swiss Jura Mountains." Journal of Zoology (1993): Y N Wilting, Andreas, et al. "Density of the Vulnerable Sunda clouded leopard Neofelis diardi in two commercial forest reserves in Sabah, Malaysian Borneo." Oryx (2012): N N Brodie, Jedediah, and Anthony J. Giordano. "Density of the Vulnerable Sunda clouded leopard Sunda Neofelis diardi in a protected area in Sabah, Malaysian Borneo." Oryx (2012): N N clouded leopard Christiansen, Per. "Species distinction and evolutionary differences in the clouded leopard (Neofelis nebulosa) and Diard's clouded leopard (Neofelis diardi)." Journal of Mammalogy 89.6 (2008): Y N Sollmann, Rahel, et al. "Bringing clarity to the clouded leopard Neofelis diardi: first density estimates from Sumatra." Oryx (2014): Y N Clouded leopard Kitchener, Andrew C., Mark A. Beaumont, and Douglas Richardson. "Geographical variation in the clouded leopard, Neofelis nebulosa, reveals two species." Current Biology (2006): N N

249 231 Species Article title Prey Status Howard, JoGayle, et al. "Successful ovulation induction and laparoscopic intrauterine artificial insemination in the clouded leopard (Neofelis nebulosa)." Zoo Biology 15.1 (1996): N N Austin, Sean C., et al. "Ecology and conservation of the leopard cat Prionailurus bengalensis and clouded leopard Neofelis nebulosa in Khao Yai National Park, Thailand." (2007): N N Christiansen, Per. "Species distinction and evolutionary differences in the clouded leopard (Neofelis nebulosa) and Diard's clouded leopard (Neofelis diardi)." Journal of Mammalogy 89.6 (2008): Y N Borah, Jimmy, et al. "Abundance and density estimates for common leopard Panthera pardus and clouded leopard Neofelis nebulosa in Manas National Park, Assam, India." Oryx (2014): 149- Y N 155. Mohamad, Shariff Wan, et al. "The first description of population density and habitat use of the mainland clouded leopard Neofelis nebulosa within a logged-primary forest in South East Asia." Population Ecology 57.3 (2015): Y N Loveridge, A. J., et al. "The impact of sport-hunting on the population dynamics of an African lion population in a protected area." Biological Conservation (2007): Y Y Saberwal, Vasant K., et al. "Lion human conflict in the Gir Forest, India." Conservation Biology 8.2 (1994): Y Y Lion Bauer, H., and S. Van Der Merwe. "Inventory of free-ranging lions Panthera leo in Africa." Oryx (2004): Y N Packer, Craig, et al. "Conservation biology: lion attacks on humans in Tanzania." Nature (2005): Y Y Packer, C., et al. "Effects of trophy hunting on lion and leopard populations in Tanzania." Conservation Biology 25.1 (2011): Y Y CREEL, SCOTT, and NANCY CREEL. "Lion density and population structure in the Selous Game Reserve: evaluation of hunting quotas and offtake." African Journal of Ecology 35.2 (1997): Y N Jaguar Silver, Scott C., et al. "The use of camera traps for estimating jaguar Panthera onca abundance and density using capture/recapture analysis." Oryx (2004): Y Y Sanderson, Eric W., et al. "Planning to save a species: the jaguar as a model." Conservation Biology 16.1 (2002): Y Y

250 232 Species Article title Prey Status Eizirik, Eduardo, et al. "Phylogeography, population history and conservation genetics of jaguars (Panthera onca, Mammalia, Felidae)." Molecular Ecology 10.1 (2001): Y N Maffei, Leonardo, Erika Cuéllar, and Andrew Noss. "One thousand jaguars (Panthera onca) in Bolivia's Chaco? Camera trapping in the Kaa Iya National Park." Journal of Zoology (2004): Y N Rabinowitz, Alan, and Kathy A. Zeller. "A range-wide model of landscape connectivity and conservation for the jaguar, Panthera onca." Biological conservation (2010): Y N Conforti, Valeria Amorim, and Fernando Cesar Cascelli de Azevedo. "Local perceptions of jaguars (Panthera onca) and pumas (Puma concolor) in the Iguacu National Park area, south Brazil." Y Y Biological Conservation (2003): Hayward, M. W., et al. "Prey preferences of the leopard (Panthera pardus)." Journal of Zoology (2006): Y Y Balme, Guy, Luke Hunter, and Rob Slotow. "Feeding habitat selection by hunting leopards Panthera pardus in a woodland savanna: prey catchability versus abundance." Animal Behaviour 74.3 (2007): Y Y Ramakrishnan, Uma, Richard G. Coss, and Neil W. Pelkey. "Tiger decline caused by the reduction of large ungulate prey: evidence from a study of leopard diets in southern India." Biological Y Y Leopard Conservation 89.2 (1999): Packer, C., et al. "Effects of trophy hunting on lion and leopard populations in Tanzania." Conservation Biology 25.1 (2011): Y Y Miththapala, Sriyanie, John Seidensticker, and Stephen J. O'Brien. "Phylogeographic subspecies recognition in leopards (Panthera pardus): molecular genetic variation." Conservation Biology 10.4 N N (1996): Marker, L. L., and A. J. Dickman. "Factors affecting leopard () spatial ecology, with particular reference to Namibian farmlands." South African Journal of Wildlife Research 35.2 (2005): Y Y Tiger Karanth, K. Ullas, and James D. Nichols. "Estimation of tiger densities in India using photographic captures and recaptures." Ecology 79.8 (1998): Y Y

251 233 Species Article title Prey Status O'Brien, Timothy G., Margaret F. Kinnaird, and Hariyo T. Wibisono. "Crouching tigers, hidden prey: Sumatran tiger and prey populations in a tropical forest landscape." Animal Conservation 6.02 Y Y (2003): Karanth, K. Ullas, et al. "Assessing tiger population dynamics using photographic capture-recapture sampling." Ecology (2006): Y Y Luo, Shu-Jin, et al. "Phylogeography and genetic ancestry of tigers (Panthera tigris)." PLoS Biol 2.12 (2004): e442. N N Linkie, Matthew, et al. "Assessing the viability of tiger subpopulations in a fragmented landscape." Journal of Applied Ecology 43.3 (2006): Y Y Wikramanayake, Eric D., et al. "An ecology based method for defining priorities for large mammal conservation: the tiger as case study." Conservation Biology 12.4 (1998): Y Y Mishra, Charudutt, et al. "The role of incentive programs in conserving the snow leopard." Conservation Biology 17.6 (2003): Y Y Oli, Madan K., Iain R. Taylor, and M. Elizabeth Rogers. "Snow leopard Panthera uncia predation of livestock: an assessment of local perceptions in the Annapurna Conservation Area, Nepal." Biological Conservation 68.1 (1994): Y Y Snow leopard Jackson, Rodney M., et al. "Estimating Snow Leopard Population Abundance Using Photography and Capture Recapture Techniques." Wildlife Society Bulletin 34.3 (2006): Y N Bagchi, S., and C. Mishra. "Living with large carnivores: predation on livestock by the snow leopard (Uncia uncia)." Journal of Zoology (2006): Y Y Oli, M. K., I. R. Taylor, and D. ME Rogers. "Diet of the snow leopard (Panthera uncia) in the Annapurna Conservation Area, Nepal." Journal of Zoology (1993): Y N Lovari, S., et al. "Restoring a keystone predator may endanger a prey species in a human altered ecosystem: the return of the snow leopard to Sagarmatha National Park." Animal Conservation 12.6 (2009): Y Y Puma Kelly, Marcella J., et al. "Estimating puma densities from camera trapping across three study sites: Bolivia, Argentina, and Belize." Journal of Mammalogy 89.2 (2008): Y Y Franklin, William L., et al. "Ecology of the Patagonia puma Felis concolor patagonica in southern Chile." Biological Conservation 90.1 (1999): Y N

252 234 Species Article title Prey Status Conforti, Valeria Amorim, and Fernando Cesar Cascelli de Azevedo. "Local perceptions of jaguars (Panthera onca) and pumas (Puma concolor) in the Iguacu National Park area, south Brazil." Y Y Biological Conservation (2003): Ernest, Holly B., et al. "Genetic structure of mountain lion (Puma concolor) populations in California." Conservation Genetics 4.3 (2003): Y Y Novack, Anthony J., et al. "Foraging ecology of jaguar (Panthera onca) and puma (Puma concolor) in hunted and non-hunted sites within the Maya Biosphere Reserve, Guatemala." Journal of Zoology Y Y (2005): Palmeira, Francesca BL, et al. "Cattle depredation by puma (Puma concolor) and jaguar (Panthera onca) in central-western Brazil." Biological conservation (2008): Y N

253 235 B. Supplementary Material for: Range Contractions of the World s Large Carnivores Figure B.1. Predictor variables used in the model for predicting range contractions. For the rural population and cattle density variables, the values were log transformed (after adding 1). All variables were then scaled to have average 0 and standard deviation 1 so that their effects on the likelihood of range contraction can be compared on the same scale.

254 236 Figure B.2. Percentage range contraction versus carnivore body mass. Overall, percentage range contraction does not appear to be closely linked to either carnivore species mass or taxonomic family.

255 237 Figure B.3. Current and historic species richness histograms by biome. Vertical lines indicate mean richness. Panels are sorted by difference in mean richness and indicate that the most extensive range contractions occurred in Flooded Grasslands & Savannas and in Topical & Subtropical Dry Broadleaf Forests. Overlap between current and historic range histogram bars is shown in dark purple.

256 238 Figure B.4. Results for a generalized linear mixed model predicting the increase in the odds of range contraction per one standard deviation increase in each predictor variable while accounting for the other variables (estimates shown with 95% confidence intervals). The p-values for all coefficients were significant (< ). To account for potential dependence the model includes random intercepts by species along with a spatial autocovariate constructed using the residuals of the corresponding non-spatial model.

257 239 Figure B.5. Effects of cattle density, cropland, and rural population on the odds of species range contraction by region of the world based on a spatially explicit generalized linear mixed model with random slopes (and intercepts) by geographic region and random intercepts by species. The panels show the estimated increases in the odds of range contraction per one standard deviation increase in each predictor variable (with 95% prediction intervals). All predictor variables were included together in the model. These results show substantial variation by geographic region in terms of the estimated effect sizes.

258 240 Table B.1. Sources of the historic range maps used in our analysis. Elevation limits (lower and upper) are in meters. Modifications to the source maps are listed in the footnotes. Scientific Name Common Name Map source Lower Upper Acinonyx jubatus Cheetah Morrison et al. (2007) 4000 Canis lupus Gray wolf Morrison et al. (2007) Canis lupus dingo Dingo Letnic et al. (2012) Canis rufus Red wolf Morrison et al. (2007) 2400 Canis simensis Ethiopian wolf Ray et al. (2005) Crocuta crocuta Spotted hyena Ray et al. (2005) 4100 Cuon alpinus Dhole IUCN canid action plan Helarctos malayanus Sun bear Morrison et al. (2007) 2100 Parahyaena brunnea Brown hyena Ray et al. (2005) Hyaena hyaena Striped hyena Morrison et al. (2007) 3300 Lycaon pictus African wild dog Ray et al. (2005) 4000 Lynx lynx Eurasian lynx IUCN felid action plan Melursus ursinus Sloth bear Morrison et al. (2007) 2000 Neofelis diardi Sunda clouded leopard File:Clouded_leopard_prevalence.png Neofelis nebulosa Clouded leopard Clouded_leopard_historic_prevalence.png Panthera leo Lion Morrison et al. (2007) 4200 Panthera onca Jaguar Panthera 3000 Panthera pardus Leopard Morrison et al. (2007) 5200 Panthera tigris Tiger Panthera 4500 Panthera uncia Snow leopard Morrison et al. (2007) Puma concolor Puma Panthera 5800 Tremarctos ornatus Andean black bear Morrison et al. (2007) Ursus americanus American black bear Morrison et al. (2007) Ursus arctos Brown bear Morrison et al. (2007) 5000 Ursus thibetanus Asiatic black bear Morrison et al. (2007) Added Japan, Sakhalin island (above Japan), and the corner of northeastern Russia 2 Extended a bit northward on the basis of the current IUCN Red List fact sheet and input from Jan Kamler 3 Elevation limit from the Animal Diversity Web (Myers et al. 2015) 4 Only for Europe (treated historic range in Asia as matching the current range, reviewed by Bodil Elmhagen) 5 Clipped northern portion of historic range to match with current range

259 241 Table B.2. Summary data for large carnivore range contractions. Historic, current, and lost range areas are in square kilometers. % Lost is the estimated percentage range contraction. Scientific Name Common Name Historic Current Lost % Lost Canis rufus Red wolf 2,205,755 5,771 2,199, % Canis simensis Ethiopian wolf 888,157 6, , % Panthera tigris Tiger 16,622, ,646 15,841, % Panthera leo Lion 26,914,341 1,703,935 25,210, % Lycaon pictus African wild dog 18,924,058 1,278,603 17,645, % Acinonyx jubatus Cheetah 34,997,842 2,964,276 32,033, % Cuon alpinus Dhole 19,321,239 3,396,114 15,925, % Panthera pardus Leopard 41,990,824 8,647,609 33,343, % Panthera uncia Snow leopard 5,440,630 1,216,226 4,224, % Tremarctos ornatus Andean black bear 1,190, , , % Neofelis nebulosa Clouded leopard 4,950,609 1,798,205 3,152, % Ursus thibetanus Asiatic black bear 8,645,920 3,142,301 5,503, % Neofelis diardi Sunda clouded leopard 1,184, , , % Helarctos malayanus Sun bear 3,285,879 1,628,906 1,656, % Panthera onca Jaguar 17,774,713 8,818,148 8,956, % Ursus arctos Brown bear 46,588,688 26,891,864 19,696, % Melursus ursinus Sloth bear 2,481,079 1,518, , % Ursus americanus American black bear 15,829,679 9,714,012 6,115, % Puma concolor Puma 31,259,847 21,240,084 10,019, % Parahyaena brunnea Brown hyena 2,876,377 2,093, , % Canis lupus Gray wolf 64,169,543 47,702,213 16,467, % Crocuta crocuta Spotted hyena 19,146,204 14,541,846 4,604, % Hyaena hyaena Striped hyena 27,675,695 23,510,432 4,165, % Canis lupus dingo Dingo 7,641,425 6,713, , % Lynx lynx Eurasian lynx 23,163,633 20,424,410 2,739, %

260 242 C. Supplementary Material for: Rewilding the World s Large Carnivores Figure C.1. The six largest contiguous low footprint regions inside the lost (historic minus current) ranges of each large carnivore species. Low footprint regions were defined using the bottom 10% threshold for each species. For each carnivore species, variables shown are the mean human footprint across the protected area, the region of the world, and whether or not the large carnivore guild becomes complete following reintroduction of the carnivore species.

261 243 Figure (set) C.2. Potential sites for reintroducing large carnivores. The first panel in each figure shows the six largest strictly protected areas within the large carnivore species lost range (i.e. where the species has been extirpated). The second panel shows the six largest low footprint regions within the lost range of the species. Low footprint regions were determined based on contiguous regions within the last of the wild regions for each large carnivore species lost range. Last of the wild regions are those in the bottom 10% for human footprint within each species lost range. Legends correspond to both low footprint regions (region IDs are given before the semicolons) and protected areas (names are given after the semicolons). In both cases, the areas are sorted by geographic area from largest to smallest. For example, for the African wild dog, the largest protected area (shown in red; left map) is Namib-Naukluft and the largest low footprint region (also shown in red; right map) is region number 1. Circles are drawn around small areas to make them more visible.

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286 268 Figure C.3. All strictly (category I-III) protected areas inside the lost (historic minus current) ranges of each large carnivore species (without any manual validation). For each carnivore species, variables shown are the mean human footprint across the protected area and the region of the world. There are a total of 3,470 protected areas shown here. The species for which we identified the most protected areas were the gray wolf (n = 509), puma (n = 435), leopard (n = 353), dhole (n = 341), and tiger (n = 338), while the fewest protected areas were identified for the red wolf (n = 3), brown hyena (n = 7), Ethiopian wolf (n = 10), spotted hyena (n = 11), and Andean black bear (n = 16) (Figure S1). More than 100 protected areas were found in each of the world s major geographic regions: Africa (n = 196), the Americas (n = 652), Asia (excluding South-Eastern Asia) (n = 3,41), Europe (n = 269), Oceania (n = 193), and South-Eastern Asia (n = 261).

287 269 Figure C.4. All contiguous low footprint regions inside the lost (historic minus current) ranges of each large carnivore species. Low footprint regions were defined using the bottom 10% threshold for each species. For each carnivore species, variables shown are the mean human footprint across the protected area and the region of the world. A total of 22,234 low footprint regions were identified. The species for which we identified the most low footprint regions were the gray wolf (n = 3,544), brown bear (n = 2,366), American black bear (n = 1,987), Eurasian lynx (n = 1,884), and leopard (n = 1,825), while the fewest regions were identified for the spotted hyena (n = 96), snow leopard (n = 151), Andean black bear (n = 162), Ethiopian wolf (n = 165), and sloth bear (n = 184). Low footprint regions were found throughout the world: Africa (n = 4,833), the Americas (n = 8,507), Asia (excluding South-Eastern Asia) (n = 3,490), Europe (n = 2,725), Oceania (n = 476), and South-Eastern Asia (n = 2,203).

288 Table C.1. Photo credits for the images used in Figure 4.1. Scientific Name Common Name Credit License URL Canis lupus Gray wolf John and Karen Hollingsworth/USFWS Attribution 2.0 Generic (CC BY 2.0) Canis lupus dingo Dingo Paul Balfe Attribution 2.0 Generic (CC BY 2.0) Canis rufus Red wolf B. Crawford/USFWS Attribution 2.0 Generic (CC 2003 BY 2.0) Canis simensis Ethiopian wolf Stuart Orford Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Cuon alpinus Dhole Ozzy Delaney Attribution 2.0 Generic (CC BY 2.0) Lycaon pictus African wild dog Derek Keats Attribution 2.0 Generic (CC BY 2.0) Acinonyx jubatus Cheetah Thomas Hawk Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0) Lynx lynx Eurasian lynx dogrando Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Neofelis diardi Sunda clouded leopard Spencer Wright Attribution 2.0 Generic (CC BY 2.0) Neofelis nebulosa Clouded leopard Charles Barilleaux Attribution 2.0 Generic (CC BY 2.0) Panthera leo Lion Mathias Appel CC0 1.0 Universal (CC0 1.0) Public Domain Dedication Panthera onca Jaguar Eric Kilby Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Panthera pardus Leopard Hamish Irvine Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0) Panthera tigris Tiger thedigme Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0) Panthera uncia Snow leopard pipilongstockings Attribution 2.0 Generic (CC BY 2.0) Puma concolor Puma Green Fire Attribution-ShareAlike 2.0 Productions Generic (CC BY-SA 2.0) Crocuta crocuta Spotted hyena Paul Mannix Attribution 2.0 Generic (CC BY 2.0) Hyaena brunnea Brown hyena Bernard DUPONT Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0)

289 271 Scientific Name Common Name Credit License URL Hyaena hyaena Striped hyena Eric Kilby Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Helarctos malayanus Sun bear Mark Dumont Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0) Melursus ursinus Sloth bear Shannon Kringen Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Tremarctos ornatus Andean black bear Nigel Swales Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0) Ursus americanus American black bear Jethro Taylor Attribution-NonCommercial 2.0 Generic (CC BY-NC 2.0) Ursus arctos Brown bear Gregory "Slobirdr" Attribution-ShareAlike 2.0 Smith Generic (CC BY-SA 2.0) Ursus thibetanus Asiatic black bear flowcomm Attribution 2.0 Generic (CC BY 2.0)

290 Table C.2. The 25 largest category I-III protected areas in the lost (historic minus current) ranges of each large carnivore species. The columns are: Species (species common name), Protected area (protected area name), Cat (IUCN protected area category indicating level of protection), Area (terrestrial area of the protected area in km 2 ), FP (mean human footprint across the protected area), % FP (percentage of protected area within the bottom 10% of species lost range for human footprint), Near (distance to nearest category I-III protected area in km), Country (primary country for the protected area), Guild (if true, rewilding the species there would result in a complete large carnivore guild), Prey (preferred prey species of the predator that are present in the protected area), # Prey (number of preferred prey species present in the protected area), Total (total number of preferred prey species identified for the large carnivore), and Status (if available, specifies the status of the large carnivore in the protected area i.e., whether it is present, absent, or its status is unknown). Where applicable, the source website for the status data and notes for the status entry are given as footnotes. Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Gray wolf Vindelfjällen Ib % 0 Sweden TRUE Lepus timidus,capreolus 4 51 Absent 6 capreolus,cervus elaphus,alces alces Gray wolf Taman Negara II % 113 Malaysia FALSE Sus scrofa,rusa unicolor 2 51 Unknown Gray wolf Lenya II % 0 Myanmar FALSE Muntiacus vaginalis,lepus 4 51 Unknown peguensis,sus scrofa,rusa unicolor Gray wolf Thungyai Naresuan Ia % 0 Thailand TRUE Muntiacus vaginalis,lepus 4 51 Unknown peguensis,sus scrofa,rusa unicolor Gray wolf Olympic II % 30 United States FALSE Castor canadensis,lepus 4 51 Absent 7 of America americanus,odocoileus hemionus,oreamnos americanus Gray wolf Tanintharyi National II % 0 Myanmar TRUE Muntiacus vaginalis,lepus 4 51 Unknown Park peguensis,sus scrofa,rusa unicolor Gray wolf Hardangervidda II % 10 Norway FALSE Lepus timidus,rangifer 5 51 tarandus,capreolus capreolus,cervus elaphus,alces alces Gray wolf Virachey II % 0 Cambodia FALSE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Riding Mountain II % 45 Canada FALSE Castor canadensis,lepus

291 273 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status National Park of Canada americanus,lepus townsendii,odocoileus virginianus,alces alces Gray wolf Kaengkrachan Forest II % 0 Thailand TRUE Muntiacus vaginalis,lepus 4 51 Complex peguensis,sus scrofa,rusa unicolor Gray wolf Kaldoaivin erämaa Ib % 20 Finland TRUE Lepus timidus,alces alces 2 51 Gray wolf Sjaunja Ia % 0 Sweden TRUE Lepus timidus,capreolus 3 51 capreolus,alces alces Gray wolf Huai Kha Khaeng Ia % 0 Thailand TRUE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Um Phang Ia % 0 Thailand TRUE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Saltfjellet-Svartisen II % 0 Norway FALSE Lepus timidus,capreolus 4 51 capreolus,cervus elaphus,alces alces Gray wolf Doi Phukha II % 0 Thailand FALSE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Khuen Si Nakarin II % 0 Thailand TRUE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Hammastunturin Ib % 25 Finland TRUE Lepus timidus,alces alces 2 51 erämaa Gray wolf Varangerhalvøya II % 0 Norway TRUE Lepus timidus,alces alces 2 51 Gray wolf Sanjay II % 67 India FALSE Muntiacus vaginalis,lepus 5 51 nigricollis,sus scrofa,axis axis,rusa unicolor Gray wolf Chiang Dao Ia % 0 Thailand FALSE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Alaungdaw II % 68 Myanmar FALSE Muntiacus vaginalis,lepus 4 51 peguensis,sus scrofa,rusa unicolor Gray wolf Phu Khiew Ia % 0 Thailand FALSE Muntiacus vaginalis,lepus 5 51 peguensis,sus scrofa,axis porcinus,rusa unicolor Gray wolf Paistunturin erämaa Ib % 25 Finland TRUE Lepus timidus,alces alces 2 51 Gray wolf Kishtwar II % 52 India FALSE Lepus capensis 1 51 Dingo Cape Arid II % 0 Australia TRUE Oryctolagus cuniculus 1 6 Absent 8 Dingo Grampians II % 10 Australia TRUE Macropus rufogriseus,wallabia 3 6 Absent 9 bicolor,oryctolagus cuniculus Dingo Mungo II % 0 Australia TRUE Macropus robustus,macropus 3 6 Absent 8 rufus,oryctolagus cuniculus Dingo Stirling Range II % 0 Australia TRUE Oryctolagus cuniculus 1 6 Absent 8 8 Letnic et al. map ; probably absent -- current map appears highly accurate 9

292 274 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Dingo Yathong Ia % 0 Australia TRUE Macropus robustus,macropus 3 6 Absent 8 rufus,oryctolagus cuniculus Dingo Great Otway II % 0 Australia TRUE Macropus rufogriseus,wallabia 3 6 Absent 8 bicolor,oryctolagus cuniculus Dingo Nombinnie Ia % 0 Australia TRUE Macropus robustus,macropus 3 6 rufus,oryctolagus cuniculus Dingo Hincks Ib % 25 Australia TRUE Macropus robustus,oryctolagus 2 6 cuniculus Dingo Beekeepers Ia % 0 Australia TRUE Macropus robustus,oryctolagus 2 6 cuniculus Dingo Gundabooka II % 0 Australia TRUE Macropus robustus,macropus 4 6 rufus,wallabia bicolor,oryctolagus cuniculus Dingo Billiatt Ib % 7 Australia TRUE Macropus rufus,oryctolagus 2 6 cuniculus Dingo Mallee Cliffs Ia % 39 Australia TRUE Macropus robustus,macropus 3 6 rufus,oryctolagus cuniculus Dingo Tone-Perup Ia % 0 Australia TRUE Oryctolagus cuniculus 1 6 Dingo Goonoo II % 0 Australia TRUE Macropus robustus,macropus 4 6 rufogriseus,wallabia bicolor,oryctolagus cuniculus Dingo Toorale II % 0 Australia TRUE Macropus robustus,macropus 4 6 rufus,wallabia bicolor,oryctolagus cuniculus Dingo Wandana Ia % 15 Australia TRUE Macropus robustus,macropus 3 6 rufus,oryctolagus cuniculus Dingo Murrumbidgee Valley II % 0 Australia TRUE Macropus robustus,macropus 4 6 rufus,wallabia bicolor,oryctolagus cuniculus Dingo Wandoo II % 5 Australia TRUE Oryctolagus cuniculus 1 6 Dingo Nombinnie II % 0 Australia TRUE Macropus robustus,macropus 3 6 rufus,oryctolagus cuniculus Dingo Goobang II % 10 Australia TRUE Macropus robustus,macropus 4 6 rufogriseus,wallabia bicolor,oryctolagus cuniculus Dingo Lane Poole Reserve II % 0 Australia TRUE Oryctolagus cuniculus 1 6 Dingo Ravine des Casoars Ib % 0 Australia TRUE 0 6 Dingo Murray Valley II % 0 Australia TRUE Wallabia bicolor,oryctolagus 2 6 cuniculus Dingo Hambidge Ib % 22 Australia TRUE Macropus robustus,oryctolagus 2 6 cuniculus Dingo Pilliga West II % 0 Australia TRUE Macropus robustus,macropus rufogriseus,macropus rufus,wallabia bicolor,oryctolagus cuniculus 5 6

293 275 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Red wolf Everglades Ib % 0 United States TRUE Sylvilagus floridanus,sylvilagus 3 3 Absent 10 of America palustris,odocoileus virginianus Red wolf Biscayne II % 0 United States FALSE 0 3 Unknown of America Red wolf Collier-Seminole II % 11 United States TRUE Sylvilagus floridanus,sylvilagus 3 3 Unknown of America palustris,odocoileus virginianus Ethiopian wolf Boma II % 0 South Sudan TRUE 0 4 Unknown Ethiopian wolf Gambella II % 14 Ethiopia FALSE 0 4 Unknown Ethiopian wolf Boma Extension II % 0 South Sudan TRUE 0 4 Unknown Ethiopian wolf Omo II % 15 Ethiopia TRUE Otomys typus 1 4 Unknown 11 Ethiopian wolf Yangudi Rassa II % 214 Ethiopia FALSE 0 4 Unknown Ethiopian wolf Yabello II % 103 Ethiopia FALSE 0 4 Unknown Ethiopian wolf Abijatta-Shalla Lakes II % 83 Ethiopia FALSE Otomys typus 1 4 Ethiopian wolf Mago II % 15 Ethiopia TRUE 0 4 Ethiopian wolf Nechisar II % 103 Ethiopia FALSE Otomys typus 1 4 Ethiopian wolf Awash II % 181 Ethiopia FALSE Otomys typus 1 4 Dhole Great Gobi Ia % 15 Mongolia TRUE 0 15 Unknown Dhole Gobi Gurvansaikhan II % 21 Mongolia TRUE 0 15 Unknown range Dhole Tajik National Park II % 50 Tajikistan FALSE Sus scrofa 1 15 Unknown Dhole Gobiin baga /A/, /B/ Ib % 60 Mongolia FALSE 0 15 Unknown Dhole Khan Khentii Ib % 0 Mongolia TRUE Sus scrofa 1 15 Unknown Dhole Khuvsgul II % 0 Mongolia TRUE Sus scrofa 1 15 Unknown Dhole Khangai nuruu II % 0 Mongolia FALSE Sus scrofa 1 15 Dhole Tengis-Shishged II % 0 Mongolia TRUE Sus scrofa 1 15 Dhole Har Us Nuur II % 40 Mongolia FALSE Sus scrofa 1 15 Dhole Altai Tavan range II % 18 Mongolia FALSE Sus scrofa 1 15 Dhole Issyk-Kul Ia % 10 Kyrgyzstan FALSE Sus scrofa 1 15 Dhole Zed-Khantai-Buteeliin Ia % 64 Mongolia FALSE Sus scrofa 1 15 nuruu Dhole Tarvagatai nuruu II % 0 Mongolia FALSE Sus scrofa 1 15 Dhole Eastern Mongolian Ib % 208 Mongolia FALSE 0 15 Steppe Dhole Munkhkhairkhan uul- II % 25 Mongolia TRUE Sus scrofa 1 15 Uenchiin khavtsal Dhole Uvs Nuur Basin Ia % 34 Mongolia FALSE Sus scrofa urce=bl&ots=qjlfyi5yju&sig=x-

294 276 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Dhole Ulaan Taiga Ib % 0 Mongolia FALSE Sus scrofa 1 15 Dhole Shorsky II % 27 Russian FALSE 0 15 Federation Dhole Lenya II % 0 Myanmar FALSE Muntiacus vaginalis,muntiacus 4 15 feae,sus scrofa,rusa unicolor Dhole Bureinsky Ia % 42 Russian FALSE Sus scrofa 1 15 Federation Dhole Khan Khukhii- II % 14 Mongolia FALSE 0 15 Khyragas Lake Dhole Khunjerab II % 103 Pakistan FALSE 0 15 Dhole Azas Ia % 0 Russian TRUE 0 15 Federation Dhole Numrug Ib % 250 Mongolia FALSE Sus scrofa 1 15 Dhole Ele Alatau II % 0 Kazakhstan FALSE Sus scrofa 1 15 African wild dog Namib-Naukluft II % 122 Namibia FALSE Tragelaphus strepsiceros 1 5 Absent 12 African wild dog Gemsbok Ib % 190 Botswana TRUE Tragelaphus strepsiceros 1 5 Unknown 13 African wild dog Etosha II % 110 Namibia TRUE Tragelaphus strepsiceros,aepyceros 2 5 Unknown 14 melampus African wild dog Skeleton Coast Park II % 0 Namibia TRUE Aepyceros melampus 1 5 Unknown African wild dog National Park Iona II % 0 Angola TRUE Tragelaphus strepsiceros,aepyceros 2 5 Absent 15 melampus African wild dog National Park Cameia II % 195 Angola FALSE Tragelaphus scriptus 1 5 Unknown &source=bl&ots=gclh1yts0m&sig=lac6vn2lb9gbpao8pasa_ynnzyq&hl=en&sa=x&ved=0ahukewjzkpznz5duahuh02mkhfuydr4q6aeinz AF#v=onepage&q=african%20%22wild%20dog%22%20%22gemsbok%20national%20park%22&f=false ; reintroduction attempted 14 &source=bl&ots=gclh1yts0m&sig=lac6vn2lb9gbpao8pasa_ynnzyq&hl=en&sa=x&ved=0ahukewjzkpznz5duahuh02mkhfuydr4q6aeinz AF#v=onepage&q=african%20%22wild%20dog%22%20%22gemsbok%20national%20park%22&f=false ; 3 failed reintroduction attempts 15 DUO0F&sig=mjMLBHHFmAs1U3KubdUCuaOTDVM&hl=en&sa=X&ved=0ahUKEwjl3Nrbj9LUAhXmyFQKHYXfDm0Q6AEINzAF#v=onepage&q=af rican%20wild%20dog%20national%20park%20iona&f=false ; May have been to dry to have historically supported this species 16 ; May have been to dry to have historically supported this species

295 277 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status African wild dog Upemba II % 10 Democratic FALSE Tragelaphus scriptus 1 5 Republic of the Congo African wild dog Serengeti II % 0 United TRUE Tragelaphus scriptus,tragelaphus 5 5 Republic of Tanzania imberbis,tragelaphus strepsiceros,aepyceros melampus,eudorcas thomsonii African wild dog National Park Quiçama II % 240 Angola FALSE Tragelaphus scriptus 1 5 African wild dog Kundelungu II % 10 Democratic Republic of the Congo African wild dog Virunga II % 55 Democratic Republic of the Congo FALSE Tragelaphus scriptus,tragelaphus strepsiceros 2 5 FALSE Tragelaphus scriptus 1 5 African wild dog National Park Bicuar II % 14 Angola FALSE Tragelaphus strepsiceros 1 5 African wild dog Kahuzi-Biega II % 92 Democratic FALSE Tragelaphus scriptus 1 5 Republic of the Congo African wild dog Bomu Ib % 28 Democratic FALSE Tragelaphus scriptus 1 5 Republic of the Congo African wild dog W (Benin) II % 0 Benin TRUE Tragelaphus scriptus 1 5 African wild dog Gambella II % 14 Ethiopia FALSE Tragelaphus scriptus 1 5 African wild dog National Park II % 131 Angola FALSE Tragelaphus scriptus 1 5 Mavinga African wild dog Banc d'arguin II % 34 Mauritania FALSE 0 5 African wild dog National Park Mupa II % 14 Angola FALSE Tragelaphus strepsiceros 1 5 African wild dog Garamba II % 0 Democratic FALSE Tragelaphus scriptus 1 5 Republic of the Congo African wild dog Mole II % 62 Ghana FALSE Tragelaphus scriptus 1 5 African wild dog Ai-Ais Hot Springs II % 135 Namibia FALSE Tragelaphus strepsiceros 1 5 African wild dog Mbam et Djerem II % 67 Cameroon FALSE Tragelaphus scriptus 1 5 African wild dog Bomu II % 28 Democratic FALSE Tragelaphus scriptus 1 5 Republic of the Congo African wild dog Conkouati-Douli II % 553 Congo FALSE Tragelaphus scriptus 1 5 Cheetah Niassa II % 243 Mozambique TRUE Aepyceros melampus 1 5 Unknown 17 Cheetah Dakhla National Park II % 34 Morocco FALSE 0 5 Unknown Cheetah National Park Cameia II % 195 Angola FALSE 0 5 Present ; May not have historically occurred here

296 278 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Cheetah Upemba II % 10 Democratic FALSE 0 5 Present 19 Republic of the Congo Cheetah 'Uruq Bani Ma'arid II % 391 Saudi Arabia FALSE 0 5 Unknown Cheetah At-Tubayq III % 139 Saudi Arabia FALSE 0 5 Unknown Cheetah South Luangwa II % 10 Zambia TRUE Aepyceros melampus 1 5 Present 20 Cheetah National Park II % 240 Angola FALSE 0 5 Unknown 21 Quiçama Cheetah Dinder II % 181 Sudan TRUE 0 5 Present 22 Cheetah Niokolo Koba II % 0 Senegal TRUE 0 5 Present 23 Cheetah Kundelungu II % 10 Democratic FALSE 0 5 Present 24 Republic of the Congo Cheetah Virunga II % 55 Democratic FALSE 0 5 Present 25 Republic of the Congo Cheetah National Park Bicuar II % 14 Angola FALSE 0 5 Present 26 Cheetah Bomu Ib % 28 Democratic FALSE 0 5 Unknown Republic of the Congo Cheetah Kainji Lake II % 85 Nigeria TRUE 0 5 Cheetah National Park II % 131 Angola FALSE 0 5 Mavinga Cheetah Banc d'arguin II % 34 Mauritania FALSE 0 5 Cheetah National Park Mupa II % 14 Angola FALSE 0 5 Cheetah Kaplangurskiy Ia % 199 Turkmenistan FALSE 0 5 Cheetah Garamba II % 0 Democratic FALSE 0 5 Republic of the Congo Cheetah Wadi El-Gemal - II % 325 Egypt FALSE ; seen here in ; might be incorrectly listed as present for advertising reasons

297 279 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Hamata Cheetah North Luangwa II % 10 Zambia TRUE Aepyceros melampus 1 5 Cheetah Mole II % 62 Ghana FALSE 0 5 Cheetah Jabal Samhan Nature II % 271 Oman TRUE 0 5 Reserve Cheetah Urumieh lake II % 53 Iran (Islamic FALSE 0 5 Republic of) Eurasian lynx Podolskie Tovtry II % 0 Ukraine FALSE Capreolus capreolus,cervus elaphus 2 5 Unknown Eurasian lynx Parco nazionale del II % 0 Italy FALSE Capreolus capreolus 1 5 Unknown Pollino Eurasian lynx Parco nazionale del II % 59 Italy FALSE 0 5 Unknown Cilento e Vallo di Diano Eurasian lynx Parco nazionale dello II % 0 Italy FALSE Rupicapra rupicapra,capreolus 3 5 Present 27 Stelvio capreolus,cervus elaphus Eurasian lynx Parco nazionale del II % 90 Italy FALSE Capreolus capreolus 1 5 Absent 28 Gargano Eurasian lynx Rila II % 85 Bulgaria TRUE Rupicapra rupicapra,capreolus 3 5 Unknown capreolus,cervus elaphus Eurasian lynx Parco nazionale della II % 32 Italy FALSE Capreolus capreolus,cervus elaphus 2 5 Unknown 29 Sila Eurasian lynx Parco nazionale del II % 78 Italy FALSE Rupicapra rupicapra,capreolus 3 5 Gran Paradiso capreolus,cervus elaphus Eurasian lynx Parco nazionale dei II % 83 Italy TRUE Capreolus capreolus 1 5 Monti Sibillini Eurasian lynx Parco nazionale II % 0 Italy FALSE Capreolus capreolus 1 5 dell'appennino Lucano-Val d'agri- Lagonegrese Eurasian lynx Mercantour II % 93 France FALSE Rupicapra rupicapra,capreolus 2 5 capreolus Eurasian lynx Parco nazionale II % 72 Italy FALSE Capreolus capreolus 1 5 dell'aspromonte Eurasian lynx Hohe Tauern II % 0 Austria FALSE Rupicapra rupicapra,capreolus 3 5 capreolus,cervus elaphus Eurasian lynx Parco nazionale Abruzzo, Lazio e II % 83 Italy TRUE Capreolus capreolus,cervus elaphus

298 280 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Molise Eurasian lynx Kiskunsági II % 95 Hungary FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx Pyrénées II % 144 France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx Hohe Tauern II % 0 Austria FALSE Rupicapra rupicapra,capreolus 3 5 capreolus,cervus elaphus Eurasian lynx Bükki II % 145 Hungary FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx Aukstaitijos II % 40 Lithuania FALSE Capreolus capreolus,cervus elaphus 2 5 nacionalinis parkas Eurasian lynx Parco nazionale delle II % 112 Italy FALSE Capreolus capreolus,cervus elaphus 2 5 Foreste Casentinesi, Monte Falterona e Campigna Eurasian lynx Parco nazionale delle II % 60 Italy FALSE Rupicapra rupicapra,capreolus 3 5 Dolomiti Bellunesi capreolus,cervus elaphus Eurasian lynx Galichica II % 0 The former TRUE Capreolus capreolus 1 5 Yugoslav Republic of Macedonia Eurasian lynx Ferto-Hansági II % 55 Hungary FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx Eurasian lynx Sunda clouded leopard Sunda clouded leopard Sunda clouded leopard Sunda clouded leopard Sunda clouded leopard Sunda clouded leopard Parco nazionale dell'appennino Tosco-Emiliano Zemaitijos nacionalinis parkas II % 43 Italy FALSE Rupicapra rupicapra,capreolus capreolus,cervus elaphus 3 5 II % 54 Lithuania FALSE Capreolus capreolus,cervus elaphus 2 5 Muara Kendawangan Ia % 115 Indonesia TRUE 0 0 Unknown Danau Sentarum II % 30 Indonesia TRUE 0 0 Present 30 Way Kambas II % 127 Indonesia FALSE 0 0 Present 31 Gunung Nyiut Ia % 66 Indonesia TRUE 0 0 Unknown Penrissen Tesso Nilo II % 51 Indonesia TRUE 0 0 Present 32 Teluk Kelumpang Selat Laut Selat Sebuku Ia % 21 Indonesia TRUE 0 0 Unknown Sunda clouded Bukit Dua Belas II % 60 Indonesia FALSE 0 0 Present

299 281 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status leopard Sunda clouded Teluk Apar Ia % 20 Indonesia TRUE 0 0 Unknown leopard Sunda clouded Kepulauan Karimata Ib % 58 Indonesia TRUE 0 0 Unknown leopard Sunda clouded Teluk Pamukan Ia % 21 Indonesia TRUE 0 0 Unknown leopard Sunda clouded Bidu-Bidu Ia % 5 Malaysia TRUE 0 0 leopard Sunda clouded Mount Pock Ia % 15 Malaysia FALSE 0 0 leopard Sunda clouded Timbun Mata Ia % 15 Malaysia FALSE 0 0 leopard Sunda clouded Gomantong Ia % 5 Malaysia TRUE 0 0 leopard Sunda clouded Dolok Sibual-buali Ia % 5 Indonesia TRUE 0 0 leopard Sunda clouded Pin-Supu Ia % 5 Malaysia TRUE 0 0 leopard Sunda clouded Gunung Raya Passi Ia % 66 Indonesia TRUE 0 0 leopard Sunda clouded Lubuk Raya Ia % 5 Indonesia TRUE 0 0 leopard Sunda clouded Mandor III % 74 Indonesia TRUE 0 0 leopard Clouded leopard Doi Phukha II % 0 Thailand FALSE 0 0 Unknown Clouded leopard Sri Lanna II % 0 Thailand FALSE 0 0 Present 34 Clouded leopard Preah Monivong II % 10 Cambodia FALSE 0 0 Present 35 (Bokor) Clouded leopard Doi Luang II % 0 Thailand FALSE 0 0 Unknown Clouded leopard Khao Bantad Ia % 0 Thailand FALSE 0 0 Unknown Clouded leopard Tham Phathai II % 0 Thailand FALSE 0 0 Unknown Clouded leopard Mae Tuen Ia % 0 Thailand FALSE 0 0 Unknown Clouded leopard Huai Nam Dang II % 0 Thailand FALSE 0 0 Unknown Clouded leopard Phong Nha-Ke Bang II % 63 Viet Nam FALSE 0 0 Clouded leopard Om Koi Ia % 0 Thailand FALSE 0 0 Clouded leopard Lum Nam Pai Ia % 0 Thailand FALSE 0 0 Clouded leopard Mae Charim II % 0 Thailand FALSE 0 0 Clouded leopard Natma Taung II % 68 Myanmar FALSE

300 282 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Clouded leopard Yok Don II % 60 Viet Nam FALSE 0 0 Clouded leopard Mae Ping II % 0 Thailand FALSE 0 0 Clouded leopard Lam Nam Nan II % 0 Thailand FALSE 0 0 Clouded leopard Yushan II % 25 Taiwan, TRUE 0 0 Province of China Clouded leopard Si Nan II % 0 Thailand FALSE 0 0 Clouded leopard Mae Tho II % 0 Thailand FALSE 0 0 Clouded leopard Namtok Phacharoen II % 0 Thailand FALSE 0 0 Clouded leopard Taroko II % 0 Taiwan, TRUE 0 0 Province of China Clouded leopard Salak Phra Ia % 0 Thailand FALSE 0 0 Clouded leopard Bardia II % 0 Nepal FALSE 0 0 Clouded leopard Doi Phunang II % 0 Thailand FALSE 0 0 Clouded leopard Nunthaburi II % 0 Thailand FALSE 0 0 Lion Parc Culturel du II % 924 Algeria TRUE 0 7 Unknown Tassili (Illizi) Lion Namib-Naukluft II % 122 Namibia FALSE Oryx gazella,equus zebra,giraffa 3 7 Absent 36 camelopardalis Lion Dakhla National Park II % 34 Morocco FALSE 0 7 Unknown Lion National Park Cameia II % 195 Angola FALSE 0 7 Absent 37 Lion Odzala Kokoua II % 65 Congo TRUE Syncerus caffer 1 7 Unknown 38 Lion Upemba II % 10 Democratic FALSE Syncerus caffer,equus quagga 2 7 Present 39 Republic of the Congo Lion Badingilo II % 0 South Sudan TRUE Syncerus caffer,giraffa 2 7 Present 40 camelopardalis Lion National Park II % 240 Angola FALSE Syncerus caffer 1 7 Present 41 Quiçama Lion Kundelungu II % 10 Democratic Republic of the FALSE 0 7 Present ; Source may be inaccurate here. We were not able to find additional verification

301 283 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Congo Lion Badingilo Extension II % 0 South Sudan TRUE Syncerus caffer,giraffa 2 7 Unknown camelopardalis Lion National Park Bicuar II % 14 Angola FALSE Connochaetes taurinus 1 7 Lion Kahuzi-Biega II % 92 Democratic FALSE Syncerus caffer 1 7 Republic of the Congo Lion Gashaka-Gumti II % 0 Nigeria TRUE Syncerus caffer 1 7 Lion National Park II % 131 Angola FALSE Syncerus caffer,equus 4 7 Mavinga quagga,connochaetes taurinus,giraffa camelopardalis Lion Banc d'arguin II % 34 Mauritania FALSE 0 7 Lion National Park Mupa II % 14 Angola FALSE Connochaetes taurinus 1 7 Lion Wadi El-Gemal - II % 325 Egypt FALSE 0 7 Hamata Lion Mole II % 62 Ghana FALSE Syncerus caffer 1 7 Lion Kavir II % 100 Iran (Islamic FALSE 0 7 Republic of) Lion Urumieh lake II % 53 Iran (Islamic FALSE 0 7 Republic of) Lion Ai-Ais Hot Springs II % 135 Namibia FALSE Oryx gazella,equus zebra,giraffa 3 7 camelopardalis Lion Mbam et Djerem II % 67 Cameroon FALSE Syncerus caffer 1 7 Lion Conkouati-Douli II % 553 Congo FALSE Syncerus caffer 1 7 Lion Cross River II % 0 Nigeria FALSE Syncerus caffer 1 7 Lion Nki II % 20 Cameroon TRUE Syncerus caffer 1 7 Jaguar Juruena II % 0 Brazil TRUE Hydrochoerus 8 22 Present 43 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Mapinguari II % 0 Brazil TRUE Hydrochoerus 8 22 Unknown hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Maicuru Ia % 0 Brazil TRUE Hydrochoerus hydrochaeris,priodontes 9 22 Present

302 284 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Campos Amazônicos II % 0 Brazil TRUE Hydrochoerus 8 22 Unknown 45 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Pacaás Novos II % 18 Brazil TRUE Hydrochoerus 8 22 Unknown 46 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar La Payunia Ia % 67 Argentina TRUE Chaetophractus villosus 1 22 Unknown Jaguar Guaporé Ia % 18 Brazil TRUE Hydrochoerus 8 22 Unknown hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Rio Novo II % 78 Brazil TRUE Hydrochoerus 9 22 Unknown hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Serra do Pardo II % 0 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Campos Amazonicos National park 46 Pacaás Novos National park

303 285 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Jaguar Rio Trombetas Ia % 110 Brazil TRUE Hydrochoerus 9 22 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Jaru Ia % 30 Brazil TRUE Hydrochoerus 8 22 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Nascentes da Serra Ia % 57 Brazil TRUE Hydrochoerus 9 22 do Cachimbo hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Serra da Cutia II % 15 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca 8 22 Jaguar Grande Sertão Veredas II % 22 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,tolypeutes tricinctus,cabassous tatouay,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Igarapés do Juruena II % 0 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Sumapaz II % 40 Colombia TRUE Pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca

304 286 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Jaguar Iquê Ia % 255 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Talampaya II % 5 Argentina TRUE Cabassous 3 22 chacoensis,chaetophractus villosus,chaetophractus vellerosus Jaguar Guajará-Mirim II % 10 Brazil TRUE Hydrochoerus 8 22 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Serra da Canastra II % 170 Brazil TRUE Hydrochoerus hydrochaeris,priodontes maximus,cabassous tatouay,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus paca,euphractus sexcinctus Jaguar Laguna del Diamante II % 36 Argentina TRUE Chaetophractus villosus 1 22 Jaguar Cuniã Ia % 21 Brazil TRUE Hydrochoerus 8 22 hydrochaeris,priodontes maximus,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus kappleri,dasypus novemcinctus,cuniculus paca Jaguar Nevado Del Huila II % 0 Colombia TRUE Pecari tajacu,dasypus 4 22 kappleri,dasypus novemcinctus,cuniculus paca Jaguar Catatumbo - Bari II % 0 Colombia TRUE Cabassous centralis,pecari 4 22 tajacu,dasypus novemcinctus,cuniculus paca Jaguar Veredas do Oeste Baiano III % 60 Brazil TRUE Hydrochoerus hydrochaeris,tolypeutes tricinctus,cabassous tatouay,cabassous unicinctus,pecari tajacu,tayassu pecari,dasypus novemcinctus,dasypus septemcinctus,cuniculus 10 22

305 287 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status paca,euphractus sexcinctus Leopard Dakhla National Park II % 34 Morocco FALSE 0 3 Unknown Leopard At-Tubayq III % 139 Saudi Arabia FALSE 0 3 Present 47 Leopard Banc d'arguin II % 34 Mauritania FALSE 0 3 Unknown Leopard Wadi El-Gemal - II % 325 Egypt FALSE 0 3 Absent 48 Hamata Leopard Urumieh lake II % 53 Iran (Islamic FALSE 0 3 Unknown Republic of) Leopard Khakaborazi II % 242 Myanmar FALSE 0 3 Unknown Leopard Virachey II % 0 Cambodia FALSE 0 3 Absent 49 Leopard Cross River II % 0 Nigeria FALSE Tragelaphus scriptus 1 3 Leopard Liuwa Plain II % 131 Zambia TRUE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Kirthar II % 76 Pakistan FALSE 0 3 Leopard Al Wusta Wildlife II % 271 Oman FALSE 0 3 Reserve Leopard Digya II % 40 Ghana FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Desert II % 263 India FALSE 0 3 Leopard Taba III % 85 Egypt FALSE 0 3 Leopard Old Oyo II % 85 Nigeria FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Yangambi Ia % 215 Democratic TRUE 0 3 Republic of the Congo Leopard Parc W Niger II % 0 Niger FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Fazao-Malfakassa II % 103 Togo FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Yankari II % 216 Nigeria FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Doi Phukha II % 0 Thailand FALSE 0 3 Leopard Bui II % 62 Ghana FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Shambe II % 106 South Sudan FALSE Sylvicapra grimmia,tragelaphus 2 3 scriptus Leopard Chiang Dao Ia % 0 Thailand FALSE 0 3 Leopard Hingol II % 65 Pakistan FALSE 0 3 Leopard Phu Khiew Ia % 0 Thailand FALSE

306 288 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Tiger Sinyaya II % 5 Russian TRUE 0 4 Unknown Federation Tiger Olekminsky Ia % 161 Russian TRUE 0 4 Unknown Federation Tiger Dzhugdzhursky Ia % 202 Russian TRUE 0 4 Unknown Federation Tiger Ugam-Chatkal II % 0 Uzbekistan TRUE Sus scrofa 1 4 Unknown Tiger Altai Tavan range II % 18 Mongolia FALSE Sus scrofa 1 4 Unknown Tiger Issyk-Kul Ia % 10 Kyrgyzstan FALSE Sus scrofa 1 4 Unknown Tiger Lenskie stolby II % 5 Russian TRUE 0 4 Federation Tiger Urumieh lake II % 53 Iran (Islamic FALSE Sus scrofa 1 4 Republic of) Tiger Khakaborazi II % 242 Myanmar FALSE Sus scrofa,rusa unicolor 2 4 Tiger Shorsky II % 27 Russian FALSE 0 4 Federation Tiger Shey-Phoksundo II % 35 Nepal FALSE Sus scrofa,rusa unicolor 2 4 Tiger Bureinsky Ia % 42 Russian FALSE Sus scrofa 1 4 Federation Tiger Virachey II % 0 Cambodia FALSE Sus scrofa,rusa unicolor 2 4 Tiger Ele Alatau II % 0 Kazakhstan FALSE Sus scrofa 1 4 Tiger Norsky Ia % 261 Russian FALSE 0 4 Federation Tiger Altun Emel II % 45 Kazakhstan FALSE Sus scrofa 1 4 Tiger Doi Phukha II % 0 Thailand FALSE Sus scrofa,rusa unicolor 2 4 Tiger Khangchendzonga II % 29 India TRUE Sus scrofa,rusa unicolor 2 4 Tiger Langtang II % 20 Nepal FALSE Sus scrofa 1 4 Tiger Alaungdaw II % 68 Myanmar FALSE Sus scrofa,rusa unicolor 2 4 Tiger Khao Laem II % 0 Thailand FALSE Sus scrofa,rusa unicolor 2 4 Tiger Sri Lanna II % 0 Thailand FALSE Sus scrofa,rusa unicolor 2 4 Tiger Siilxem nuruu /A/, /B/ II % 18 Mongolia FALSE Sus scrofa 1 4 Tiger Preah Monivong II % 10 Cambodia FALSE Sus scrofa,rusa unicolor 2 4 (Bokor) Tiger Makalu-Barun II % 0 Nepal TRUE Sus scrofa,rusa unicolor 2 4 Snow leopard Gobiin baga /A/, /B/ Ib % 60 Mongolia FALSE Capra sibirica 1 2 Unknown Snow leopard Khangai nuruu II % 0 Mongolia FALSE Capra sibirica 1 2 Unknown Snow leopard Zed-Khantai-Buteeliin Ia % 64 Mongolia FALSE 0 2 Unknown nuruu Snow leopard Tarvagatai nuruu II % 0 Mongolia FALSE Capra sibirica 1 2 Unknown Snow leopard Ulaan Taiga Ib % 0 Mongolia FALSE 0 2 Unknown Snow leopard Myangan-Ugalzat II % 25 Mongolia FALSE Capra sibirica 1 2 Unknown Snow leopard Mongol Els II % 40 Mongolia FALSE 0 2 Snow leopard Ulaagchini khar nuur II % 56 Mongolia FALSE 0 2 Snow leopard Khoridol Saridag Ia % 0 Mongolia FALSE Capra sibirica 1 2 Snow leopard Altun Emel II % 45 Kazakhstan FALSE 0 2

307 289 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Snow leopard Jigme Singye II % 0 Bhutan FALSE 0 2 Wangchuck Snow leopard Khakassky Ia % 27 Russian FALSE 0 2 Federation Snow leopard Zag Baidragiin goliin II % 0 Mongolia FALSE Capra sibirica 1 2 ekhen sav Snow leopard Royal Manas II % 0 Bhutan FALSE 0 2 Snow leopard Orxoni xundii II % 0 Mongolia FALSE 0 2 Snow leopard Thrumshingla II % 0 Bhutan FALSE 0 2 Snow leopard Bulgan gol-ikh Ongog II % 25 Mongolia FALSE Capra sibirica 1 2 Snow leopard Khorgo Terkh Zagaan II % 20 Mongolia FALSE 0 2 nuur Snow leopard Xugnu Tarna II % 55 Mongolia FALSE 0 2 Snow leopard Great Himalayan II % 14 India FALSE 0 2 Snow leopard Ergaki II % 75 Russian FALSE 0 2 Federation Snow leopard Torsa Ia % 16 Bhutan TRUE Pseudois nayaur 1 2 Snow leopard Band-e-Amir II % 231 Afghanistan FALSE Capra sibirica 1 2 Snow leopard Noyon Khangai II % 0 Mongolia FALSE Capra sibirica 1 2 Snow leopard Zapadno-Altayskiy Ia % 47 Kazakhstan FALSE 0 2 Puma Cordillera Azul II % 0 Peru TRUE Odocoileus virginianus 1 3 Unknown Puma Wabakimi Provincial Ib % 0 Canada TRUE Odocoileus virginianus,erethizon 2 3 Unknown Park dorsatum Puma Asatiwisipe Aki II % 0 Canada FALSE Odocoileus virginianus,erethizon 2 3 Unknown Traditional Use Planning Area dorsatum Puma Algonquin Provincial II % 10 Canada TRUE Odocoileus virginianus,erethizon 2 3 Unknown Park dorsatum Puma Spatsizi Plateau Ib % 0 Canada TRUE Odocoileus hemionus,erethizon 2 3 Unknown Wilderness Park dorsatum Puma Northern Rocky Mountains Park Ib % 0 Canada TRUE Odocoileus hemionus,erethizon dorsatum 2 3 Unknown Puma Puma Puma Quetico Provincial Park (Wilderness Class) Woodland Caribou Provincial Park (Wilderness Class) Opasquia Provincial Park Atikaki Provincial Park Ib % 0 Canada TRUE Odocoileus virginianus,erethizon dorsatum Ib % 0 Canada TRUE Odocoileus virginianus,erethizon dorsatum Ib % 136 Canada TRUE Erethizon dorsatum 1 3 Puma II % 0 Canada FALSE Odocoileus virginianus,erethizon 2 3 dorsatum Puma Huascarán II % 64 Peru FALSE Odocoileus virginianus 1 3 Puma Dune Za Keyih Park Ib % 0 Canada TRUE Odocoileus hemionus,erethizon 2 3 [a.k.a. Frog-Gataga dorsatum

308 290 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Park] Puma Lac La Ronge II % 14 Canada FALSE Erethizon dorsatum 1 3 Provincial Park Puma Riding Mountain II % 45 Canada FALSE Odocoileus virginianus,erethizon 2 3 National Park of Canada dorsatum Puma Otishi II % 0 Peru TRUE Odocoileus virginianus 1 3 Puma Río Abiseo II % 0 Peru TRUE Odocoileus virginianus 1 3 Puma Pauingassi First Nation Traditional Use Planning Area II % 0 Canada FALSE Odocoileus virginianus,erethizon dorsatum 2 3 Puma Mount Edziza Park Ib % 0 Canada TRUE Odocoileus hemionus,erethizon 2 3 dorsatum Puma Stikine River Park Ib % 0 Canada TRUE Odocoileus hemionus,erethizon 2 3 dorsatum Puma Atlin/A Teix Gi Aan II % 0 Canada TRUE Odocoileus hemionus,erethizon 2 3 Tlein Park dorsatum Puma Isle Royale Ib % 10 United States TRUE 0 3 of America Puma Megantoni III % 0 Peru TRUE Odocoileus virginianus 1 3 Puma Pukaskwa National II % 5 Canada TRUE Odocoileus virginianus,erethizon 2 3 Park of Canada dorsatum Puma Seager Wheeler Lake Ib % 25 Canada FALSE Erethizon dorsatum 1 3 Puma Lake Nipigon Conservation Reserve II % 0 Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Spotted hyena Maiko II % 92 Democratic TRUE 0 1 Unknown Republic of the Congo Spotted hyena Bomu Ib % 28 Democratic FALSE 0 1 Unknown Republic of the Congo Spotted hyena Ai-Ais Hot Springs II % 135 Namibia FALSE Oryx gazella 1 1 Unknown Spotted hyena Cross River II % 0 Nigeria FALSE 0 1 Unknown Spotted hyena Mpem et Djim II % 67 Cameroon FALSE 0 1 Unknown Spotted hyena Takamanda II % 0 Cameroon FALSE 0 1 Unknown Spotted hyena Matopos II % 174 Zimbabwe FALSE 0 1 Spotted hyena Waterberg Plateau II % 110 Namibia FALSE Oryx gazella 1 1 Park Spotted hyena Pomene II % 310 Mozambique FALSE 0 1 Spotted hyena Mlilwane Wildlife II % 25 Swaziland FALSE 0 1 Sanctuary Spotted hyena Daan Viljoen Game Park II % 122 Namibia FALSE Oryx gazella 1 1

309 291 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Brown hyena National Park II % 0 Angola TRUE 0 0 Unknown 50 Luengue-Luiana Brown hyena National Park II % 240 Angola FALSE 0 0 Unknown Quiçama Brown hyena Sioma Ngwezi II % 0 Zambia TRUE 0 0 Unknown Brown hyena Mudumu II % 18 Namibia TRUE 0 0 Unknown Brown hyena Nkasa Rupara II % 10 Namibia TRUE 0 0 Unknown Brown hyena Kasane II % 0 Botswana FALSE 0 0 Unknown Brown hyena Mosi-Oa-Tunya II % 5 Zambia FALSE 0 0 Striped hyena Manovo-Gounda- II % 61 Central African TRUE 0 0 Unknown Saint Floris Republic Striped hyena 'Uruq Bani Ma'arid II % 391 Saudi Arabia FALSE 0 0 Unknown Striped hyena Kahuzi-Biega II % 92 Democratic FALSE 0 0 Unknown Republic of the Congo Striped hyena Langtang II % 20 Nepal FALSE 0 0 Unknown Striped hyena Kishtwar II % 52 India FALSE 0 0 Unknown Striped hyena Akagera II % 78 Rwanda FALSE 0 0 Unknown Striped hyena Sundarban II % 80 India FALSE 0 0 Striped hyena Andre Felix II % 106 Central African FALSE 0 0 Republic Striped hyena Great Himalayan II % 14 India FALSE 0 0 Striped hyena Amu-Darya Ia % 90 Turkmenistan FALSE 0 0 Striped hyena Borjomi-Kharagauli II % 0 Georgia FALSE 0 0 Striped hyena Papikonda II % 150 India FALSE 0 0 Striped hyena Tigrovaya Balka Ia % 111 Tajikistan FALSE 0 0 Striped hyena Simlipal II % 226 India FALSE 0 0 Striped hyena Dilijan II % 47 Armenia FALSE 0 0 Striped hyena Lake Mburo II % 87 Uganda FALSE 0 0 Striped hyena Dashtidjum Ia % 119 Tajikistan FALSE 0 0 Striped hyena Zaamin II % 0 Uzbekistan FALSE 0 0 Striped hyena Dachigam II % 81 India FALSE 0 0 Striped hyena Shirkent historical II % 51 Tajikistan FALSE 0 0 and natural park Striped hyena Kolkheti II % 30 Georgia FALSE 0 0 Striped hyena Khosrov Forest Ia % 50 Armenia FALSE 0 0 Striped hyena Kanger Valley II % 124 India FALSE 0 0 Striped hyena Tbilisi II % 30 Georgia FALSE 0 0 Striped hyena Lake Arpi II % 0 Armenia FALSE nivores%20in%20luengue- ; Recently photographed in a nearby area

310 292 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Sun bear Jigme Singye II % 0 Bhutan FALSE 0 0 Unknown Wangchuck Sun bear Sri Lanna II % 0 Thailand FALSE 0 0 Unknown Sun bear Doi Luang II % 0 Thailand FALSE 0 0 Present 51 Sun bear Thung Salaeng Luang II % 0 Thailand FALSE 0 0 Unknown Sun bear Khao Bantad Ia % 0 Thailand FALSE 0 0 Unknown Sun bear Tham Phathai II % 0 Thailand FALSE 0 0 Unknown Sun bear Yok Don II % 60 Viet Nam FALSE 0 0 Present 52 Sun bear Royal Manas II % 0 Bhutan FALSE 0 0 Unknown Sun bear Si Nan II % 0 Thailand FALSE 0 0 Sun bear Mae Tho II % 0 Thailand FALSE 0 0 Sun bear Thrumshingla II % 0 Bhutan FALSE 0 0 Sun bear Nunthaburi II % 0 Thailand FALSE 0 0 Sun bear Phu Pa - Yol (Huai II % 5 Thailand FALSE 0 0 Huat) Sun bear Chae Son II % 0 Thailand FALSE 0 0 Sun bear Khao Pu - Khao Ya II % 0 Thailand FALSE 0 0 Sun bear Phu Phan II % 0 Thailand FALSE 0 0 Sun bear Lam Nam Kok II % 0 Thailand FALSE 0 0 Sun bear Nam Yung Nam Som II % 50 Thailand FALSE 0 0 Sun bear Phu Chong - Na Yoi II % 0 Thailand FALSE 0 0 Sun bear Ob Luang II % 0 Thailand FALSE 0 0 Sun bear Tham Pla - Pha Seu II % 0 Thailand FALSE 0 0 Sun bear Chu Yang Sin II % 18 Viet Nam FALSE 0 0 Sun bear Doi Phamuang Ia % 5 Thailand FALSE 0 0 Sun bear Mae Wa II % 0 Thailand FALSE 0 0 Sun bear Khao Luang II % 0 Thailand FALSE 0 0 Sloth bear Jigme Singye II % 0 Bhutan FALSE 0 0 Unknown Wangchuck Sloth bear Sundarban II % 80 India FALSE 0 0 Unknown Sloth bear Dudhwa II % 25 India FALSE 0 0 Present 53 Sloth bear Mouling II % 225 India FALSE 0 0 Unknown Sloth bear Knuckles Ia % 16 Sri Lanka FALSE 0 0 Unknown Sloth bear Peak Wilderness NR Ia % 27 Sri Lanka FALSE 0 0 Unknown Sloth bear Sinharaja National Ia % 20 Sri Lanka FALSE 0 0 Unknown &sig=0qd17bn3h4tw5qfg6q8d_s07pz0&hl=en&sa=x&ved=0ahukewjhwdkk8ojuahug- 2MKHWs8CCAQ6AEIKDAA#v=onepage&q=%22Yok%20Don%22%20sun%20bear&f=false 53

311 293 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Heritage Wilderness Area Sloth bear Shivapuri-Nagarjun II % 20 Nepal FALSE 0 0 Sloth bear Neora Valley II % 21 India FALSE 0 0 Sloth bear Pedro Ia % 0 Sri Lanka FALSE 0 0 Forest/Pidurutalagala Sloth bear Kaudulla II % 0 Sri Lanka FALSE 0 0 Sloth bear Bundala II % 11 Sri Lanka FALSE 0 0 Sloth bear Ilukpelessa Ib % 0 Sri Lanka FALSE 0 0 Sloth bear Mulatiyana Ib % 20 Sri Lanka FALSE 0 0 Sloth bear Mihintale Ib % 5 Sri Lanka FALSE 0 0 Sloth bear Yagirala Ib % 20 Sri Lanka FALSE 0 0 Sloth bear Baroiyadhala II % 47 Bangladesh FALSE 0 0 Sloth bear Tengragiri II % 14 Bangladesh FALSE 0 0 Sloth bear Nuwaragama Ib % 5 Sri Lanka FALSE 0 0 Sloth bear Tumbikulama Ib % 5 Sri Lanka FALSE 0 0 Sloth bear Kandapola Ia % 0 Sri Lanka FALSE 0 0 Sloth bear Yodaela Ib % 10 Sri Lanka FALSE 0 0 Andean black bear Darién II % 0 Panama TRUE 0 0 Unknown Andean black bear Huascarán II % 64 Peru FALSE 0 0 Present 54 Andean black bear Tinigua II % 0 Colombia TRUE 0 0 Unknown Andean black bear Los Katios II % 0 Colombia TRUE 0 0 Present 55 Andean black bear Cerro Saroche II % 5 Venezuela, FALSE 0 0 Unknown Bolivarian Republic of Andean black bear La Tatacoa II % 27 Colombia FALSE 0 0 Unknown Andean black bear Serrania De Minas II % 15 Colombia TRUE 0 0 Unknown Andean black bear Pampa Hermosa III % 45 Peru FALSE 0 0 Unknown Andean black bear Cutervo II % 85 Peru FALSE 0 0 Andean black bear Rabanal En El II % 45 Colombia TRUE 0 0 Municipio De Samaca Andean black bear Calipuy III % 64 Peru FALSE 0 0 Andean black bear Ampay III % 21 Peru FALSE 0 0 Andean black bear Parque Natural II % 5 Colombia TRUE 0 0 Regional Cerro La Judia Andean black bear Parque Natural II % 35 Colombia FALSE 0 0 Regional San Miguel De Los Farallones Andean black bear Loma de León III % 5 Venezuela, FALSE

312 294 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Bolivarian Republic of Andean black bear Sector Oriental II % 45 Colombia TRUE 0 0 Serrania El Peligro American black bear Grasslands National II % 118 Canada FALSE 0 0 Unknown Park of Canada American black bear Moose Mountain II % 136 Canada FALSE 0 0 Unknown Provincial Park American black bear Great Sand Hills Ib % 69 Canada FALSE 0 0 Unknown American black bear Spruce Woods II % 10 Canada FALSE 0 0 Unknown Provincial Park American black bear Bob Creek Wildland Ib % 5 Canada TRUE 0 0 Unknown American black bear Cypress Hills II % 0 Canada FALSE 0 0 Unknown American black bear Elk Island National II % 90 Canada FALSE 0 0 Park of Canada American black bear Cypress Hills II % 0 Canada FALSE 0 0 Provincial Park American black bear Turtle Mountain II % 10 Canada FALSE 0 0 Provincial Park American black bear Douglas Provincial II % 137 Canada FALSE 0 0 Park American black bear Douglas Marsh II % 10 Canada FALSE 0 0 Protected Area American black bear Dinosaur Ia % 127 Canada FALSE 0 0 American black bear Saskatchewan II % 90 Canada FALSE 0 0 Landing Provincial Park American black bear Whitemud III % 15 Canada FALSE 0 0 Watershed Wildlife Management Area American black bear Milk River Ia % 47 Canada FALSE 0 0 American black bear Neys Provincial Park II % 16 Canada FALSE 0 0 (Natural Environment Class) American black bear Gateway II % 418 United States FALSE 0 0 of America American black bear North Channel II % 14 Canada FALSE 0 0 Inshore Provincial Park (Waterway Class) American black bear Biscayne II % 0 United States FALSE 0 0 of America American black bear Rondeau Provincial II % 85 Canada FALSE 0 0 Park American black bear Crimson Lake II % 81 Canada TRUE 0 0

313 295 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status American black bear Whitewater Lake III % 10 Canada FALSE 0 0 Wildlife Management Area American black bear Writing-On-Stone II % 85 Canada FALSE 0 0 Brown bear Ukkusiksalik National II % 99 Canada TRUE 0 0 Present 56 Park of Canada Brown bear Khangai nuruu II % 0 Mongolia FALSE 0 0 Unknown Brown bear Har Us Nuur II % 40 Mongolia FALSE 0 0 Unknown Brown bear Asatiwisipe Aki II % 0 Canada FALSE 0 0 Unknown Traditional Use Planning Area Brown bear Tarvagatai nuruu II % 0 Mongolia FALSE 0 0 Unknown Brown bear Kaplangurskiy Ia % 199 Turkmenistan FALSE 0 0 Unknown Brown bear Eastern Mongolian Ib % 208 Mongolia FALSE 0 0 Unknown 57 Steppe Brown bear Kavir II % 100 Iran (Islamic FALSE 0 0 Republic of) Brown bear Uvs Nuur Basin Ia % 34 Mongolia FALSE 0 0 Brown bear Atikaki Provincial II % 0 Canada FALSE 0 0 Park Brown bear Prince Albert II % 25 Canada TRUE 0 0 National Park of Canada Brown bear Olympic II % 30 United States FALSE 0 0 of America Brown bear Pink Lake Ib % 55 Canada TRUE 0 0 Brown bear Shey-Phoksundo II % 35 Nepal FALSE 0 0 Brown bear Numaykoos Lake Ib % 25 Canada TRUE 0 0 Provincial Park Brown bear Khan Khukhii- II % 14 Mongolia FALSE 0 0 Khyragas Lake Brown bear Hardangervidda II % 10 Norway FALSE 0 0 Brown bear Lac La Ronge II % 14 Canada FALSE 0 0 Provincial Park Brown bear Numrug Ib % 250 Mongolia FALSE 0 0 Brown bear Riding Mountain II % 45 Canada FALSE 0 0 National Park of Canada Brown bear Myangan-Ugalzat II % 25 Mongolia FALSE 0 0 Brown bear Pauingassi First II % 0 Canada FALSE

314 296 Species Protected area Cat Area FP % FP Near Country Guild Prey # Prey Total Status Nation Traditional Use Planning Area Brown bear Mongol Els II % 40 Mongolia FALSE 0 0 Brown bear Ix Bogd mountain II % 35 Mongolia FALSE 0 0 Brown bear Podolskie Tovtry II % 0 Ukraine FALSE 0 0 Asiatic black bear Tajik National Park II % 50 Tajikistan FALSE 0 0 Unknown Asiatic black bear Taman Negara II % 113 Malaysia FALSE 0 0 Unknown Asiatic black bear Hemis II % 52 India TRUE 0 0 Unknown Asiatic black bear Khunjerab II % 103 Pakistan FALSE 0 0 Unknown Asiatic black bear Kirthar II % 76 Pakistan FALSE 0 0 Present 58 Asiatic black bear Sri Lanna II % 0 Thailand FALSE 0 0 Present 59 Asiatic black bear Endau Rompin II % 43 Malaysia FALSE 0 0 Unknown (Johor) Asiatic black bear Doi Luang II % 0 Thailand FALSE 0 0 Present 60 Asiatic black bear Thung Salaeng Luang II % 0 Thailand FALSE 0 0 Unknown 61 Asiatic black bear Khao Bantad Ia % 0 Thailand FALSE 0 0 Asiatic black bear Tham Phathai II % 0 Thailand FALSE 0 0 Asiatic black bear Chitwan II % 54 Nepal TRUE 0 0 Asiatic black bear Mae Charim II % 0 Thailand FALSE 0 0 Asiatic black bear Yok Don II % 60 Viet Nam FALSE 0 0 Asiatic black bear Bolon'sky Ia % 102 Russian FALSE 0 0 Federation Asiatic black bear Si Nan II % 0 Thailand FALSE 0 0 Asiatic black bear Mae Tho II % 0 Thailand FALSE 0 0 Asiatic black bear Bardia II % 0 Nepal FALSE 0 0 Asiatic black bear Nunthaburi II % 0 Thailand FALSE 0 0 Asiatic black bear Phu Pa - Yol (Huai II % 5 Thailand FALSE 0 0 Huat) Asiatic black bear Rajaji II % 49 India FALSE 0 0 Asiatic black bear Chae Son II % 0 Thailand FALSE 0 0 Asiatic black bear Khao Pu - Khao Ya II % 0 Thailand FALSE 0 0 Asiatic black bear Phu Phan II % 0 Thailand FALSE 0 0 Asiatic black bear Lam Nam Kok II % 0 Thailand FALSE

315 Table C.3. The 25 largest contiguous low (bottom 10% within lost range) human footprint regions in each carnivore species lost range. Variables descriptions are given in Table C.2 with the exceptions of ID (the area rank of the region) and % P (the percentage of the region overlapping category I-III protected areas). Country is based on the country that contains the greatest area of the low footprint region. Species ID Area FP % P Country Guild Prey # Prey Total African wild dog % Niger FALSE 0 5 African wild dog % Mauritania FALSE 0 5 African wild dog % Mali FALSE 0 5 African wild dog % Central African Republic FALSE Tragelaphus scriptus 1 5 African wild dog % Chad FALSE 0 5 African wild dog % Namibia FALSE 0 5 African wild dog % Chad FALSE 0 5 African wild dog % Mali FALSE 0 5 African wild dog % Namibia FALSE 0 5 African wild dog % Namibia FALSE 0 5 African wild dog % Mali FALSE 0 5 African wild dog % Central African Republic FALSE Tragelaphus scriptus 1 5 African wild dog % Angola FALSE Tragelaphus scriptus,tragelaphus strepsiceros 2 5 African wild dog % Mozambique FALSE Tragelaphus scriptus,tragelaphus strepsiceros,aepyceros melampus 3 5 African wild dog % Botswana FALSE 0 5 African wild dog % Central African Republic FALSE Tragelaphus scriptus 1 5 African wild dog % Namibia FALSE Tragelaphus strepsiceros 1 5 African wild dog % Angola FALSE Tragelaphus scriptus,tragelaphus strepsiceros 2 5 African wild dog % Kenya FALSE Tragelaphus imberbis,tragelaphus strepsiceros 2 5 African wild dog % Angola FALSE Tragelaphus scriptus,tragelaphus strepsiceros 2 5 African wild dog % Botswana FALSE Tragelaphus strepsiceros 1 5 African wild dog % Namibia FALSE 0 5 African wild dog % Angola FALSE Tragelaphus strepsiceros 1 5 African wild dog % Angola FALSE Tragelaphus scriptus 1 5 African wild dog % Sudan FALSE 0 5 American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % Mexico FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black bear % United States of America FALSE

316 298 Species ID Area FP % P Country Guild Prey # Prey Total American black % United States of America FALSE 0 0 bear American black % Mexico FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % Mexico FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % United States of America FALSE 0 0 bear American black % Canada FALSE 0 0 bear American black % United States of America FALSE 0 0 bear Andean black bear % Peru FALSE 0 0 Andean black bear % Bolivia (Plurinational State FALSE 0 0 of) Andean black bear % Bolivia (Plurinational State FALSE 0 0 of) Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0

317 299 Species ID Area FP % P Country Guild Prey # Prey Total Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Peru TRUE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Bolivia (Plurinational State TRUE 0 0 of) Andean black bear % Bolivia (Plurinational State FALSE 0 0 of) Andean black bear % Colombia TRUE 0 0 Andean black bear % Bolivia (Plurinational State FALSE 0 0 of) Andean black bear % Peru FALSE 0 0 Andean black bear % Ecuador FALSE 0 0 Andean black bear % Ecuador TRUE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Ecuador FALSE 0 0 Andean black bear % Ecuador FALSE 0 0 Andean black bear % Peru FALSE 0 0 Andean black bear % Bolivia (Plurinational State FALSE 0 0 of) Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Russian Federation FALSE 0 0 Asiatic black bear % Russian Federation FALSE 0 0 Asiatic black bear % Malaysia FALSE 0 0 Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Cambodia FALSE 0 0 Asiatic black bear % Tajikistan FALSE 0 0 Asiatic black bear % China FALSE 0 0 Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Lao People's Democratic FALSE 0 0 Republic Asiatic black bear % Malaysia FALSE 0 0 Asiatic black bear % Cambodia FALSE 0 0 Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Pakistan FALSE 0 0 Asiatic black bear % Cambodia FALSE 0 0 Asiatic black bear % China FALSE 0 0 Asiatic black bear % Iran (Islamic Republic of) FALSE 0 0 Asiatic black bear % Iran (Islamic Republic of) FALSE 0 0 Asiatic black bear % China FALSE 0 0

318 Species ID Area FP % P Country Guild Prey # Prey Total Asiatic black bear % Myanmar FALSE 0 0 Asiatic black bear % Cambodia FALSE 0 0 Asiatic black bear % China FALSE 0 0 Asiatic black bear % Myanmar FALSE 0 0 Asiatic black bear % Afghanistan FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % Canada TRUE 0 0 Brown bear % China FALSE 0 0 Brown bear % Canada TRUE 0 0 Brown bear % China FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % China FALSE 0 0 Brown bear % Russian Federation TRUE 0 0 Brown bear % Canada TRUE 0 0 Brown bear % China FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % United States of America FALSE 0 0 Brown bear % China FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % China FALSE 0 0 Brown bear % Canada FALSE 0 0 Brown bear % China FALSE 0 0 Brown bear % China FALSE 0 0 Brown bear % United States of America TRUE 0 0 Brown bear % Russian Federation TRUE 0 0 Brown bear % China FALSE 0 0 Brown bear % Russian Federation TRUE 0 0 Brown bear % Russian Federation TRUE 0 0 Brown bear % Mongolia FALSE 0 0 Brown hyena % Botswana FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Angola FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Angola FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Mozambique FALSE 0 0 Brown hyena % Namibia TRUE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Mozambique FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Namibia FALSE

319 301 Species ID Area FP % P Country Guild Prey # Prey Total Brown hyena % Mozambique FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Botswana TRUE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % Namibia FALSE 0 0 Brown hyena % South Africa FALSE 0 0 Brown hyena % Botswana FALSE 0 0 Brown hyena % South Africa FALSE 0 0 Brown hyena % Mozambique FALSE 0 0 Brown hyena % Mozambique FALSE 0 0 Cheetah % Niger FALSE 0 5 Cheetah % Algeria FALSE 0 5 Cheetah % Mauritania FALSE 0 5 Cheetah % Libya TRUE 0 5 Cheetah % Chad FALSE 0 5 Cheetah % Mali FALSE 0 5 Cheetah % Egypt FALSE 0 5 Cheetah % Algeria FALSE 0 5 Cheetah % Libya TRUE 0 5 Cheetah % Mauritania FALSE 0 5 Cheetah % Libya TRUE 0 5 Cheetah % Central African Republic FALSE 0 5 Cheetah % Yemen FALSE 0 5 Cheetah % Libya TRUE 0 5 Cheetah % Algeria TRUE 0 5 Cheetah % Egypt FALSE 0 5 Cheetah % Libya TRUE 0 5 Cheetah % Mauritania FALSE 0 5 Cheetah % Algeria FALSE 0 5 Cheetah % Mali FALSE 0 5 Cheetah % Chad FALSE 0 5 Cheetah % Mali FALSE 0 5 Cheetah % Sudan FALSE 0 5 Cheetah % Niger FALSE 0 5 Cheetah % Egypt FALSE 0 5 Clouded leopard % Cambodia FALSE 0 0 Clouded leopard % Lao People's Democratic FALSE 0 0 Republic Clouded leopard % Lao People's Democratic FALSE 0 0 Republic Clouded leopard % Cambodia FALSE 0 0 Clouded leopard % Cambodia FALSE 0 0 Clouded leopard % Myanmar FALSE 0 0 Clouded leopard % Cambodia FALSE 0 0 Clouded leopard % Lao People's Democratic FALSE 0 0

320 302 Species ID Area FP % P Country Guild Prey # Prey Total Republic Clouded leopard % Lao People's Democratic FALSE 0 0 Republic Clouded leopard % Viet Nam FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Myanmar FALSE 0 0 Clouded leopard % Myanmar FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Lao People's Democratic FALSE 0 0 Republic Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Myanmar FALSE 0 0 Clouded leopard % Viet Nam FALSE 0 0 Clouded leopard % Myanmar FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Thailand FALSE 0 0 Clouded leopard % Cambodia FALSE 0 0 Clouded leopard % Viet Nam FALSE 0 0 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % China FALSE 0 15 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Mongolia FALSE 0 15 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE Sus scrofa 1 15 Dhole % Russian Federation FALSE Sus scrofa 1 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation FALSE Sus scrofa 1 15 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation TRUE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % China FALSE 0 15 Dhole % Russian Federation FALSE 0 15 Dhole % Russian Federation TRUE Sus scrofa 1 15 Dhole % China FALSE 0 15

321 303 Species ID Area FP % P Country Guild Prey # Prey Total Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus rufus,oryctolagus cuniculus 2 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,oryctolagus cuniculus 2 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,oryctolagus cuniculus 2 6 Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus robustus,oryctolagus cuniculus 2 6 Dingo % Australia TRUE Macropus robustus,wallabia bicolor,macropus rufogriseus,oryctolagus 4 6 cuniculus Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus robustus,wallabia bicolor,macropus rufogriseus,oryctolagus 4 6 cuniculus Dingo % Australia TRUE Macropus robustus,oryctolagus cuniculus 2 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,wallabia bicolor,oryctolagus cuniculus 4 6 Dingo % Australia TRUE Oryctolagus cuniculus 1 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Dingo % Australia TRUE Macropus robustus,macropus rufus,oryctolagus cuniculus 3 6 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE Otomys typus 1 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4

322 304 Species ID Area FP % P Country Guild Prey # Prey Total Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Ethiopian wolf % Ethiopia FALSE 0 4 Eurasian lynx % Norway FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Greece FALSE 0 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Russian Federation TRUE 0 5 Eurasian lynx % Norway FALSE Capreolus capreolus,rangifer tarandus,cervus elaphus 3 5 Eurasian lynx % Greece FALSE Cervus elaphus 1 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Romania FALSE 0 5 Eurasian lynx % Sweden FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Italy FALSE Capreolus capreolus 1 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % France FALSE Capreolus capreolus 1 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Bulgaria FALSE Capreolus capreolus 1 5 Eurasian lynx % Italy FALSE Capreolus capreolus,rupicapra rupicapra 2 5 Eurasian lynx % Turkey FALSE Cervus elaphus 1 5 Eurasian lynx % The former Yugoslav FALSE 0 5 Republic of Macedonia Eurasian lynx % Croatia FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Turkey FALSE 0 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % Croatia FALSE Capreolus capreolus,cervus elaphus 2 5 Eurasian lynx % France FALSE Capreolus capreolus,cervus elaphus 2 5 Gray wolf % Finland FALSE Alces alces,lepus timidus 2 51 Gray wolf % Sweden FALSE Alces alces,lepus timidus 2 51 Gray wolf % United States of America FALSE Odocoileus hemionus 1 51 Gray wolf % United States of America FALSE Odocoileus hemionus 1 51 Gray wolf % United States of America FALSE Alces alces,odocoileus virginianus,castor canadensis,lepus americanus 4 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus californicus 3 51 Gray wolf % Canada TRUE 0 51 Gray wolf % Canada FALSE Alces alces,odocoileus virginianus,castor canadensis,lepus americanus 4 51 Gray wolf % Canada FALSE Alces alces,odocoileus virginianus,castor canadensis,lepus americanus 4 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus townsendii 3 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus californicus 3 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus californicus 3 51

323 305 Species ID Area FP % P Country Guild Prey # Prey Total Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus californicus,lepus townsendii 4 51 Gray wolf % United States of America FALSE Alces alces,odocoileus hemionus,odocoileus virginianus,castor 5 51 canadensis,lepus townsendii Gray wolf % Canada FALSE Odocoileus hemionus,odocoileus virginianus,castor canadensis,lepus 4 51 townsendii Gray wolf % United States of America FALSE Odocoileus hemionus,odocoileus virginianus,castor canadensis,lepus 4 51 californicus Gray wolf % Myanmar FALSE Muntiacus vaginalis,rusa unicolor,sus scrofa 3 51 Gray wolf % Canada FALSE Alces alces,odocoileus virginianus,castor canadensis,lepus americanus 4 51 Gray wolf % United States of America FALSE Odocoileus hemionus,lepus californicus 2 51 Gray wolf % United States of America FALSE Odocoileus hemionus,odocoileus virginianus,castor canadensis 3 51 Gray wolf % Mexico FALSE Odocoileus virginianus 1 51 Gray wolf % United States of America FALSE Odocoileus hemionus,lepus californicus 2 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus americanus 3 51 Gray wolf % Malaysia FALSE Rusa unicolor,sus scrofa 2 51 Gray wolf % United States of America FALSE Odocoileus hemionus,castor canadensis,lepus californicus,lepus townsendii 4 51 Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 7 22 paca,cabassous unicinctus,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 9 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,dasypus septemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,euphractus sexcinctus,priodontes maximus 9 22

324 306 Species ID Area FP % P Country Guild Prey # Prey Total Jaguar % Venezuela, Bolivarian TRUE Pecari tajacu,hydrochoerus hydrochaeris,cuniculus paca,cabassous 7 22 Republic of unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % United States of America FALSE 0 22 Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Venezuela, Bolivarian TRUE Pecari tajacu,hydrochoerus hydrochaeris,cuniculus paca,cabassous 7 22 Republic of unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Venezuela, Bolivarian TRUE Pecari tajacu,hydrochoerus hydrochaeris,cuniculus paca,cabassous 7 22 Republic of unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 7 22 paca,cabassous unicinctus,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % United States of America FALSE 0 22 Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Venezuela, Bolivarian TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 Republic of paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Argentina TRUE 0 22 Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Jaguar % Brazil TRUE Pecari tajacu,tayassu pecari,hydrochoerus hydrochaeris,cuniculus 8 22 paca,cabassous unicinctus,dasypus kappleri,dasypus novemcinctus,priodontes maximus Leopard % Mauritania FALSE 0 3 Leopard % Niger FALSE 0 3 Leopard % Oman FALSE 0 3 Leopard % Algeria FALSE 0 3 Leopard % Algeria FALSE 0 3 Leopard % Sudan FALSE 0 3 Leopard % Sudan FALSE 0 3 Leopard % Saudi Arabia FALSE 0 3 Leopard % Egypt FALSE 0 3 Leopard % Yemen FALSE 0 3

325 Species ID Area FP % P Country Guild Prey # Prey Total Leopard % Egypt FALSE 0 3 Leopard % Algeria FALSE 0 3 Leopard % Western Sahara FALSE 0 3 Leopard % Iran (Islamic Republic of) FALSE 0 3 Leopard % Mali FALSE 0 3 Leopard % Morocco FALSE 0 3 Leopard % Egypt FALSE 0 3 Leopard % Western Sahara FALSE 0 3 Leopard % Western Sahara FALSE 0 3 Leopard % Western Sahara FALSE 0 3 Leopard % Sudan FALSE 0 3 Leopard % Botswana FALSE Sylvicapra grimmia,aepyceros melampus 2 3 Leopard % Algeria FALSE 0 3 Leopard % Iran (Islamic Republic of) FALSE 0 3 Leopard % Egypt FALSE 0 3 Lion % Mauritania FALSE 0 7 Lion % Mali FALSE 0 7 Lion % Mauritania FALSE 0 7 Lion % Niger FALSE 0 7 Lion % Algeria FALSE 0 7 Lion % Algeria FALSE 0 7 Lion % Sudan FALSE 0 7 Lion % Mauritania FALSE 0 7 Lion % Western Sahara FALSE 0 7 Lion % Chad FALSE 0 7 Lion % Botswana FALSE Oryx gazella,connochaetes taurinus 2 7 Lion % Niger FALSE 0 7 Lion % Algeria TRUE 0 7 Lion % Congo TRUE Syncerus caffer 1 7 Lion % Egypt FALSE 0 7 Lion % Mali FALSE 0 7 Lion % Algeria FALSE 0 7 Lion % Namibia FALSE 0 7 Lion % Western Sahara FALSE 0 7 Lion % Mauritania FALSE 0 7 Lion % Mauritania FALSE 0 7 Lion % Mali FALSE 0 7 Lion % Western Sahara FALSE 0 7 Lion % Botswana FALSE Oryx gazella,connochaetes taurinus 2 7 Lion % Algeria FALSE 0 7 Puma % Canada FALSE Erethizon dorsatum 1 3 Puma % Canada TRUE Odocoileus hemionus,erethizon dorsatum 2 3 Puma % Canada FALSE Erethizon dorsatum 1 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus hemionus,erethizon dorsatum

326 308 Species ID Area FP % P Country Guild Prey # Prey Total Puma % Peru TRUE 0 3 Puma % Peru TRUE 0 3 Puma % Canada FALSE Odocoileus hemionus,odocoileus virginianus,erethizon dorsatum 3 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus hemionus,odocoileus virginianus,erethizon dorsatum 3 3 Puma % Peru TRUE 0 3 Puma % Peru TRUE 0 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada FALSE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Bolivia (Plurinational State TRUE 0 3 of) Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus hemionus,odocoileus virginianus,erethizon dorsatum 3 3 Puma % United States of America FALSE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Puma % Canada TRUE Odocoileus virginianus,erethizon dorsatum 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus,sylvilagus palustris 3 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus,sylvilagus palustris 3 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus,sylvilagus palustris 3 3

327 Species ID Area FP % P Country Guild Prey # Prey Total Red wolf % United States of America FALSE Odocoileus virginianus,sylvilagus floridanus 2 3 Sloth bear % Myanmar FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % Myanmar FALSE 0 0 Sloth bear % Bangladesh FALSE 0 0 Sloth bear % Bhutan FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % Bhutan FALSE 0 0 Sloth bear % Bhutan FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % Nepal FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % Nepal FALSE 0 0 Sloth bear % Bhutan FALSE 0 0 Sloth bear % Nepal FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % Nepal FALSE 0 0 Sloth bear % India FALSE 0 0 Sloth bear % Sri Lanka FALSE 0 0 Snow leopard % China FALSE 0 2 Snow leopard % Russian Federation FALSE 0 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % Russian Federation FALSE 0 2 Snow leopard % China FALSE 0 2 Snow leopard % Russian Federation FALSE 0 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % China FALSE 0 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % Russian Federation FALSE 0 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % China FALSE Pseudois nayaur

328 Species ID Area FP % P Country Guild Prey # Prey Total Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % China TRUE Pseudois nayaur 1 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % Mongolia FALSE 0 2 Snow leopard % China FALSE Pseudois nayaur 1 2 Spotted hyena % Niger FALSE 0 1 Spotted hyena % Mauritania FALSE 0 1 Spotted hyena % Mauritania FALSE 0 1 Spotted hyena % Mauritania FALSE 0 1 Spotted hyena % Chad FALSE 0 1 Spotted hyena % Mali FALSE 0 1 Spotted hyena % Niger FALSE 0 1 Spotted hyena % Mali FALSE 0 1 Spotted hyena % Chad FALSE 0 1 Spotted hyena % Mauritania FALSE 0 1 Spotted hyena % Niger FALSE 0 1 Spotted hyena % Namibia FALSE Oryx gazella 1 1 Spotted hyena % Chad FALSE 0 1 Spotted hyena % Namibia FALSE Oryx gazella 1 1 Spotted hyena % Chad FALSE 0 1 Spotted hyena % Namibia FALSE 0 1 Spotted hyena % Namibia FALSE 0 1 Spotted hyena % Mali FALSE 0 1 Spotted hyena % Mauritania FALSE 0 1 Spotted hyena % Namibia FALSE Oryx gazella 1 1 Spotted hyena % Namibia FALSE Oryx gazella 1 1 Spotted hyena % Namibia FALSE Oryx gazella 1 1 Spotted hyena % Mali FALSE 0 1 Spotted hyena % Mali FALSE 0 1 Spotted hyena % Central African Republic FALSE 0 1 Striped hyena % Saudi Arabia FALSE 0 0 Striped hyena % Chad FALSE 0 0 Striped hyena % Saudi Arabia FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Central African Republic FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE

329 311 Species ID Area FP % P Country Guild Prey # Prey Total Striped hyena % Central African Republic FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Central African Republic FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Central African Republic FALSE 0 0 Striped hyena % Saudi Arabia FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Striped hyena % Sudan FALSE 0 0 Sun bear % Myanmar FALSE 0 0 Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Thailand FALSE 0 0 Sun bear % Viet Nam FALSE 0 0 Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Viet Nam FALSE 0 0 Sun bear % India FALSE 0 0 Sun bear % Thailand FALSE 0 0 Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Viet Nam FALSE 0 0 Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Cambodia FALSE 0 0 Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Viet Nam FALSE 0 0 Sun bear % Thailand FALSE 0 0 Sun bear % India FALSE 0 0 Sun bear % Myanmar FALSE 0 0 Sun bear % Lao People's Democratic Republic FALSE 0 0

330 312 Species ID Area FP % P Country Guild Prey # Prey Total Sun bear % Lao People's Democratic FALSE 0 0 Republic Sun bear % Thailand FALSE 0 0 Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia TRUE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia TRUE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia TRUE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia TRUE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded leopard % Indonesia FALSE 0 0

331 313 Species ID Area FP % P Country Guild Prey # Prey Total Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Sunda clouded % Indonesia FALSE 0 0 leopard Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % China FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation FALSE Sus scrofa 1 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % China FALSE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation FALSE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4 Tiger % Russian Federation TRUE 0 4

332 314 D. Supplementary Material for: Bayesian Characterization of Uncertainty in Species Interaction Strengths D.1 On Novak and Wootton s Species x This paper expands on the observational method for estimating attack rates presented by Novak & Wootton (2008): a i = F i A x (F x A x )h i N i, (eqn D.1) where a i is the attack rate, h i is the handling time, and N i is the abundance, all for the i th prey species. A i and F i are the proportions of all predators and feeding predator respectively feeding on the i th prey species. x refers to an arbitrarily chosen prey species that is the same for all a i. Here we show that this equation can also be written in a more simplified form, showing that the estimates are not dependent on the choice of species x. Define A 0 to be the observed proportion of predators that are not feeding, so that A 0 = 1 S A i. Then, the F i s can be obtained by normalizing A i s: F i = i=1 A i 1 A 0. Noting that: F x A x = A i = A j A x A x = A x A x (1 A 0 ) = A x[1 (1 A 0 )] = A xa 0. (eqn D.2) 1 A 0 1 A 0 1 A 0 1 A 0 S j=1 It follows that F i A x F x A x = A i 1 A 0 A x = A ia x = A i. A x A 0 A 1 A x A 0 A 0 0 (eqn D.3)

333 315 This can be further simplified by noting that the A is have a common denominator (total number surveyed). This means that the original attack rate equation can be written as a i = A i A 0 1 # f eeding on i = h i N i # not f eeding 1 h i N i. (eqn D.4) This shows that the estimate does not involve species x. Moreover, the total number surveyed need not be known to estimate a subset of the attack rates. D.2 A Bayesian Attack Rate Estimator The Bayesian machinery is built around Bayes theorem: f (θ data) f (data θ) f (θ). (eqn D.5) Here, f (data θ) is the likelihood: a function specifying the likelihood of the observed data in terms of unknown parameters θ. f (θ) is the prior: a probability density function reflecting prior beliefs or uncertainty about the parameters. Together, these inform f (θ data): the posterior distribution of the parameters given the data. Here, we consider only objective (also called non-informative) priors, assuming an absence of prior beliefs or information about the parameters in question (Berger, 2006). In other situations, informative priors constructed from previously obtained knowledge or data may be useful. A parametric formulation of the attack rate estimator (5.2) is ξ i = α i α 0 1 ν i η i. (eqn D.6)

334 316 Here, for the i th prey species, ξ i is the unknown attack rate, ν i is the population prey abundance, η i is the population handling time, α i is the population proportion of predators feeding, and α 0 is the population proportion of predators that are not feeding on any prey species. In each case, the parameters refer to the broader (statistical) population, rather than sampled data only. By framing the attack rates this way, we are able to estimate them in the context of the broader population about which inference is desired. Note that eqn D.6 is derived from a snapshot estimator of attack rates (5.2), and does not imply, for example, that attack rates vary inversely with abundances. Rather, attack rates are parameters in the multi-species Type II functional response (5.1) and assumed fixed throughout. Frequentist approaches for combining data from multiple sources to estimate functions of parameters (as in eqn D.6) generally rely on bootstrap methods or asymptotics like the multivariate delta-method. Both of these approaches exhibit poor small-sample performance (Efron & Tibshirani, 1994; Kilian, 1998). This is relevant when dealing with predator feeding surveys as the A i in 5.2 are often very small for the rare prey species that typify predator diets (Rossberg et al., 2006). Small values of A i (analogous to having a small sample) can be problematic even when the total number of predators surveyed is large (Agresti & Coull, 1998). Ignoring variation in abundance and handling time estimates to focus on the variation within the feeding surveys may avoid this problem, but will lead to underestimation of the uncertainty in the attack rate estimates. The Bayesian framework circumvents this problem. If data on prey-specific feeding proportions (F ), abundances (A), and handling times (H) are collected independently, the joint likelihood of these distributions

335 317 may be written as: f (F,A,H α,ν,η) = f (F α) f (A ν) f (H η). (eqn D.7) Provided that the corresponding priors are also independent, Bayes theorem implies that f (α F ) f (F α) f (α), f (ν A) f (A ν) f (ν), f (η H) f (H η) f (η). (eqn D.8a) (eqn D.8b) (eqn D.8c) These may therefore be fit with independent models for each component. That is, the posterior distributions of the attack rates in eqn D.6 may be estimated by using Markov Chain Monte Carlo (MCMC) to obtain samples from each of the three posterior distributions in eqn D.8 and combining these using eqn D.6. If the three types of data are not gathered independently, then it is necessary to consider likelihood or prior models that account for this dependence (see Appendix D.7). D.3 Model formulation (mathematical details) Here, we present additional model details for our case study with likelihood and prior distributions given in statistical notation. This supplements the model setup description given in the Bayesian model formulation section of the main text.

336 318 Modeling the feeding surveys Letting P be the total number of predators surveyed, X i the number observed feeding on prey i, and X 0 the number not feeding, we model the combined feeding survey data using a multinomial likelihood with Dirichlet prior: (X 0,X 1,...,X S ) Mult P (α 0,α 1,...,α S ) (eqn D.9a) (α 0,α 1,...,α S ) Dirich(c,c,...,c). (eqn D.9b) The resulting posterior distribution is also Dirichlet: (α 0,α 1,...,α S ) x Dirich(c + x 0,c + x 1,...,c + x S ). (eqn D.10) Modeling the abundance surveys Letting Y 1,...,Y n correspond to the n prey abundance measurements, and by conditioning on whether or not a zero occurs, we can write the likelihood density of the zero-inflated gamma (ZIG) distribution as g(y;α,β,ρ) = ρ I[y=0] [(1 ρ) f (y,α,β)] I[y>0],y 0, (eqn D.11) where ρ is the probability of a zero, f (y;α,β) is the usual gamma density with shape α, rate β, and mean α β, and I[ ] is the indicator function that equals 1 when its argument is true and 0 otherwise (Ospina & Ferrari, 2012). The ZIG density is separable in ρ and (α,β) that is, it can be expressed as the product of a function of ρ and a function of (α,β). So, we can model the zero-inflation parameter separately, provided that a separable prior is used. Thus, for each prey species, we model the number of observed zeros using a binomial distribution with a uniform prior on ρ and we take the gamma distribution parameter priors to be log(α) Uni f ( 100, 100) and log(β) Uni f ( 100, 100) to approximate the in-

337 319 dependent scale-invariant non-informative prior f (α,β) = f (α) f (β) α 1 1 β, which is equivalent to an (improper) uniform prior on the logarithmic scale (Syversveen, 1998). Modeling the handling time experiments We consider the i th handling time observation for a given prey species to be associated with a covariates vector X i consisting of 1 followed by temperature, predator size, and prey size (all log transformed). We then model the likelihood of the i th handling time with a modifiednormal likelihood written as H i N li (e XT i β,σ 2 ) (eqn D.12) where the subscript l i refers to the censoring window length and indicates that we added a Uni f ( l i 2, l i 2 ) error to the normal distribution (corresponding to the interval censoring with which handling times were observed). As noted in the main text, the exponential link of eqn D.12 avoids negative mean handling time estimates. Treating the field covariates (predator size, prey size, and temperature) as random to account for sampling variability, we model the distributions of the (logtransformed) covariate observations X 1,...,X N, where N is the total number of field observations, as being independent, identically distributed, and drawn from a multivariate normal distribution with mean vector µ and covariance matrix Σ. We use non-informative multivariate normal and inverse Wishart priors for µ and Σ respectively (Fink, 1997). Letting X follow the posterior predictive distribution (our estimate of the distribution of the covariates), we may write the mean handling time as E(H) = E[E(H X )] = E(e βt X ). (eqn D.13)

338 320 As described in the main text, we can estimate this expectation by sampling from the regression parameters posterior distribution, sampling new covariates from their posterior predictive distribution, computing e βt X for each sample, and averaging across all samples. D.4 Model implementation: Putting the pieces together to estimate per capita attack rates Using the likelihoods and priors of the feeding surveys, abundances and handling times, we draw samples from the parameters posterior distributions using Markov Chain Monte Carlo (MCMC). We use JAGS with the R package rjags for MCMC sampling (Plummer & Stukalov, 2014). We then combine parameter samples to produce samples from the attack rate posterior distribution on each prey species (see eqn D.6). This treats handling times, H, as being independent of the predator feeding surveys, F, even though we use covariate observations of predator size, prey size and temperature from the feeding surveys informing F to inform H by combining them with the laboratory-based handling time regression coefficients associated with these covariates. We establish the validity of this assumption by examining the relationship between feeding proportions and covariate averages between the individual surveys (Appendix D.7). We verify Markov chain convergence using trace plots and the Gelman and Rubin convergence diagnostic (Gelman & Rubin, 1992), remove samples obtained before the chains had converged (i.e. burn-in time), and thin each chain to ensure independence among the remaining samples. We compute scale reduction factors a convergence diagnostic that compares within versus between chain variability

339 321 using 250 independent chains with random initial values. We select burn-in times and thinning values separately for feeding survey, prey abundance, and handling time models based on trace plots and autocorrelation function plots. We base inferences on 1,000 samples after confirming that independent sets of 1,000 samples led to the same conclusions. D.5 F-distribution median In general, the median of the F-distribution does not have a closed form. However, we can derive an approximation by relating the F-distribution to the betadistribution. Let X Fn m. We can express X as the ratio of scaled, independent Chi-squared distributions C m χm 2 and C n χn: 2 X = C m/m C n /n (eqn D.14) It follows that we can express X as the ratio of scaled independent gamma distributions G m gamma( m 2,2) and G n gamma( n 2,2): X = G m/m G n /n = n G m m G n (eqn D.15) (eqn D.16) We can then normalize the gamma distributions: X = n m G m G m +G n G n G m +G n (eqn D.17)

340 322 Letting (D 1,D 2 ) Dirich( m 2, 2 n ) and using the relationship between Dirichlet and gamma distributions, X = n D 1 m D 2 (eqn D.18) Using the marginal distribution for Dirichlet components result and the fact that D 1 + D 2 = 1, we have that X = n B m 1 B (eqn D.19) where B Beta( m 2, 2 n ). Note that this is a monotone transformation of B, so it preserves the median. When m > 2 and n > 2, the median of B is approximately m (Kerman, 2011). Substituting this result, we have that m 2 + n med(x) = n med(b) m 1 med(b) (eqn D.20) m = n m = n m m 2 + n n m 2 + n m n = n 3m 2 m 3n 2 = n 2n 2 3m 2 m (eqn D.21) (eqn D.22) (eqn D.23) (eqn D.24)

341 323 D.6 A Hierarchical Model for Abundances We also consider a hierarchical model as in Cressie et al. (2009) to account for the spatial and temporal structure in the prey abundance data. Although we lack sufficient data to estimate the parameters in this model (i.e. MCMC chains fail to converge with non-informative priors), we present the details here to show how our Bayesian approach can be extended to account for dependence due to spatial, temporal, or other structure. For a single prey species, the data have the form Y i jkl where i is the year (2005 or 2006), j is the season (Summer or Winter), k is the transect (1 or 2), and l is the quadrat (1 to 5). There are no data for summer Transects are different for each year and season. To account for the structure of the data, the following hierarchical model can be used (distributions independent except for µ s): Y i jkl ZIG(α = µ 2 i jk τ,β i j = µ i jk τ,ρ) ρ Uni f (0,1) f (τ) 1 τ log(µ i jk ) = µ + θ i + ψ j + φ k(i j) µ N(0, ) θ i N(0,σ 2 θ ), ψ j N(0,σ 2 ψ), φ k(i j) N(0,σ 2 φ ) f (σθ 2 ) 1 σθ 2, f (σψ) 2 1 σψ 2, f (σφ 2 ) 1 σφ 2 In this model, the responses are ZIG with non-informative prior on the gamma

342 324 variances and probability of a zero. The mean responses are related to covariates using a log link. The overall mean of the logarithms has non-informative prior µ N(0, ). The year, season, and transects are independent and normally distributed with non-informative priors on the normal distribution variances. The parameter of interest the overall mean is (1 ρ)e µ. Hierarchical modeling of predator feeding survey and handling time data (field measurements of predator/prey size and temperature) can be done with a similar approach when sufficient data are available. In particular, more data at broader scales (e.g. year, transect) is needed to estimate the variability at these scales. D.7 Accounting for dependence among information sources In our dataset, predator feeding surveys included covariate information (predator size, prey size, and temperature) that was used to estimate field handling times on the basis of regression models for handling times parameterized using laboratory data. In estimating attack rates we treat the field covariates as part of the handling times data H and assume they are independent of the feeding proportions data F. We assess the validity of this assumption by plotting the regression covariates versus the observed feeding proportions, as shown in Fig. D.1. In this figure, every point represents a single feeding survey. The x-axes are the averages of the (logtranformed) covariate and the y-axes are the proportions of predators feeding. Only two species had sufficient data to be plotted and showed little evidence of a dependence. If a lack of independence were evident it would need to be accounted for in the

343 325 covariates distribution model. That is, although our model for the covariates was a multivariate normal, feeding survey level information (specifically proportions of predators feeding on each prey species) could be added to the model to affects its multivariate mean. This way, the mean covariate vector would be a function of the proportion of predators feeding on that prey type. Posterior distribution sampling could then be done by first sampling from the feeding proportions posterior distributions and then using the sampled feeding proportions to obtain samples from the handling times.

344 326 D.8 Supporting Figures and Tables 25% log 10 Predator Size (mm) log 10 Prey Size (mm) log 10 Temperature ( C) 20% 15% Chamaesipho columna 10% Predators Feeding 5% 25% 20% 15% 10% Xenostrobus pulex 5% Figure D.1. Average field covariates versus feeding proportions. Each point corresponds to a single feeding survey. Only species that appeared in more than three separate feeding surveys are shown. Of the eight species and three covariates, only Xenostrobus pulex showed any evidence of a relationship between feeding proportions and feeding covariates (i.e., between F and H in eqn D.7)

345 Predators feeding (X i ) log 10 θ^bayes X i X Predators feeding (X i ) c opt Predators not feeding (X 0 ) Predators not feeding (X 0 ) Figure D.2. Given the skewed nature of prey-specific per capita attack rate posterior probability distributions, the distribution median serves as a more appropriate point estimate than the mean. Fig. 5.1 illustrates the difference between the posterior median and maximum likelihood estimate of the ratio of feeding and nonfeeding predators as a function of the number of feeding individuals, showing how the neutral (c = 1 3 ) prior minimizes this difference. As a generalization of Fig. 5.1, in the left panel, we illustrate this difference as a function of both the number of predators observed feeding and the number observed not feeding. The right panel shows that the optimal value of c that minimizes this difference (a function of both feeding and non-feeding individuals) is typically around 3 1. In both cases, the survey data from our example are shown as black dots

346 328 Table D.1. Summary of notation used in this manuscript. We use capital letters for random variables (e.g. X i ) and lower-case letters for realizations of the random variables (e.g. x i ). Minor notation in the appendix that is not used elsewhere is generally not shown here General type II functional response F i a i h i N i S functional response on the i th prey species attack rate on the i th prey species handling time for the i th prey species abundance of the i th prey species number of prey species Observed data F,A,H X i,x i X 0,x 0 N X i l i data for feeding surveys, abundances, and handling times respectively number of predators observed feeding on the i th prey species number of predators observed not feeding total number of feeding predator field observations covariates vector for the i th feeding predator length of censoring window for the i th handling time experiment Probability distributions

347 329 f (x) Bin(n, p) Mult P (α 0,...,α S ) generic probability distribution function binomial distribution with size n and probability p multinomial distribution with size P and probabilities α 0,...,α S Dirich(c,...,c) Dirichlet distribution with concentration parameters c,...,c (α 0,...,α S ) x distribution of (α 0,...,α S ) conditional on x Uni f ( 100, 100) uniform distribution with minimum -100 and maxmimum 100 N li (µ,σ 2 ) normal dist. (mean µ, var. σ 2 ) plus Uni f ( l i 2, l i 2 ) censoring error Parameters α i population proportion of predators feeding on the i th prey species α 0 population proportion of predators not feeding γ i c α β ρ σ 2 ratio of multinomial probabilities α i α 0 Dirichlet distribution concentration parameters gamma distribution shape gamma distribution rate probability of a zero for the zero-inflated gamma distribution handling time model variance

348 330 µ mean vector for (log-transformed) field covariates Σ ξ i ν i η i covariance matrix for field covariates population attack rate on the i th prey species population abundance of the i th prey species population handling time for the i th prey species Other X random variable following the posterior dist. of the field covariates

349 331 Table D.2. Predator feeding survey results grouped by predator size class. Predators were split into eight groups based on their size in millimeters (shown in top row). For the most frequently observed prey species (Chamaesipho columna and Xenostrobus pulex), we applied our Bayesian method using feeding survey results from each size class separately to assess how attack rates varied with predator size Prey Species Austrolittorina antipodum Austrolittorina cincta Chamaesipho columna Epopella plicata Mytilus galloprovincialis Notoacmea Radial Risellopsis varia Xenostrobus pulex Not Feeding Total Surveyed

350 332 E. Supplementary Material for: A Unification of Priors for Modeling Rare Events in Nonlinear Regression E.1 Type II: bias calculation ( ) Suppose S Binomial n, p = βx 1+βx. Then, β = 1 x [ ] 1 S E x n S + 1 = 1 x = 1 x n s=1 n s=1 ( ) n p s (1 p) n s s s n s + 1 ( ) n p s (1 p) n s s 1 ( n = 1 x (1 p)n n = 1 x s=1 (1 p)n n 1 k=0 ( n k = 1 x (1 p)n p 1 p [ n k=0 p 1 p and (eqn E.1) (eqn E.2) )( ) p s (eqn E.3) s 1 1 p )( ) p k+1 (eqn E.4) 1 p ( )( ) n p k ( )( ) ] n p n 1 n k k 1 p n 1 p (eqn E.5) = 1 [( x (1 p p)n 1 + p ) n ( ) p n ] (eqn E.6) 1 p 1 p 1 p = 1 [ ] x (1 p 1 p)n 1 p (1 p) n pn (1 p) n (eqn E.7) = 1 [ x (1 p 1 p n ] p)n 1 p (1 p) n (eqn E.8) = 1 p x 1 p [1 pn ] (eqn E.9) = β(1 p n ) (eqn E.10)

351 333 This shows that the absolute bias is E( ˆβ) β = β p n and the absolute relative bias is = p n. E( ˆβ) β β E.2 Type II: alternate extension Another way to generalize to the unequal covariate values case is by using the same prior as in the equal covariate values case, with a suitable choice of center x. That is, we d like for x to be near the center of the covariates distribution, so we may use, for example x = x, x = median(x 1,...,x n ), a trimmed mean, or something similar. With a = 0 and b = 2 (to reduce the bias of the posterior mean), the unnormalized (equal covariate values) prior is So, the posterior is f (β s) f (β) n i=1 β s 1 β(1 + xβ) 2 (eqn E.11) (1 + βx i ) where we need to choose x. In the case where n i=1 1 (1 + βx i ) 1, (eqn E.12) β(1 + xβ) 2 1 (1 + βx ) n (eqn E.13) for some x, it seems reasonable to take x = x since then the likelihood function is similar to when x 1 =... = x n = x. So, the resulting posterior distribution will have approximately the desired mean.

352 334 Viewing the expressions in eqn E.13 as functions of β (as in the posterior distribution), we want to select x to minimize the distance between these functions with respect to some weighting function. Since we cannot use the likelihood to select the prior, it seems reasonable to use the prior (with unknown x ) to weight the distance between these functions. Thus, using the L 2 distance, we let x = argmin x R + 0 n i=1 1 1 (1 + βx (1 + βx i ) ) n 2 1 dβ. (eqn E.14) β(1 + xβ) 2 This weighted distance increases outside x (1) < x < x (n), so we restrict the optimization to this set to simplify the computation. Figure E.7 shows the distance between the true and approximate functions based on using x = x versus x = x. Alternatively, we can use the equally weighted L 2 distance (also shown in Figure E.7). As expected, the approximation error tends to be lower when we minimize the weighted or unweighted L 2 distance, and is lowest for small β when we minimize the weighted L 2 distance (Figure E.7). To explore the performance of these alternate procedures, we included them in the Type II function simulations. The results show that their performance is generally inferior to that of the information prior, so we do not discuss these other approaches further (Figure E.8).

353 335 E.3 Type III: functional uniform prior In the Type III setting, g 3 (x;α,β) = So, for α > 1 and β > 0, βxα 1+βx α, which means that α g 3(x;α,β) = βxα lnx (1 + βx α ) 2 (eqn E.15) β g x α 3(x;α,β) = (1 + βx α. ) 2 (eqn E.16) f 3 (α,β) ( (α,β) g 3 (x;α,β))( (α,β) g 3 (x;α,β)) T dx 0 = β 2 x2α ln2 x β x2α lnx (1+βx α ) 4 (1+βx α ) 4 dx 0 β x2α lnx x 2α (1+βx α ) 4 (1+βx α ) 4 β 2 x 2α ln 2 x dx β x 2α lnx dx (1+βx = 0 α ) 4 (1+βx 0 α ) 4 β x 2α lnx x dx 2α dx (1+βx 0 α ) 4 (1+βx 0 α ) 4 ( ) β 4 α 2 (α 2 1) 2 π 4 sin 4 ( α π = ) α2 (α 4 π + 3) 2 sin 2 ( α π ) 36α 10 β 2 α 1 α 5 sin( α π ) (α 2 1) 2 π 2 sin 2 ( α π ) α2 (α 4 + 3). (eqn E.17) (eqn E.18) (eqn E.19) (eqn E.20) (eqn E.21) Mathematica code to solve the integrals in eqn E.19 is provided in section E.4.

354 336 E.4 Source Code Mathematica prior calculations 1 (* Type I function: single observation Fisher information for \ 2 Jeffreys prior *) 3 L[y_, beta_, x_] := Likelihood[BinomialDistribution[1, x*beta], {y }] 4 FullSimplify[ Expectation[D[Log[L[y, beta, x]], {{beta}, 2}], 6 y \[Distributed] BinomialDistribution[1, x*beta]]] 7 FullSimplify[ 8 Expectation[D[Log[L[y, beta, x]], {{beta}, 1}]ˆ2, 9 y \[Distributed] BinomialDistribution[1, x*beta]]] (* Type III function: single observation Fisher information for \ 12 Jeffreys prior *) 13 L[y_, beta_, alpha_, x_] := 14 Likelihood[ 15 BinomialDistribution[1, xˆalpha*beta/(1 + xˆalpha*beta)], {y}] 16 MatrixForm[ FullSimplify[ 18 Expectation[ 19 FullSimplify[D[Log[L[y, beta, alpha, x]], {{alpha, beta}, 2}]], 20 y \[Distributed] 21 BinomialDistribution[1, xˆalpha*beta/(1 + xˆalpha*beta)]]]] (* Type III function: functional uniform prior *) 24 g[x_, alpha_, beta_] := beta * xˆalpha / (1 + beta * xˆalpha) 25 FullSimplify[Grad[g[x, alpha, beta], {alpha, beta}]] 26 FullSimplify[

355 Outer[Times, Grad[g[x, alpha, beta], {alpha, beta}], 28 Grad[g[x, alpha, beta], {alpha, beta}]]] 29 FullSimplify[ 30 Det[Refine[ 31 Integrate[ 32 FullSimplify[ 33 Outer[Times, Grad[g[x, alpha, beta], {alpha, beta}], 34 Grad[g[x, alpha, beta], {alpha, beta}]]], {x, 0, 35 Infinity}], {alpha > 1, beta > 0}]]] 36 FullSimplify[ 37 Sqrt[Det[Refine[ 38 Integrate[ 39 FullSimplify[ 40 Outer[Times, Grad[g[x, alpha, beta], {alpha, beta}], 41 Grad[g[x, alpha, beta], {alpha, beta}]]], {x, 0, 42 Infinity}], {alpha > 1, beta > 0}]]]] Type I function (Stan code) 1 data { 2 int<lower=1> n; 3 int y[n]; 4 vector[n] x; 5 int prior; // 1: Information, 2: Jeffreys, 3: unif, 4: log unif, 5: FUP 6 real beta_max; 7 } 8 parameters { 9 real<lower=0,upper=beta_max> beta; 10 } 11 model { 12 real inc; 13 vector[n] summands;

356 inc = 0; for(i in 1:n){ 17 if(beta * x[i] < 1){ 18 target += y[i]*log(beta*x[i]) + (1-y[i]) * log(1-beta*x[i]); 19 } } if(prior == 1){ 24 for(i in 1:n){ 25 if(beta * x[i] < 1){ 26 summands[i] = x[i]/beta/(1-beta*x[i]); 27 } else{ 28 summands[i] = 0; 29 } 30 } 31 inc = sum(summands); 32 target += log(inc); 33 } else if(prior == 2){ 34 for(i in 1:n){ 35 if(beta * x[i] < 1){ 36 summands[i] = x[i]/beta/(1-beta*x[i]); 37 } else{ 38 summands[i] = 0; 39 } 40 } 41 inc = sum(summands); 42 target += log(pow(inc,0.5)); 43 } else if(prior == 4){ 44 target += -log(beta); 45 } else if(prior == 5){

357 target += -1.5*log(beta); 47 } } Type II function (Stan code) 1 data { 2 int<lower=1> n; 3 int y[n]; 4 vector[n] x; 5 real x_center; 6 int prior; // 0: x_center, 1: Information, 2: Jeffreys, 3: unif, 4: log unif, 5: FUP, 6: Inf_med 7 } 8 parameters { 9 real<lower=0> beta; 10 } 11 model { 12 real inc; 13 inc = 0; for(i in 1:n){ 16 y[i] binomial(1, beta * x[i] / (1 + beta * x[i])); 17 } if(prior == 0){ 20 target += -log(beta)-2*log(1+x_center*beta); 21 } else if(prior == 1){ 22 for(i in 1:n){ 23 inc = inc + x[i]/beta/pow(1+beta*x[i],2); 24 } 25 target += log(inc);

358 } else if(prior == 2){ 27 for(i in 1:n){ 28 inc = inc + x[i]/beta/pow(1+beta*x[i],2); 29 } 30 target += log(pow(inc,0.5)); 31 } else if(prior == 4){ 32 target += -log(beta); 33 } else if(prior == 5){ 34 target += -1.5*log(beta); 35 } else if(prior == 6){ 36 for(i in 1:n){ 37 inc = inc + x[i]/pow(beta,2.0/3)/pow(1+beta*x[i],5.0/3); 38 } 39 target += log(inc); 40 } 41 } Type III function (Stan code) 1 data { 2 int<lower=1> n; 3 int y[n]; 4 vector[n] x; 5 int prior; // 0: "jeffreys", 1:"FUP", 2:"logunif", 3:"unif", 4:"cond_mode", 5:"cond_unif", 6:"cond_logunif" 6 } 7 parameters { 8 real<lower=0> beta; 9 real<lower=1> alpha; 10 } 11 model { 12 real inc; 13 real temp;

359 real tl; 15 real br; 16 real offdiag; inc = 0; 19 tl = 0; 20 br = 0; 21 offdiag = 0; for(i in 1:n){ 24 y[i] binomial(1, beta * pow(x[i],alpha) / (1 + beta * pow(x[i ],alpha))); 25 } if (prior == 0){ // jeffreys 28 for(i in 1:n){ 29 temp = pow(x[i],alpha)/pow(1+beta*pow(x[i],alpha),2); 30 tl = tl + temp * pow(log(x[i]),2); 31 br = br + temp; 32 offdiag = offdiag + temp * log(x[i]); 33 } 34 target += 0.5*log(tl*br-pow(offdiag,2)); 35 } else if(prior == 1){ // FUP 36 target += (-2-1/alpha)*log(beta) - 5*log(alpha) - log(sin( pi()/alpha)) * log(pow(pi()*(pow(alpha,2)-1),2) / pow(sin(pi()/ alpha),2) - pow(alpha,2)*(pow(alpha,4)+3)); 38 } else if(prior == 2){ // logunif 39 target += -log(beta) - log(alpha); 40 } else if(prior == 4){ // cond_mode 41 for(i in 1:n){ 42 inc = inc + pow(x[i],0.5*alpha+0.5)/(1+beta*pow(x[i],alpha));

360 } 44 target += log(inc); 45 } else if(prior == 5){ // cond_unif 46 for(i in 1:n){ 47 inc = inc + pow(x[i],alpha)/beta/pow(1+beta*pow(x[i],alpha),2) ; 48 } 49 target += log(inc); 50 } else if(prior == 6){ // cond_logunif 51 for(i in 1:n){ 52 inc = inc + pow(x[i],alpha)/beta/pow(1+beta*pow(x[i],alpha),2) ; 53 } 54 target += log(inc); 55 target += -log(alpha); 56 } 57 }

361 a: 0 a: 0.01 a: 0.02 a: 1 Relative bias b: 1.01 b: 1.99 b: 2 b: 2.01 b: Odds Figure E.1. Estimation of β in the Type II function. In this example, x 1 =... = x 3 = ( ) 3,. The estimators considered have the 1, and thus S = 3 Y i Binomial i=1 S+a β 1+β form β = n S+b 1, which is the posterior mean when the prior is f (β) β a 1 (1+ xβ) a b. The y-axis shows the absolute relative bias E( β) β β. The downward spikes in many of the panels indicate where the bias changes sign. Values of a are shown on the column labels, and values of b are shown on the row labels. The parameter, β, can be expressed in terms of the rarity p = P(Y = 1): β = p 1 p. When a = 0 and b = 2 (and x 1 =... = x n ), the bias decreases geometrically with respect to n and also approaches 0 as p 0.

362 344 p: p: p: p: 0.01 p: 0.01 p: 0.01 p: 0.1 p: 0.1 p: % 75% 50% 25% 100% 75% 50% 25% 100% 75% 50% 25% 100% 75% 50% 25% 100% 75% 50% 25% CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 Information Jeffreys Uniform Log uniform Functional uniform Interval coverage Sample size Figure E.2. Type I function simulation credible interval coverage results based on 1,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen based on the desired coefficient of variation (standard deviation divided by mean). Coefficients of variation are shown in the second row of the panel column labels. The first row shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). Within each panel, the x-axis shows the sample size and the y-axis shows the approximate coverage probability of 90% equal-tailed credible intervals with point estimates and 95% confidence intervals for the probability. Open circles show cases where the average value of ˆR (across simulations) exceeded 1.1 (suggesting frequent failure of chains to converge). Each row corresponds to a different prior distribution.

363 345 p: p: p: p: 0.01 p: 0.01 p: 0.01 p: 0.1 p: 0.1 p: % 75% 50% 25% 0% 100% 75% 50% 25% 0% 100% 75% 50% 25% 0% 100% 75% 50% 25% 0% 100% 75% 50% 25% 0% CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 CV: 0.1 CV: 1 CV: 10 Information Jeffreys Uniform Log uniform Functional uniform Interval coverage Sample size Figure E.3. Type II function simulation credible interval coverage results based on 5,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen based on the desired coefficient of variation (standard deviation divided by mean). Coefficients of variation are shown in the second row of the panel column labels. The first row shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). Within each panel, the x-axis shows the sample size and the y-axis shows the approximate coverage probability of 90% equal-tailed credible intervals with point estimates and 95% confidence intervals for the probability. Each row corresponds to a different prior distribution.

364 346 p : 0.01 p : 0.01 p : 0.1 p : % α : 1.25 α : 2 α : 1.25 α : 2 Interval coverage 90% 80% 100% 90% 80% 100% 90% 80% 100% 90% 80% Jeffreys Uniform Log uniform Functional uniform α β α β α β α β Figure E.4. Type III function simulation credible interval coverage results based on 1,000 simulations for each parameter configuration. The distribution of the covariate is lognormal with µ log = and σlog 2 chosen based on the desired coefficient of variation (standard deviation divided by mean). Values of α are shown in the second row of the panel column labels. The first row shows the overall (i.e. unconditional) rarity level: p = P(Y = 1). Within each panel, the x-axis shows the parameter being considered and the y-axis shows the approximate coverage probability of 90% equal-tailed credible intervals with point estimates and 95% confidence intervals for the probability. Open circles show cases where the average value of ˆR (across simulations) exceeded 1.1 (suggesting frequent failure of chains to converge). Each row corresponds to a different prior distribution.

365 Log posterior (unnormalized) Prior Information Log uniform β Figure E.5. Example posterior distributions for the Type I function using the information and log uniform priors (Section 6.2). Simulation settings are: n = 5, 000, CV = 10, and p = 0.1 (Table 6.2). The maximum value of β shown in the plot is 1 min x i, beyond which the likelihood is zero. The vertical spikes in the information {i:y i =0} prior occur at 1 x i when Y i = 1. These spikes can make sampling from the posterior distribution (or integrating it) difficult, but when the βx i are small, the informationprior and log uniform prior are approximately equal (see results in Figure 6.2).

366 348 Figure E.6. Type II function quantiles using different versions of the functional uniform prior. Panel titles indicate the maximum value assumed for the covariate x max. The prior has the form f (β) (1 + x max β) 3. The lines correspond to the 1%,...,99% quantiles of β. Thus, adjacent lines can be interpreted as defining a region where functions sampled according to the prior fall with probability Since the x-axis spans (0,10), using x max = 10 leads to quantile lines that appear to be evenly spread out, whereas x max = 1 and x max = 100 tend to put more mass at high and low values of p respectively across x (0,10). This illustrates how the functional uniform prior is sensitive to the range of x-values considered, or, more generally, the distance function upon which it is based.