Modeling Eurasian lynx (Lynx lynx) distribution and estimation of patch and population size in the Alps

Transcription

1 Becker, T Modeling Eurasian lynx (Lynx lynx) distribution and estimation of patch and population size in the Alps. Thesis: University of London. Keywords: 8AT/8CH/8DE/8FR/Alps/distribution/Eurasian lynx/gps telemetry/habitat/habitat model/lynx/lynx lynx/malme/maxent/model/modelling/patch model/population estimation/suitability/suitable habitat Abstract: Eurasian lynx (Lynx lynx) exist in central Europe in relatively small, isolated populations particularly in the Jura Mountains and the Northwest Swiss Alps. Population sizes have fluctuated over the years, and distribution has expanded only through translocations to Northeastern Switzerland and Austria. There is a pressing need to establish greater connectivity between the populations, particularly throughout the European Alps, where the genetically isolated, relatively small populations exist in a highly fragmented environment. However, natural dispersal alone likely would be insufficient to establish this interconnectivity, and further translocations would be required. Therefore, it is necessary to identify areas of potential suitable habitat where viable populations could exist. In this study, I used Maxent and extensive VHF and GPS telemetry data from lynx monitoring studies to develop a species distribution model to assess where and how much suitable territory for lynx exists in the Alps. I found that approximately 103,600 km2 of suitable lynx habitat exists in the Alps, covering approximately 54% of the total Alpine Convention area. I identified 22 patches of suitable habitat ranging from 400 to over 17,000 km2, representing individual lynx sub-populations. Assuming densities of one to three individuals per 100 km2, the Alps could support approximately 1,000 to 3,000 lynx. However, the patches of suitable habitat, although geographically close, are fragmented by anthropogenic and natural barriers that may hinder increased connectivity between lynx sub-populations. Model results depended heavily on the choice of background locations, environmental variables, and threshold suitability values.

2 Modeling Eurasian lynx (Lynx lynx) distribution and estimation of patch and population size in the Alps Tiffany Becker 15 September 2013 Research report submitted in partial fulfillment of the requirements for the MSc in Biodiversity Conservation and Management for Distance Learning Students of the University of London, Centre for Development, Environment and Policy (CeDEP), School of Oriental and African Studies (SOAS)

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4 TABLE OF CONTENTS LIST OF TABLES... 4 LIST OF FIGURES... 4 LIST OF ABBREVIATIONS AND ACRONYMS... 5 ABSTRACT... 6 ACKNOWLEDGEMENTS... 7 I. INTRODUCTION... 8 I.1. Lynx... 8 I.2. Species distribution modeling I.3. Research aims and questions II. LITERATURE REVIEW II.1. Lynx ecology II.2. Lynx distribution and conservation status II.3. Metapopulations and connectivity II.4. Species distribution models III. METHODOLOGY III.1. Study area III.2. Lynx data III.3. Environmental variables III.4. Model III.4.1. Model development III.4.2. Model evaluation III.5. Lynx population and patch size IV. RESULTS IV.1. Model and variables IV.1.1. Lynx presence points and background IV.1.2. Environmental variables IV.1.3. Model evaluation IV.2. Lynx population and patch size V. ANALYSIS/DISCUSSION V.1. Model and variables V.2. Lynx suitable habitat, population and patch size VI. CONCLUSION REFERENCES USED BIBLIOGRAPHY APPENDICES

5 LIST OF TABLES 1. Lynx presence data by location and telemetry source 2. Reclassification of CORINE land use categories 3. Environmental variables used 4. Sub-sampling performance results 5. Variable importance 6. Variable importance for model version chosen for population and patch analysis 7. Evaluation results of selected models 8. Summary of large patches and number of lynx at different densities A1. Correlation matrix for environmental variables A2. Model parameters and data, for versions selected for further analysis. LIST OF FIGURES 1. Study area showing Alpine Convention boundary and area of analysis for modeling 2. Lynx presence locations 3. Habitat suitability maps for selected model versions 4. Final habitat suitability map 5. Map showing uncertainty of the predictive map 6. Suitable habitat at two thresholds 7. Suitable habitat patches after subdivision by barriers A1. Variable response curves from Maxent results 4

6 LIST OF ABBREVIATIONS AND ACRONYMS 3D AUC DEM EGM EU GPS IUCN KORA LAEA Maxent MCP NDVI NGO ROWAlps SCALP SDM SRTM VHF WISO WWF Three-dimensional Area under the (receiver operator characteristic) curve Digital elevation model EuroGlobalMap European Union Global positioning system International Union for the Conservation of Nature Raubtierökologie und Wildtiermanagement/ Carnivore ecology and wildlife management Lambert Azimuthal Equal Area projection Maximum Entropy Species Distribution Modeling software Minimum convex polygon Normalized Difference Vegetation Index Non-governmental organization Recovery of Wildlife in the Alps Status and Conservation of the Alpine Lynx Population Species distribution model Shuttle Radar Topographic Mission Very high (radio) frequency Large Carnivores, Wild Ungulates & Society World Wide Fund for Nature 5

7 ABSTRACT Eurasian lynx (Lynx lynx) exist in central Europe in relatively small, isolated populations particularly in the Jura Mountains and the Northwest Swiss Alps. Population sizes have fluctuated over the years, and distribution has expanded only through translocations to Northeastern Switzerland and Austria. There is a pressing need to establish greater connectivity between the populations, particularly throughout the European Alps, where the genetically isolated, relatively small populations exist in a highly fragmented environment. However, natural dispersal alone likely would be insufficient to establish this interconnectivity, and further translocations would be required. Therefore, it is necessary to identify areas of potential suitable habitat where viable populations could exist. In this study, I used Maxent and extensive VHF and GPS telemetry data from lynx monitoring studies to develop a species distribution model to assess where and how much suitable territory for lynx exists in the Alps. I found that approximately 103,600 km 2 of suitable lynx habitat exists in the Alps, covering approximately 54% of the total Alpine Convention area. I identified 22 patches of suitable habitat ranging from 400 to over 17,000 km 2, representing individual lynx sub-populations. Assuming densities of one to three individuals per 100km 2, the Alps could support approximately 1,000 to 3,000 lynx. However, the patches of suitable habitat, although geographically close, are fragmented by anthropogenic and natural barriers that may hinder increased connectivity between lynx sub-populations. Model results depended heavily on the choice of background locations, environmental variables, and threshold suitability values. 6

8 ACKNOWLEDGEMENTS I would like to sincerely thank KORA, a Swiss-based NGO focused on large carnivore research and conservation, who generously shared their lynx presence data collected from numerous VHF and GPS telemetry studies, thus making my entire dissertation feasible. Similarly, I thank Christian Fuxjäger of Nationalpark O.ö. Kalkalpen, Anja Molinari-Jobin and Paolo Molinari, Claudio Groff of Provincia Autonoma di Trento - Servizio Foreste e Fauna, and Jean-Michel Vandel of the Office National de la Chasse et de la Faune Sauvage, who provided additional lynx presence data for Austria, two locations in Italy, and France respectively. Many thanks in particular to Urs Breitenmoser, Christine Breitenmoser-Würsten, and Fridolin Zimmermann at KORA for suggesting to use Maxent, sharing useful information on lynx ecology and species distribution modeling, offering helpful ideas for analysis of model variables and results, and providing comments on the manuscript. I also thank Emiel von Loon and his students for their input on modeling aspects of my research. Finally I am grateful to my colleagues and boss at WWF who put me in touch with KORA, and my advisor Ben Daley for his feedback and positive encouragement. 7

9 I. INTRODUCTION I.1. Lynx Eurasian lynx (Lynx lynx) are one of the few large carnivore species existing in the wild in Europe. In central Europe, these charismatic megafauna persist only in relatively small, isolated populations, leading to a vital need to broaden their distribution and establish connectivity between the populations to support their continued existence. The European Alps would play a key role geographically to facilitate connectivity between lynx populations throughout central Europe. Lynx are protected by the Council of Europe s Convention on the Conservation of European Wildlife and Natural Heritage (Bern Convention) and the European Union s Council Directive 92/43/EEC on the conservation of natural habitats and of wild fauna and flora (Habitats Directive) (COE 2013). In addition to this legal protection, establishment of a pan-alpine lynx population is consistent with objectives of the European Union (EU) and the Alpine Convention organization to create ecological networks and corridors as part of wider conservation efforts. Following their extirpation from the Alps by the end of the 19th century, lynx were reintroduced in central Europe in the 1970s and 1980s, with populations persisting in the Swiss Jura Mountains and Northwest Swiss Alps, Slovenia, and French Vosges and Chartreuse Alps mountains (Breitenmoser 1998). The current size of the main populations in the Jura Mountains and the Swiss Alps are 100 and individuals respectively (Breitenmoser et al 2013). Per the widely accepted minimum viable population 50/500 "rule of thumb" attributed to Soule (Gilpin & Soule 1986), this would be sufficient for short-term survival but not long-term endurance and genetic viability. Population sizes have fluctuated over the years, but distribution has not significantly expanded until beginning in 2001 when lynx were translocated to Northeastern Switzerland (Ryser et al 2004), and to Austria in Lynx' current distribution in central Europe, including the Alps, is driven by sites that were used for reintroductions where they were successful and for translocations. The central European lynx populations are relatively isolated, and limited movement occurs between populations (Zimmermann & Breitenmoser 2007). In the highly fragmented Alps, dispersal is constrained by barriers including high mountain peaks and glaciers, major 8

10 highways, large rivers and settlements. Furthermore, dispersing sub-adult lynx show a strong tendency to establish home ranges in territories adjacent to conspecifics (Zimmermann et al 2005). Thus environmental and ecological factors combine making it unlikely that lynx will spontaneously colonize new areas in the Alps. Limited dispersal results in genetic isolation, which combined with small founder populations, can result in inbreeding depression and genetic drift (Allendorf & Luikart 2007). The Swiss lynx populations show reduced heterozygosity and genetic drift compared to the Slovak Carpathian founder population (Breitenmoser-Würsten & Obexer-Ruff 2003), and Ryser- Degiorgis et al (2004) noted congenital abnormalities but was not able to link them conclusively to genetic factors. Heart defects correlated to genetic factors in the Northwest Swiss Alps population mean this population can no longer be used as source for future translocations (Breitenmoser et al 2013). Thus, although lynx populations are established and recent translocations appear to be successful, there is a pressing need to establish greater connectivity between the subpopulations. This is particularly true in the Alps, where there are genetically isolated, relatively small populations and a highly fragmented environment. A conservation priority is to link existing lynx populations within the Alps, and from the Alps to the Jura and Dinaric Mountains (Molinari-Jobin et al 2003), potentially to the Vosges and Bohemian-Black Forest populations, and long-term possibly even to Carpathian populations (European Commission 2013). Natural dispersal alone likely would be insufficient to establish this interconnectivity, making translocations and reintroductions necessary (e.g. Zimmermann & Breitenmoser 2007, Molinari-Jobin et al 2010). However, the presence and reintroduction of large carnivores can be controversial. Lynx will very occasionally kill sheep and domestic animals, the loss of which is financially compensated and thus attacks on livestock are not considered a major problem. However, especially hunters view lynx as competition in particular for roe deer (Capreolus capreolus), lynx' preferred prey (Breitenmoser et al 2000). To overcome potential resistance to translocations and establish a viable Alpine lynx metapopulation, cross-border conservation efforts are needed. Current efforts in this regard are being conducted as part of the Large Carnivores, Wild Ungulates & Society (WISO) platform under the Alpine Convention organization (Alpine Convention 2011). In parallel, the Recovery of Wildlife in the Alps (ROWAlps) project is being conducted by NGOs and governments of the Alpine countries, aimed at providing conservation and management 9

11 options for large carnivores in line with the WISO guidelines. The WISO and ROWAlps projects include modeling the potential distribution and abundance of future Alpine lynx populations, determining options to increase public tolerance and acceptance of large carnivores, and developing management options for the recovery and conservation of lynx in the Alps, taking into account ecological and socioeconomic factors (WSL 2013). I.2. Species distribution modeling Species distribution modeling has become a common tool for conservationists to analyze and predict suitable habitat for a range of species including mammals, birds, reptiles, insects, and plants, at scales ranging from local to continental to global. Species distribution models (SDMs) have been used to identify survey locations to find new populations of rare species (e.g. Owens et al 2012); assess possible locations for protected areas, translocations or other conservation measures (e.g. Cianfrani et al 2013); forecast the potential spread of invasive species (e.g. Thuiller et al 2005); and assess how climate change may impact species' distributions (e.g. Webber et al 2011). Various modeling methods exist, but in general they all involve evaluating the distribution of one or more species based on spatially explicit known occurrence, and sometimes absence, locations and environmental conditions at those locations, to determine additional areas of suitable habitat with similar environmental conditions (Elith & Leathwick 2009). If lynx are to expand their territory in the Alps, most probably requiring external support through translocations, it is necessary to identify areas of potential suitable habitat where viable populations could exist. In this study, I developed an SDM for that purpose, to assess where in the Alps and how much suitable territory for lynx exists. The SDM was constructed using Maximum Entropy Species Distribution Modeling software (Maxent), a popular SDM software using a machine-learning algorithm to determine suitable habitat based on species occurrence and environmental data. Maxent uses the concept of maximum entropy to create the most evenly spread distribution possible that has average environmental conditions consistent with the mean at presence locations used to build the model (Phillips et al 2006). Maxent was preferred for this study because i) only presence data are needed to calibrate the model, which is good for cryptic, rare species such as lynx for which actual absence data are difficult to ascertain; ii) it is known to be effective for small or biased sample data, and is relatively robust with correlated variables; iii) it is rated highly in terms of accuracy of results (Elith et al 2006); and iv) it is relatively easy to use. 10

12 Other SDMs for lynx in the Alps have been developed in the past (section II.4). This study was intended to update those models by using more recent modeling tools and techniques, the most accurate environmental variables, and a broader set of lynx presence data including GPS telemetry data. This is the first habitat suitability study that combined lynx presence data from the Jura Mountains and six locations in the Alps to assess suitable habitat for lynx throughout the full Alpine region. It is also one of few examples where Maxent was applied with a significant volume of telemetry data to develop an SDM, and various options were explored about how the distribution of the presence data impacted the final habitat suitability model. I.3. Research aims and questions The re-establishment of a pan-alpine lynx population would be a desirable conservation outcome to support the long-term viability of the species in the European landscape. In this regard, the purpose of this research was to: 1. Determine the location and extent of suitable habitat for Eurasian lynx in the Alps 2. Explore what factors and species distribution model parameters most influence maps of lynx habitat suitability in the Alpine region, given the nature of telemetry presence data used for modeling 3. Determine how many lynx could be supported in that habitat 4. Suggest potential conservation implications for lynx based on the above In this context, this study aimed to answer the following research questions: 1. What is the potential distribution of lynx in the Alps as defined by suitable habitat? 2. What factors and model parameters are most effective to create accurate maps of lynx habitat suitability in the Alpine region based on telemetry data? 3. How many habitat patches (assumed to represent sub-populations of lynx) are identified in the Alps? 4. What is the potential size of the entire Alpine lynx population and of each of the identified habitat patches? The species distribution model that I created for my dissertation could be used to inform conservation decisions about target sites for future lynx translocation projects, or to demonstrate to governments and other stakeholders land areas of conservation priority for large carnivores such as lynx. The study could for example fulfill the first objective of the 11

13 WISO/ROWAlps project, to model suitable habitat and population sizes for Eurasian lynx in the European Alps. II. LITERATURE REVIEW II.1. Lynx ecology The Eurasian lynx is one of four lynx species worldwide. Lynx are well-studied in Switzerland in particular and Europe in general and much is known about their biology and ecology, especially aspects that impact the distribution and movement of lynx. Lynx are a solitary, territorial species, with a home range in the Alps of 211 km 2 on average for males and 101 km 2 for females (summarized in Molinari-Jobin 2010), although range size varies between geographic areas (Herfindal et al 2005). Lynx density measured by VHF telemetry ranges from one to two independent lynx per 100km 2 (Breitenmoser-Würsten et al 2001). Density as high as 3.61 per 100km 2 was measured in the southern Jura Mountains by camera-trapping (Zimmermann et al 2012). Sub-adults leave their natal range at around ten months of age. On average in the Northwest Swiss Alps, they tend to disperse 26 kilometers to establish new home ranges (Zimmermann et al 2005). Contrary to the generally accepted view that dispersal is often positive density dependent, negative density dependent dispersal was identified in the lynx population in the Northwest Swiss Alps, likely due to habitat fragmentation (Zimmermann et al 2005), not lynx' biological characteristics. One study comparing dispersing lynx from populations in the Nordics, Baltics, and Dinaric Mountains as well as central Europe found that the mean dispersal distance was 39 kilometers, and 68% of dispersing lynx settled within 50 kilometers (Molinari-Jobin et al 2010). Lynx tend to establish home ranges adjacent to those of other lynx (Zimmermann et al 2005), which affects their likelihood of establishing new colonies. Thus, while a lynx population may expand in spatial size, solitary lynx are unlikely to disperse and establish entirely new, separate populations. Lynx generally prefer forest or shrub habitat, although they can adapt to semi-natural disturbed habitat as long as there is nearby forest cover (Zimmermann & Breitenmoser 2007). Lynx are mostly nocturnal, active primarily at dusk and dark (ELIOS, 2013). This has implications for the accuracy of lynx tracking data, with VHF radiotelemetry data considered biased toward day lairs (U.Breitenmoser, pers. comm.). 12

14 II.2. Lynx distribution and conservation status In addition to the central European populations, lynx are present in small numbers in the Balkans, and in larger numbers in the Dinaric Mountains, the Carpathians, across Scandinavia and in Russia (ELIOS 2013). Because of their widespread presence and large populations (outside of central Europe), lynx are considered "least concern" on the IUCN Red List status (Breitenmoser et al 2008). But per Zimmermann et al (2011) the Alpine populations could be considered as endangered if evaluated according to IUCN Red List criteria. Despite lynx' protected status, illegal poaching was ranked as a top threat to lynx in two studies (Breitenmoser et al 2007, Molinari-Jobin et al 2010). This ranking was based on subjective surveys of lynx experts, which although subjective may be considered to accurately represent real threats, because any empirical study of lynx mortality would likely understate poaching deaths (since poachers are unlikely to report their activity and only chance finds would be counted). Liberg et al (2011) identified a similar phenomenon with Scandinavian wolves, naming it "cryptic poaching," which accords well with my thinking. Breitenmoser (1998) indicated already at that time that conflict with hunters due to perceptions about lynx' impact on prey was a problem, and there are no indications in the literature that this has abated in recent years. Other threats ranked high in both of the above mentioned studies were habitat fragmentation, road accidents, and demographic viability. Genetic viability and the risk of inbreeding was raked high (#3) by Breitenmoser et al (2007), but relatively low (tied for #7 out of 10) by Molinari-Jobin et al (2010). Most literature where it is mentioned considers low genetic diversity and genetic drift a risk for the reintroduced European lynx populations, largely because of their low founder populations and relative isolation. Interestingly, unlike with many other species (Groom et al 2006), there does not seem to be much reference in the literature that habitat loss currently is a problem for lynx. Indeed, per the Alpine Convention organization, human population is moving toward cities and rural agriculture is declining (Alpine Convention 2010), thus increasing suitable habitat for lynx in mountainous areas. Therefore it would be likely that sufficient suitable habitat is available, but habitat fragmentation is likely to be a problem. 13

15 II.3. Metapopulations and connectivity Groom et al (2006) define a metapopulation as 'systems of local populations linked by occasional dispersal' (p. 217). The concept of metapopulations is important for lynx in the Alps because source populations with greater reproductive success could compensate for sink populations with higher mortality. In other words, if one sub-population were to become extinct or decrease in number, that area could be recolonized or replenished from neighboring sub-populations. The metapopulation concept is echoed in Linnell et al (2008) in their European Commission "Guidelines for population level management plans for large carnivores in Europe," which states as an objective to establish a metapopulation of interconnected sub-populations for large carnivores in Europe (lynx, wolf, bear, wolverine). Connectivity is decreased in a fragmented habitat. Zimmermann (2004) reported that the Alps were fragmented by high alpine ridges and urbanized valleys thus resulting in multiple isolated sub-populations. These isolated populations, particularly when founded by few individuals, can show low genetic diversity, this resulting in increased risk from stochastic events such as disease and lower adaptation potential to adapt to environmental changes such as climate change. A lack of gene flow in isolated populations can also result in genetic drift and a loss of rare alleles (Allendorf & Luikart 2007). Lynx populations are not only isolated, but also small, thus increasing their extinction risk. It is widely reported in textbooks (e.g. Groom et al 2006) and peer-reviewed studies that small populations and low genetic diversity are problematic. Lacy (1997) for example pointed out that small populations will lose genetic variability due to genetic drift, and that isolated populations can suffer from inbreeding depression, with a resulting negative impact on genetic viability. However, this is a simplistic assumption. Amos & Balmford (2001) reviewed several studies of different mammals that evidenced the opposite, in part because the least inbred individuals within a population had greater reproductive success, thus reducing overall inbreeding. They also pointed out that the impact of "bottlenecks" due to small founder populations is not always as severe as expected, for example with cheetahs (Acinonyx jubatus). Over recent decades, the popularity of ecological corridors grew as a solution to the extinction risk faced by small isolated populations, as a way to improve connectivity (Beier & Noss 1998). For example, Rabinowitz & Zeller (2010) determined a range-wide model for connecting jaguar populations throughout Central and South America, as just one example of a regional corridor approach. 14

16 However, there is controversy about how effective they are. Studies on corridors have confirmed movement of individuals through corridors, but there is little empirical evidence yet that they increase gene flow (Beier & Gregory 2012). Nevertheless, in the absence of any better way to facilitate movement of individuals through an environment and genetic exchange between sub-populations, other than multiple repeated translocations, corridors and increased connectivity seem to be a good approach. As noted above, a lack of genetic diversity in lynx in Europe is a risk, as is the impact of inbreeding. There is a consistent view in the literature that more interconnectivity for lynx populations would be important. Although as above, it is unlikely that connectivity would result in a natural range expansion for lynx, it would facilitate the exchange of genes between lynx sub-populations. II.4. Species distribution models Species distribution modeling is explained in the Introduction, and key aspects of the modeling process are discussed in the body of the paper. Therefore I focus here only on three related points. First, Maxent has become immensely popular, with more than 1,000 studies using Maxent published since 2006 (Merow et al 2013). Its simplicity of use is a mixed blessing, making the tool widely accessible to people without specialized training, which is also its shortcoming. Merow et al (2013) and Yackulic et al (2012) criticized the widespread use of Maxent's default settings where the researcher does not have a good understanding of the assumptions that underlie the processes. Syfert et al (2013) explored the use of complex versus simple variable features, something that is rarely done in other studies. It is not hard to find studies that misinterpret Maxent results, or where the researcher has accepted all default settings without explaining whether defaults are indeed relevant to the species and extent they are studying. Second is the question of how to evaluate the accuracy and usefulness of model results, an area about which there is no consensus in the published literature. Lobo et al (2007) criticize AUC (explained below) as a performance measure, but admit there is no better measure currently. Allouche et al (2006) propose the true skill statistic which normally requires absence records to calculate, and they are not convincing that this measure can be applied legitimately in presence-only modeling like Maxent. Other measures of model performance 15

17 exist but only one (Kappa) is in relatively wide-spread use (Pearson 2007) and it also has been criticized (Allouche et al 2006). The result is that it is relatively easy to create a predictive model in Maxent, but hard to know for sure if it is a good model. Finally, two studies have modeled lynx distribution and connectivity in the Alps previously. Zimmerman's (2004) study can now be updated by more accurate GPS telemetry location data, new modeling software, and more accurate habitat data. The other model, by Signer (2010), used a habitat suitability model developed by Zimmermann & Breitenmoser (2007) for the Jura Mountains which have a different geology and environment, and hence the model should not be used to extrapolate habitat suitability in the Alps (Graf et al 2006). Other published models have considered only parts of the Alps (Germany, Schadt et al 2002; Austria, Rüdisser 2009). Hence a need exists for an updated distribution model using latest techniques with a broad geographic range of lynx presence data, that covers the entire Alps. III. METHODOLOGY III.1. Study area The geographical area for this study was the European Alps, a mountain range extending over eight countries, including parts of Switzerland, France, Italy, Germany, Austria, and Slovenia, and all of Liechtenstein and Monaco. The specific area considered was as defined by the Alpine Convention, and covers approximately 190,000 km 2 over an arc stretching 1,200 km (Alpine Convention 2013). To facilitate analysis of map files and to examine connectivity to surrounding mountain chains, the model considered the rectangular area bounding the Alpine Convention arc, although final analysis of suitable habitat and patches was limited to the Alpine Convention area as shown in Figure 1. See Appendix 1 for additional description of the Alpine area. 16

18 Figure 1: Study area showing Alpine Convention boundary and area of analysis for modeling III.2. Lynx data Lynx occurrence data was provided by KORA, a Swiss-based NGO focused on large carnivore research and conservation, which has been conducting lynx monitoring studies for decades. I was introduced to the staff at KORA by work colleagues who knew them from previous joint conservation projects. When I approached KORA while planning my dissertation, my research ideas were still rather tentative, focusing on lynx, corridors and connectivity, and geographic information systems, to draw together several personal interests. The timing coincided with KORA's own work on the afore-mentioned WISO/ROWAlps project. As KORA was interested to see a model of lynx habitat suitability for the Alps for that project, they suggested that as a formal research topic. They agreed to provide the lynx telemetry data and to advise me as I developed and evaluated the model. Other than the fieldwork to collect the actual lynx data, I did all work on the models and maps myself, sharing results periodically with KORA for their feedback and suggestions. The lynx presence data in Switzerland and France was provided directly by KORA. Their partner colleagues and organizations, Christian Fuxjäger of Nationalpark O.ö. Kalkalpen, Anja Molinari-Jobin (SCALP Coordinator) and Paolo Molinari, and Claudio Groff of Provincia Autonoma di Trento - Servizio Foreste e Fauna, made GPS telemetry data from lynx in 17

19 Austria and two places in Italy available via KORA. All data had been collected in the context of previous or on-going studies using VHF or GPS telemetry. Details on the original collection of VHF data can be found in Haller & Breitenmoser 1986, Haller 1992, Breitenmoser & Haller 1993, Breitenmoser-Würsten et al 2001, Ryser et al 2004, and Breitenmoser-Würsten et al The GPS data is unpublished (F.Zimmermann, pers. comm.). The data is proprietary to KORA and their respective partners, and was provided for my use solely for the purpose of this study. The staff at KORA provided the data in Microsoft Excel format listing the name of the lynx, the date and for GPS points the time of the reading, and the geographic coordinates of the reading. For GPS data, only 3D-validated points were provided, as this is a higher measure of GPS data accuracy. The VHF data provided was accurate to at least the square kilometer or better. VHF data could be biased by accessibility both in terms of where the lynx was captured and the tracking activity. GPS data would be biased only by the choice of capture location, and the corresponding home range of the collared lynx. Recently translocated lynx into Austria established permanent territories close to their release site (C.Breitenmoser-Würsten, pers. comm.), therefore deletion of initial data while territories were established, as done for lynx that were translocated to Northeastern Switzerland, was not necessary. Presence data from 100 lynx were available (GPS: n=27; VHF: n=73), two of which were translocated during the study period. The total number of VHF and GPS points was 33,570 (GPS 42%; VHF 58%), ranging from five to 2,206 per lynx (average 339), with 5,072 unique locations based on one point per 1km 2 cell. Presence locations were in the Swiss and French Jura Mountains, Northwest Swiss Alps, Swiss Valais Alps, Northeastern Switzerland, Kalkalpen National Park in Austria, and Trentino and Tarvisio regions of Italy. Presence points were converted to a Lambert Azimuthal Equal Area (LAEA) projection using ArcGIS Data were highly clustered in these seven geographic areas, which due to spatial autocorrelation and overweighting negatively impacts results of distribution models in Maxent (Dormann et al 2007). I therefore randomly sub-sampled the presence points in ArcGIS maintaining a minimum distance of five kilometers between points. Appendix 2 provides details of additional versions of sub-sampled data that were tested. Table 1 and Figure 2 provide an overview of the lynx presence data. 18

20 Original Unique Subsampled Telemetry Telemetry Lynx telemetry points points points (5km) Area source dates No. % No. % No. % No. % Jura VHF, GPS , , % 12,573 37% 1,998 39% % Northwest Swiss Alps VHF, GPS , , Northeastern Switz. VHF, GPS , , % 15,314 46% 1,797 35% 95 27% 11 11% 3,020 9% % 42 12% Valais (Switz.) VHF % 686 2% 138 3% 15 4% Austria GPS % 1,006 3% 252 5% 20 6% Italy (Trentino) GPS % 515 2% 211 4% 27 8% Italy (Tarvisio) GPS % 456 1% 143 3% 8 2% Total (1) (2) % 33, % 5, % % Table 1: Lynx presence data by location and telemetry source. (1) Total lynx includes two individuals from the Northwest Swiss Alps with VHF collars, who were translocated to Northeastern Switzerland; (2) Total sub-sampled points excludes three points in cells classified as water in the CORINE land use layer, so these points were excluded from Maxent analysis (two from Northwest Swiss Alps, one from Jura). 19

21 Figure 2: Lynx presence locations. Figure 2a shows all lynx presence points. The different colors represent different lynx. Figure 2b shows sub-sampled points with a minimum distance of five kilometers between points. The maps show how the presence data is clustered, although less so after sub-sampling. Maxent uses "background points" to establish a profile of environmental conditions throughout the study area. These background points, sometimes misleadingly called pseudo-absences, are contrasted with environmental conditions at presence points while 20

22 calibrating models. With the default setting in Maxent, the background points are spread evenly and randomly throughout the study area. The selection of background points can be altered either to reflect the impact of biased sampling efforts in different geographic areas using a "bias grid" (Phillips et al 2006), or to select background points from designated areas, usually in a pre-determined vicinity of presence points, using a "mask" file. Several bias grids and masks were prepared to evaluate their impact on the habitat suitability model. Using ArcGIS the minimum convex polygon (MCP) was drawn around lynx presence points in each geographic area and buffered by five kilometers (hereafter simply "MCP"), 50 kilometers, and 100 kilometers, approximately reflecting one and two maximum dispersal distances respectively (Barve et al 2011). These essentially reflect a sampling bias whereby all areas within the buffered MCPs surrounding presence points were assumed to be sampled with equal effort, and areas outside the buffered MCPs were unsampled. Actual sampling intensity would be a factor of the number of lynx in the regions, i.e. ratio of collared to total lynx per 100km 2, which is unknown, and the duration of monitoring, so the bias grids were intended to explore differing assumptions of sampling effort when telemetry data is used. Appendix 3 provides details of additional "bias grids" and "masks" that were tested. Lynx presence points were exported from ArcGIS with georeferenced coordinates and converted to.csv files in the format required for Maxent. Mask and bias files were saved with the same extent as environmental variables and converted to.asc files for use in Maxent. III.3. Environmental variables All environmental variable files were prepared in ArcGIS The extent of analysis was a rectangle bounding the Alpine Convention area. The resolution was 1km 2 based on the climate raster resolution, which was the coarsest of map layers. All files were projected using the LAEA projection with a central meridian of 10 and latitude of origin of 52. Files were modified to have the same extent and snapped to the same base raster, and converted to.asc files for use in Maxent. The accuracy of the environmental variable layers would impact the accuracy of the resulting habitat suitability model. Therefore I sought map layers that had the highest likelihood of accuracy, preferring data that was already in widely accepted use for SDMs, had 1km 2 resolution, came from a governmental mapping agency, had a regional rather than global extent, and was as current as possible. 21

23 Climate Climate is expected to play a larger role in impacting species distributions in extreme environments such as alpine areas (Araujo & Guisan 2006), although I made no a priori assumptions about how lynx (or their prey) would react to changes in climatic conditions. Climate data were obtained from Worldclim version 14.3, which provides 19 bioclimatic variables interpolated from monthly data collected at weather stations globally between 1950 to The climate variables cover annual, seasonal and extreme temperatures and precipitation (Hijmans et al 2005). Land use Lynx are known to prefer forest and shrub habitat (Zimmermann & Breitenmoser 2007). To include the impact of land use or land cover in the model, CORINE land use data version 16 was obtained from the European Environmental Agency. The CORINE land use raster was resampled from 100m to 1km resolution using nearest neighbor interpolation. The 15 second-level CORINE categories were reclassified in ArcGIS into nine categories (Table 2) based on assumptions about lynx ecology and which categories might be important for lynx movement and distribution. CORINE Level 1 CORINE Level 2 Study classification Artificial surfaces Urban fabric 1 Industrial, commercial and transport units 1 Mine, dump and construction sites 1 Artificial, non-agricultural vegetated areas 1 Agricultural areas Arable land 2 Permanent crops 3 Pastures 4 Heterogeneous agriculture areas 5 Forest and semi-natural areas Forest 6 Scrub and/or herbaceous vegetation 7 Open spaces with little or no vegetation 8 Wetlands Inland wetlands * 4 Maritime wetlands 9 Waterbodies Inland waters 9 Marine waters 9 * Inland w etlands, immaterial in study area, are counted as pasture based on visual inspection in Google Earth Table 2: Reclassification of CORINE land use categories The CORINE data is from Visual inspection of CORINE's land use change map since 2000 showed very little change in the Alpine area. No information was available on land use prior to 2000 nor after 2006, so it was assumed to be same as the 2006 data. This may be an oversimplification considering the 30-year duration of telemetry study ( ). 22

24 Human disturbance Anthropogenic disturbance was assumed to negatively impact lynx movements and distribution. As proxies for human disturbance, road density and distance to settlement were calculated from the EU's EuroGlobalMap version 5.1 (EGM). All road classes in the EGM, including motorways, primary and secondary roads, were used since the intent was to have an indication of disturbance, not barriers to movement. Local streets and forest roads were not included in the EGM. Road density was calculated in ArcGIS as kilometers of road within a five kilometer radius, using ArcGIS's Line Density tool. Distance to settlement points was calculated in ArcGIS using Euclidian distance, and capped at the furthest distance between lynx presence points and settlements (16.7 kilometers). The Human Influence Index (HII) was obtained from SEDAC/CIESIN at Columbia University, as an additional proxy for anthropogenic disturbance. HII was created from nine global data layers - population density, human land use and infrastructure (built-up areas, nighttime lights, land use/land cover), and human access (coastlines, roads, railroads, navigable rivers) based on 2004 data. Index values range from zero indicating no impact to 64 indicating maximum human influence. Elevation Elevation and measures derived from it were considered likely to exert strong influence over species distributions in alpine environments, and assumed to restrict distribution at highest elevations. A digital elevation model (DEM) layer was obtained from the Shuttle Radar Topography Mission (SRTM) version 4 (Jarvis et al 2008). Eight tiles covering the full study area were selected and downloaded, and mosaiced together in ArcGIS to create the elevation layer. ArcGIS was used to derive slope. Ruggedness was calculated as the vector ruggedness measure using an ArcGIS script, according to methodology applied by Sappington et al (2007). Correlation Maxent is considered fairly robust to correlated environmental variables (Elith et al 2006), but correlations can result in misleading interpretations of which variables contribute most to model calibration and negatively correlated variables can have offsetting and thus no impact. Variables were tested for correlation using Spearman's rho in SPSS 19 (student version). Spearman's rho was used because descriptive statistics and visual analysis of histograms showed that some variables were not normally distributed. 23

25 If two variables had correlations r s greater than 0.7, the one that contributed least in initial model results was deleted. Elevation, slope and ruggedness were correlated but retained because of their presumed differing ecological impact. The variables that were considered in preliminary runs and those that were retained after deleting correlated variables are shown in Table 3. Variable name Description Unit Temp1_MeanAnn Bio1 Annual Mean Temperature degree C Temp2_Diurnal Bio2 Mean Diurnal Temperature Range degree C yes Temp3_Isotherm Bio3 Isothermality (Bio2/Bio7*100) value Temp4_Seasonality Bio4 Temperature Seasonality (std dev*100) % yes Temp5_MaxWarm Bio5 Max Temperature of Warmest Month degree C Temp6_MinCold Bio6 Min Temperature of Coldest Month degree C Temp7_Range Bio7 Temperature Annual Range (Bio5-Bio6) degree C Temp8_WetQtr Bio8 Mean Temperature of Wettest Quarter degree C yes Temp9_DryQtr Bio9 Mean Temperature of Driest Quarter degree C Temp10_WarmQtr Bio10 Mean Temperature of Warmest Quarter degree C Temp11_ColdQtr Bio11 Mean Temperature of Coldest Quarter degree C yes Prec12_Annual Bio12 Annual Precipitation mm Prec13_WetMo Bio13 Precipitation of Wettest Month mm Prec14_DryMo Bio14 Precipitation of Driest Month mm yes Prec15_Seasonality Bio15 Precipitation Seasonality (coeff. of var.) % yes Prec16_WetQtr Bio16 Precipitation of Wettest Quarter mm Prec17_DryQtr Bio17 Precipitation of Driest Quarter mm Prec18_WarmQtr Bio18 Precipitation of Warmest Quarter mm Prec19_ColdQtr Bio19 Precipitation of Coldest Quarter mm Used in final models Dist. to settle Distance to settlement meters yes HII Human influence index index 0-64 yes Road density Road density within five kilometer radius km/ sq km yes Elevation Elevation meter yes Slope Slope degrees yes Ruggedness Vector ruggedness measure value 0-1 yes Table 3: Environmental variables used. All variables were used in preliminary models. "Yes" means the variable was used in models selected for further analysis (section IV.1.3). 24

26 III.4. Model III.4.1. Model development All SDMs were developed using Maxent version 3.3.3k. More than 160 models were prepared to explore the impact of using different presence locations, splits of presence data between calibration (training) and validation (test) data, locations of background points, and combinations of environmental variables, Tests were also done to explore the difference between interpolation across the entire study area, and projection, which involves training the model in one area (MCPs in this case) and projecting it to another temporal or geographic area (entire study area in this case) (Elith & Leathwick 2009). Maxent has the capacity to model complex relationships between variables which produces complex response curves and may lead to overfitting (Jiménez-Valverde et al 2008) so tests were also run using only simple linear and quadratic features, compared to the default settings which also use product, threshold and hinge features. Maxent uses a parameter called regularization to control how closely the predictive model matches calibration data (Elith et al 2010), and tests were run using the default value of one and higher values up to five representing a less closely fit model. Final models were calibrated using 75% of the presence data, with a random 25% set aside for model testing. All output was done in Maxent's default logistic format which produces output values ranging from zero (not suitable) to one (highly suitable). Resulting models were converted to raster format in ArcGIS for subsequent analysis. III.4.2. Model evaluation I used three measures to evaluate the accuracy and performance of the models. First was the area under the receiver operator characteristic curve (AUC), the most-frequently used measure of accuracy for Maxent SDMs. AUC measures the ability of a model to differentiate suitable versus unsuitable sites, and is not dependent upon a threshold value to categorize habitat as suitable or unsuitable (Fielding & Bell 1997). AUC values range from zero to one, with 0.5 being no better than random and higher scores indicating better results. AUC Train and AUC Test scores are calculated in Maxent, with the latter a stronger measure of predictive value. 25

27 Other measures of accuracy are threshold-dependent, meaning that a value, often arbitrary, is selected to categorize continuous suitability values into either suitable or unsuitable (Liu et al 2005). Omission rates, i.e. false negatives (presence points in areas indicated as unsuitable) at a particular threshold, are provided for both training and test data in Maxent results and can be used to compare accuracy between models (Pearson 2007). I considered omission rates on test results at two thresholds: i) 10th percentile training presence, which is the value above which 90% of presence points are correctly classified. The threshold is calculated based on training results, and omission at that threshold is calculated for test results; and ii) equal sensitivity and specificity, which balances omission errors and commission (false positive) errors. Rodda et al (2011) propose a more subjective evaluation. Their study of invasive Burmese pythons (Python molurus bivittatus) considered how well resulting maps predicted the native range of the species, whether the model overfit as judged by fragmented suitability in similar climatic regions, and whether predicted distributions passed an "eco-plausibility test," i.e. did they predict regions to be suitable that were ecologically illogical. Rodda et al also considered the minimum training presence threshold as a measure of the model's discriminatory power, with a very low minimum suitability value indicating that the model did not discriminate well but instead found a high proportion of cells to be suitable. I applied similar criteria and assessed "eco-plausibility" based on a priori assumptions. The first was based on lynx' historic distribution throughout the Alps, for which there are no indications that they were excluded from certain areas, so a "good" SDM for lynx was expected to have a reasonably broad distribution. Second is that overweighting of presence data from the Jura Mountains and Northwest Swiss Alps is a function of historic reintroductions and focused and ad-hoc sampling in those areas. Therefore any models that show excessively high suitability only in those areas are probably overfit and not reflecting ecological preference for those areas as compared to the rest of the Alps. Third, as a habitat specialist, lynx would selectively avoid areas of low suitability if possible and thus extremely low minimum training presence thresholds would be unrealistic as they imply a higher likelihood of finding lynx in marginal habitat. Using these three measures of accuracy, one model was selected as the preferred model to be used for final suitability analysis. The preferred model was re-run with ten-fold crossvalidation to obtain mean suitability values per cell across ten replicates. Uncertainty in predictive values was assessed as standard deviations from the mean for each cell. 26

28 III.5. Lynx population and patch size The preferred model gave continuous suitability values for the whole area of analysis. To determine population and patch size within the Alpine Convention area, binary suitability maps were required. Two versions of these maps were created in ArcGIS at both the 10th percentile training presence, and equal sensitivity and specificity thresholds, by reclassifying cells with values below the threshold as unsuitable and cells with values above the threshold as suitable. Patches of suitable habitat were created using ArcGIS's RegionGroup tool to identify adjacent suitable cells that were linked together. Patches smaller than 50 km 2, the minimum size considered necessary to hold even one lynx, were eliminated. To identify possible subpopulations, large patches were subjectively split into multiple subsections using major highways, rivers, or areas of high elevation (and therefore potentially glaciers or snow/ice fields) as borders, on the assumption that lynx would rarely cross such major barriers thus creating sub-populations within larger patches. These barriers were digitized in ArcGIS using the relevant environmental variable layers, and used to categorize each suitable cell into one of the resulting subsections. The number of lynx that could inhabit each patch was calculated in Microsoft Excel at three different densities, from one to three individuals per 100 km 2, based on densities observed over time in central European lynx populations (Breitenmoser-Würsten et al 2001, Zimmermann et al 2012). IV. RESULTS IV.1. Model and variables IV.1.1. Lynx presence points and background The clustered nature of the presence points essentially mandated sub-sampling, which was tested in various ways (above and Appendix 2). Results at this stage of the process were evaluated using AUC and omission rates (Table 4). Using one unique location for cells that had multiple presence points (n=5,072) improved performance substantially compared to using all presence points (n=33,570). 27

29 Sub-sampling to select presence locations with a minimum distance between points increased model performance even more, although no material difference in performance was found whether the spacing between points was 2.5, five or ten kilometers. Splitting the presence points geographically did not improve in model performance further, and these methods were not preferred because some of the environmental variance would be lost by excluding certain geographic sections of the data. Omission on test results at AUC thresholds Presence points # points Train Test 10% training presence Equal test sens & spec All points 33, Unique presence points 5, Proportional split based on land area (1) km distance between points km distance between points km distance between points Alps only 3, Arbitrary geographic areas (2) 286 train/ test Excluding old geographic areas (3) (1) Explained in Appendix 2 (2) Area A (testing) = northern Jura, northern Northw est Sw iss Alps, Valais, Tarvisio / Area B (training) = everyw here else (3) Excludes oldest data pre-1998, corresponding to northern Northw est Sw iss Alps, and Valais Table 4: Sub-sampling performance results. 0<AUC<1, with higher scores better. Out of the three distance sub-samples, the version with five kilometers between presence points had the median AUC Training and highest AUC Test. This version was chosen as the standard set of presence data for all other analysis. The distance-based approach to subsampling is frequently used in distribution modeling studies (e.g. Barve et al 2011, Graf et al 2006) with varying distances depending on the species and area being studied. The five kilometer distance for this study seemed reasonable for a wide-ranging mammal such as lynx, and was a compromise between the 2.5 kilometer version which resulted in a data set that was still relatively clustered and the ten kilometer distance which resulted in only 128 presence points. That would be a sufficient sample size to use in Maxent but small compared to the original data set available for this study. The other major decision regarding location is that of background, which is impacted by using masks or bias grids to designate from where the background points are selected. This impacts statistical measures of model accuracy and is discussed in section IV

30 IV.1.2. Environmental variables There was little consistency between model versions about which environmental variables had the most significant impact on model results. Not only did the most important variables change as presence points, background locations, and model parameters were altered, but also using different combinations of variables together gave inconclusive results. Nevertheless, in the model versions selected for further analysis (section IV.1.3), out of 13 variables used, five stand out as frequently important. Two climate variables, mean temperature of the coldest quarter and precipitation of the driest month, and CORINE land use, elevation and slope were important for at least five out of eight models using the full set of 13 variables. CORINE land use, elevation and distance to settlement were important for all for models that excluded climate variables. # times in top 5 All variables Excl. climate Variable (8 models) (4 models) Mean diurnal temp range (T2) 4 n/a Temperature seasonality (T4) 1 n/a Mean temp of wettest quarter (T8) 3 n/a Mean temp of coldest quarter (T11) 7 n/a Precipitation of driest month (P14) 5 n/a Precipitation seasonality (P15) 3 n/a CORINE 6 4 Distance to settlement 0 4 Human Influence Index 0 2 Road density 0 2 Elevation 5 4 Slope 6 3 Ruggedness 0 1 Table 5: Variable importance. For each variable, the number of times that it was one of the top five most important variables for each model is shown. Bold font shows variables that were in the top five for at least five of eight models using all 13 variables. Results were split to consider models with climate variables (left column) separately from models without the climate variables (right column). For the final version of the model chosen for patch and population analysis, the variables that were most important to model results are shown in Table 6. CORINE land use and slope contributed the most to model "gain," a statistical measure of model fit calculated by Maxent (Phillips et al 2006). The high permutation value, which measures variables upon which the 29

31 model depends most, and training and test gains (not shown), indicate that elevation is also important. Percent contribution Permutation importance Variable CORINE Slope Mean temperature of wettest quarter Mean temperature of coldest quarter Human Influence Index Precipitation of driest month Elevation Mean diurnal temperature range Table 6: Variable importance for model version chosen for population and patch analysis, based on ten-fold cross-validation. Higher values indicate the variable is more important. Variables with both percent contribution and permutation importance less than 2.0% are not shown. IV.1.3. Model evaluation Initial versions of the model were created simply to explore the impact of changing one or more input or parameter. Results were assessed visually, and no attempt at formal evaluation was done at this preliminary stage. The initial results showed two distinctive patterns, either a notable unsuitable area in the central Alps or a generally widespread distribution across the entire Alpine area. I then began to explore in a more concerted manner, alternatively systematic and heuristic, specifically what changes in input or parameters caused the pattern of suitability to change. I identified that two options caused the suitability pattern to differ substantially. One was excluding all climate variables. The other was using the MCP mask to select background points from geographic areas from which telemetry data was obtained, as compared to Maxent's default option which spreads background points across the full study area. A final set of models was then prepared for analysis using these two options individually and combined. For comparison purposes, models were also created using the MCP mask buffered to 100 kilometers to select background points. All options were run using default variable features, and a simplified version using only linear and quadratic features with increased regularization to an intermediate value of 2.5. These final ten models were 30

32 evaluated according to the three criteria I had established. Appendix 5 provides an overview of the settings, parameters and data sets used for the final models, and a discussion about using simplified instead of default model parameters. AUC scores were high for almost all models where a background mask was not applied. The base model excluding correlated variables had an AUC Test of Simplifying the model had little impact (AUC Test 0.915). Excluding the climate variables decreased AUC Test to which is still considered a good result. AUC Test scores were for models using the MCP mask to select background points from the telemetry areas, and using the MCP mask buffered to 100 kilometers (both with climate variables). This decrease of AUC is a known reaction when the background extent is limited, and a similar decrease was observed in other studies with restricted background area (Rodda et al 2011) or restricted study area (Edrén et al 2010). Because of this, AUC cannot be used to directly compare models with different background areas and extents, and the lower AUC does not necessarily indicate a less-performing model. See Appendix 6 for further discussion on interpreting AUC scores. Omission rates were considered as an alternative accuracy measure for the final models. Omission scores on test data sets ranged from to Using masks to restrict background locations resulted in the same or lower omission rates compared to equivalent unmasked versions in half of the models; in the other half, omission rates increased with a mask. Most differences were immaterial, although using the most constraining MCP mask did produce both the largest decrease in omission at the 10% training presence threshold and the largest increase at the equal test sensitivity and specificity threshold. However, all models that produced good quantitative results failed the subjectivity test. Only the versions with the MCP mask and the versions without climate variables produced patterns of suitable areas spread throughout the Alps reflecting the a priori assumptions. The other versions showed very high suitability only in the Jura Mountains and Northwest Swiss Alps, the areas of dense presence points, and little to no suitability in the central Alps, i.e. they simultaneously overfit and were ecologically unlikely. As well, models without masks produced very low minimum training presence thresholds indicating low ability to distinguish between suitable and unsuitable sites, or a generalist species which is not the case for lynx. Table 7 shows summary results of evaluation measures, and Figure 3 show habitat suitability maps of the related models. 31

33 Ref Omission on test AUC results at thresholds Min. Description of model Background Train Test 10% train. presence Equal test sens & spec train. pres. 3a Default settings Entire extent yes no 3c Default with MCP mask MCP no maybe 3e 3g 3i Default with 100km buffered MCP mask Default without climate variables Default without climate variables, with MCP mask 100km buffer around MCP yes no Entire extent no maybe MCP no maybe 3b Simple settings Entire extent yes no 3d Simple with MCP mask MCP no yes 3f 3h 3j Simple with 100km buffered MCP mask Simple without climate variables Simple without climate variables, with MCP mask 100km buffer around MCP Subjective criteria Overfit Ecoplausibility yes no Entire extent no yes MCP no maybe Table 7: Evaluation results for selected models. "Ref" is reference to maps in Figure 3. MCP is minimum convex polygon around telemetry points. AUC, omission rates and subjective criteria are as described in the text. Red font on subjective criteria indicates negative results. 32

34 Figure 3: Habitat suitability maps for selected model versions. Models with default parameters are on the left; models with simplified features and regularization are on the right. Figure 3a and 3b are the base versions. Figures 3c to 3j show the impact of using two different masks to select background locations and excluding climate variables, respectively. 33

35 The base models with climate variables and no mask failed the subjective tests, as did the models with the MCP buffered to 100 kilometers. Of the remaining models, two produced results that appeared to be ecologically plausible and not overfit (Figures 3d, 3h). Of these, the model with simplified features and the MCP mask (Figure 3d) was selected as the preferred model for further analysis on suitable habitat, because it had the most reasonable minimum training presence suitability value and a higher AUC value (keeping in mind that the unmasked version (Figure 3h) has a similar background as and should be compared to the base models). IV.2. Lynx population and patch size The final habitat suitability map (Figure 4, based on ten-fold cross-validation of Figure 3d) shows good habitat suitability for lynx throughout the Alps except at highest elevations, with somewhat higher suitability in the western Alps. Figure 5 shows the uncertainty of the predictive suitability map, based on standard deviations of the ten replicate model runs. Model results are less certain in the southern area of the Alpine arc as it approaches the French and Italian coasts, and relatively less certain in the central-eastern Alps. Figure 4: Final habitat suitability map 34

36 Figure 5: Map showing the uncertainty of the predictive map in Figure 4, based on standard deviations from ten-fold cross-validation of the preferred model (Figure 3d). The final suitability map was thresholded into suitable and unsuitable areas at two levels of suitability: i) corresponding to the suitability value for the 10th percentile training presence; and ii) corresponding to the threshold at which sensitivity equals specificity in test results. The patches that were created by linking contiguous suitable cells at each threshold are shown in Figure 6. Figure 6b was assessed as overly pessimistic with significant gaps between patches not reflecting the perceived reality on the ground. Figure 6a was deemed reasonable and subjectively selected for further analysis of lynx population and patch size. 35

37 Figure 6: Suitable habitat at two thresholds. Colored areas are suitable habitat at the threshold indicated; white areas are unsuitable. The different colors represent areas of contiguous cells created using ArcGIS RegionGroup. Lynx presence points are the sub-sample with five kilometers between points, shown here to illustrate whether they are in suitable (colored) or unsuitable (white) areas. 36

38 Within the Alpine Convention area, a total of approximately 103,600 km 2 of suitable habitat exists excluding patches less than 50 km 2. This comprises approximately 54% of the total Alpine Convention area, and is well-spread in one continuous patch throughout most of the entire Alpine arc (Figure 6a), stretching into the Dinaric Mountains. After dividing the larger continuous patch based on assumed barriers including major highways, rivers, and areas of high elevation, thus representing different assumed lynx sub-populations, I obtained 32 patches within the Alpine Convention area ranging in size from 57 to 17,376 km 2. Of this, 22 patches (Figure 7) are greater than 400 km 2, considered large enough to support individual sub-populations of lynx, not just a few individual lynx. Table 8 presents the possible number of lynx in each patch at three different density levels reflecting actual recorded lynx densities in central Europe. In total, the Alps could support between 1,024 to 3,017 lynx in 22 sub-populations, and up to 1,035 to 3,107 lynx including isolated individuals in small patches. Figure 7: Suitable habitat patches after subdivision by barriers. The different colored patches are assumed to represent lynx sub-populations. Patches greater than 400 km 2 are numbered 1-22 in decreasing order of size. Neighboring areas with lynx populations are J- Jura, V-Vosges, and D-Dinaric Mountains. 37