Mapping range dynamics from opportunistic data: spatiotemporal modelling of the lynx distribution in the Alps over 21 years

Mapping range dynamics from opportunistic data: spatiotemporal modelling of the lynx distribution in the Alps over 21 years A. Molinari-Jobin 1,M.Kery 2, E. Marboutin 3, F. Marucco 4, F. Zimmermann 1, P. Molinari 5, H. Frick 6, C. Fuxj ager 7,S.W olfl 8, F. Bled 9, C. Breitenmoser-W ursten 1, I. Kos 1,M.W olfl 11, R. Cerne 12,O.M uller 6 & U. Breitenmoser 13 1 KORA, Muri, Switzerland 2 Swiss Ornithological Institute, Sempach, Switzerland 3 ONCFS, Gieres, France 4 Centro Conservazione e Gestione Grandi Carnivori, Cuneo, Italy 5 Italian Lynx Project, Tarvisio, Italy 6 Office of Environment, Vaduz, Liechtenstein 7 Nationalpark Kalkalpen, Molln, Austria 8 Lynx Project Bavaria, Lam, Germany 9 Carnivore Ecology Laboratory, Mississippi State University, Mississippi State, MS, USA 1 University of Ljubljana, Ljubljana, Slovenia 11 Bavarian Agency of Environment, Hof, Germany 12 Slovenia Forest Service, Ljubljana, Slovenia 13 Center for Fish and Wildlife Health, University of Berne, Bern, Switzerland Animal Conservation. Print ISSN 1367-943 Keywords autologistic; citizen science; colonization; distribution dynamics; occupancy models; Lynx lynx; opportunistic data; detection probability. Correspondence Anja Molinari-Jobin, KORA, Thunstrasse 31, 374 Muri, Switzerland. Email: a.molinari@kora.ch Editor: Julie Young Associate Editor: Sarah Converse Received 6 July 216; accepted 17 July 217 doi:1.1111/acv.12369 Abstract The Eurasian lynx is of special conservation concern based on the European Union s Habitat Directive and its populations need to be maintained or restored at favourable conservation status. To evaluate lynx population status, appropriate monitoring needs to be in place. We modelled the distribution dynamics of lynx in the Alps (2 km 2 ) during 1994 214 at a resolution of 1 km 2. Lynx distribution and detection probability varied by year, country, forest cover, elevation and distance to the nearest release site. Occupancy of neighbouring quadrats had a strong positive effect on colonization and persistence rates. Our analyses demonstrate the importance of accounting for imperfect detection: the raw data underestimated the lynx range by 55% on average, depending on country and winter. Over the past 2 years the Alpine lynx range has expanded at an average rate of 4% per year, which was partly due to the lynx translocations to new areas. Our approach to large-scale distribution modelling and analysing trends using site occupancy models can be applied retrospectively and is useful in many cases where a network of trained people is established to report the presence of target species, for example, in Europe where member states of the European Union have to report conservation status of species of community interest. Hence, dynamic occupancy models are an appealing framework for inference about the large-scale range dynamics based on opportunistic data and a useful tool for large-scale management and conservation programmes. Introduction Coexistence between large carnivores and humans is not always easy to achieve. It virtually always requires active management, such as reintroduction, translocation, hunting or lethal control of large carnivore populations (Linnell, Salvatori & Boitani, 28; Treves, 29). The type of management required depends on management goals as well as on the status of a population, whether managers deal with an established and viable population, with single individuals at an expansion front or with a population that may be facing extinction (Nichols & Williams, 26). Monitoring the dynamics of a population is therefore a crucial part of management. 168 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

Occupancy modelling of lynx range dynamics Monitoring the distribution of a species at the landscape scale presents particular challenges: (1) data collection over a large area is inherently costly, so choice of adequate methods to provide useful information with minimal costs is even more crucial than in other monitoring programs (Jones, 211); (2) species detection probability is typically far less than 1 and tends to vary over space and time (Kery & Schmid, 24; Nichols, Thomas & Conn, 29). Improvements in monitoring efficiency through more experienced observers or refined technical equipment will lead to an increase in observations. Increasing observation effort over time (e.g. more people and/or more surveys) is the rule for most citizen science monitoring schemes. This needs to be corrected (Altwegg, Wheeler & Erni, 28; Kery et al., 21), because otherwise this could result in biased trend estimates. Site occupancy models (MacKenzie et al., 22, 23; Tyre et al., 23) jointly estimate occurrence and detection probability and have become invaluable tools for monitoring the distributions and population status of a wide variety of taxa (e.g. Finley, White & Fitzgerald, 25; Olson et al., 25; Eraud et al., 27; Altwegg et al., 28; Ferraz, Sberze & Cohn-Haft, 21; Walls, Waddle & Dorazio, 211). Importantly, dynamic occupancy models directly allow estimating the parameters that govern distributional change: the probability of local extinction (or alternatively, of persistence) of an occupied site and the probability of colonization of an unoccupied site. These quantities represent valuable knowledge for managers who are engaged in species conservation or conflict management. The Eurasian lynx Lynx lynx had originally occurred in the entire range of the Alps but was completely eradicated by 193 (Breitenmoser & Breitenmoser-W ursten, 28). Reintroductions have taken place first in Switzerland (1971 1976), Italy (1975) and Austria (1977 1979), and more recently in north-eastern Switzerland (21 28), northeastern Austrian Alps (211 217) and north-eastern Italy (214). Following the early Swiss reintroductions, a lynx population became established in the north-western Alps. In contrast, the 197s reintroductions in Austria and Italy failed to establish a population (Breitenmoser & Breitenmoser- W ursten, 28). Another reintroduction took place in the Dinaric Mountains in southern Slovenia in 1973, from where lynx expanded into the south-eastern Alps of Slovenia, Italy and Austria (Cop & Frkovic, 1998). All Alpine countries have adopted the Pan-Alpine Conservation Strategy for the lynx (Molinari-Jobin et al., 23), which states the goal of re-establishing and maintaining a vital lynx population throughout the Alpine arc, in coexistence with people. Due to the lynx s secretive lifestyle and uneven survey effort, considerable uncertainty remains about the actual extent of occurrence and the range dynamics of the lynx in the Alps. Uncertainty about the effective species range may delay necessary conservation actions or in general lead to inappropriate management decisions. We established an Alp-wide network of lynx experts that aims to collect lynx occurrence data from the general public: using this citizen science approach, our objectives were to evaluate spatial and temporal variation in the lynx occurrence, detection, local extinction and colonization in the Alps over the last two decades. Specifically, we aimed to obtain accurate estimates of occupancy-based population distribution and trends by reducing biotic and methodological differences among countries that might affect species distribution measurement error to analyse the range dynamics of lynx in the Alps. Materials and methods Study area and sampling design The Alps are the largest mountain range in Europe, extending over c. 2 km 2, and comprising of seven countries: France, Italy, Switzerland, Liechtenstein, Germany, Austria and Slovenia. After the brown bear Ursus arctos and the wolf Canis lupus, the lynx is the third largest terrestrial predator and the largest felid in Europe. To monitor the lynx distribution in the Alps we relied on game wardens, hunters, naturalists and the general public to report signs of lynx presence. Conducting research with assistance from the public can be far more complex than a traditional scientist-led approach (Bonter & Cooper, 212). Improving data reliability is critical to the success of such projects. We established a network of regional experts of over 13 members in the French Alps, and c. 23 in the Italian, 15 in the Swiss, 4 in the German, 3 in the Slovenian, 1 in the Austrian Alps and 1 in Liechtenstein. They collect signs of lynx presence, for example, direct observations, photos, dead lynx, prey remains, tracks, scats and vocalizations, that are validated directly in the field or by photo-documentation and classified by national lynx experts in charge (Molinari-Jobin et al., 212). Lynx tracks and prey remains may be confounded with canid signs. Additionally, hare Lepus sp. and badger Meles meles tracks may be mistaken for lynx tracks. Network members collect lynx observations made by themselves and by the general public and send them to their national centre in charge of the monitoring at the country level. Additionally, the general public has the opportunity to report signs of presence directly to national lynx experts by means of forms available on specific webpages (e.g. http://www.kora.ch/index.php?id=158&l=, http://www.luchsprojekt.de/_nebennavigation/kontakt/in dex.html). All signs of lynx presence were classified into three reliability categories (Molinari-Jobin et al., 212): C1 are so-called hard-fact data, for example, dead lynx and lynx photos, while C2 are confirmed data, for example, mainly verified prey remains and tracks documented by photos or directly verified in the field, where verification was done by a trained lynx network member. Finally, C3 are unverified data, such as prey remains and tracks too old or badly documented and any direct observation that by its nature cannot be verified. To assess the distribution dynamics of lynx, we used only the categories C1 and C2 to avoid an inflation of occupancy probability due to false positives (Royle & Link, 26; Miller et al., 211). Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London 169

Occupancy modelling of lynx range dynamics From 1995 to 214, a total of 12 46 signs of lynx presence were reported in the Alps, of which 2152 (17%) were classified as C1 and 6263 (5%) as C2. To meet the model assumption of closure (see below), we here only used data for the three bi-monthly seasons from November to April, resulting in 691 presence signs. Eurasian lynx show the general pattern of social organization and territoriality of solitary cats (Sunquist & Sunquist, 22). Kittens are born in May/June (Breitenmoser-W ursten et al., 21) and become independent in April (Zimmermann, Breitenmoser-W ursten & Breitenmoser, 25). We documented the distribution of the lynx at the scale of the 1 9 1 km grid of the European Environment Agency (http://www.eea.europa.eu/data-and-maps/data/eeareference-grids-1). This resulted in a study area comprising 2183 hundred square kilometre quadrats. This grid cell size corresponds to the approximate home-range size of female lynx in the Alps (Breitenmoser-W ursten et al., 21; Molinari-Jobin et al., 27). We used mean elevation, per cent forest cover, human population density and distance to reintroduction sites as explanatory variables in our model. Distance to release sites was recalculated with every lynx translocation that took place during our study period. For detection probability we additionally expected variation regarding the country, (bimonthly) season and the level of search effort. To identify the per cent forest within our 1 km 2 quadrats, we used the per cent of 1 9 1 m grid cells of Corine Land Cover database from 2 (CLC2) that were classified as forest (broad-leaved, conifer and mixed forests). Human density was obtained from the NASA socioeconomic and applications centre (http://sedac.ciesin.columbia.edu/data/set/gpw-v3- population-151count/data-download) and elevation from http://srtm.csi.cgiar.org. We used a 3-level network factor to account for variation in search effort among quadrats and four periods (1995 1999, 2 24, 25 29, 21 214): means that we have no information regarding the search effort. This usually means that search effort was small, but we still assume that it is never exactly zero; 1 means that trained lynx monitoring network members are present and 2 means that experienced lynx monitoring network members are present and actively search for lynx signs. If a wolf or brown bear monitoring network was established in an area, we assigned a 1 to this area, assuming that the network members would systematically also report signs of lynx presence. To estimate the extent of the lynx distribution and identify factors that govern its dynamics, we used as data the presence of at least one lynx record in a 1-km 2 quadrat per 2-month season (secondary period) and winter (primary sampling period); the three seasons per winter (November December, January February, March April) providing the replicate detection non-detection data. Within a season we ignored more than one record per quadrat and simply distinguished between quadrat seasons in which no lynx was recorded (yielding a ) and those with at least one record (yielding a 1). We lack information from Slovenia between 1995 and 21, resulting in 93 missing data for that country. Our analysis requires two main assumptions: (1) Lynx distribution remains unchanged within each winter (November April). This closure assumption may have been violated to some degree, for example, dispersing lynx who have not established a territory by the end of October. As a consequence, our estimate of occupancy may refer to the area of use rather than of permanent presence of lynx (see MacKenzie et al., 26; and Efford & Dawson, 212 for this distinction). (2) Owing to the large number of persons and organizations that collaborate in the Alpine lynx monitoring, we assumed that there is a non-zero chance of detecting a lynx in every occupied 1 km 2 cell in each winter, that is, no occupied cell was totally devoid of monitoring effort during the study period in any winter (Molinari-Jobin et al., 212). Analysis of distribution dynamics For inference about the lynx distribution dynamics in the Alps, we used a dynamic species distribution modelling framework that formally acknowledges the possibility of false-negative detection errors: dynamic site occupancy models (MacKenzie et al., 23; also see Royle & Kery, 27; Royle & Dorazio, 28; Kery & Schaub, 212). These models describe the data as a function of three processes, which describe the initial system state, the state dynamics and the observation process: (1) Initial state: z i;1 Bernoulliðw i Þ (2) State dynamics: z i;kþ1 jz i;k Bernoulliðz i;k / i;k þð1 z i;k Þc i;k Þ (3) Observation process: y i;j;k jz i;k Bernoulliðz i;k P i;j;k Þ where z i;k and y i;j;k denote the true, latent presence absence state and the detection non-detection observation, respectively, for site i (i = 1... 2183), winter k (k = 1...21) and season j (j = 1...3). The four model parameters are the probabilities of initial occupancy (w i ), persistence (/ i;k ; this is simply 1 minus extinction probability e i;k ), colonization (c i;k ) and of detection (P i,j,k ). Occupancy probability after the first year is a function of the first three parameters. All parameters can be modelled in groups or as functions of continuous covariates to test for likely sources of variation and to accommodate their effects in the inferences. In our analysis, we expressed these parameters, on the logit scale, as a linear combination of a series of covariates, exactly as in a logistic regression (McCullagh & Nelder, 1989; Kery, Guillera-Arroita & Lahoz-Monfort, 213). We built structure into our hierarchical model based on our knowledge of both lynx biology and the specifics of the field sampling process and fitted the following model, where w, φ, c and P denote the probabilities of initial occupancy, persistence, colonization and detection, respectively, and i, j and k are the indices for sites, 2-month periods and winters, respectively: logitðw i Þ¼alpha.lpsi1þ beta.lpsi1[1] * elev i þ beta.lpsi1[2] elev 2 i þ beta.lpsi1[3] * forest i þ beta.lpsi1[4] human.density i þ beta.lpsi1[5] * human.density 2 i þ beta.lpsi1[6] * dist.release i;k¼1 ; 17 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

Occupancy modelling of lynx range dynamics logitð/ i;k Þ¼ alpha.lphi þ lphi.year k þ beta.lphi[1] * elev i þ beta.lphi[2] * elev 2 i þ beta.lphi[3] * forest i þ beta.lphi[4] * human.density i þ beta.lphi[5] human.density 2 i þ beta.lphi[6] * dist.release i;k þ beta.lphi[7] * autocov i;k ; with random winter effects lphi.year k Normal(, sd:lphi:year 2 Þ; logitðc i;k Þ¼alpha.lgamma þ lgamma.year k þ beta.lgamma[1] elev i þ beta.lgamma[2] * elev 2 i þ beta.lgamma[3] * forest i þ beta.lgamma[4] human.density i þ beta.lgamma[5] human.density 2 i þ beta.lgamma[6] dist.release i;k þ beta.lgamma[7] * autocovi,k ; with random winter effects lgamma.year k Normalð; sd.lgamma.year 2 Þ; logitðp i;j;k Þ¼alpha.lp gðiþ þ lp.year k þ beta.lp[1] * elev i þ beta.lp[2] * elev 2 i þ beta.lp[3] * forest i þ beta.lp[4] * human.density i þ beta.lp[5] human.density 2 i þ beta.lp[6] * dist.release i;k þ beta.lp[7] * autocov i;k þ beta.lp.nw nwði;kþ þ beta.lp.season j þ f i;k ; where g(i) is a variable that contains the country to which site i belongs, nw(i,k) is another variable that contains the value of network for site i and winter k, and where there are the following random effects for country, winter and each site/winter combination: alpha.lp gðiþ Normal(mu.alpha.lp, sd.lp.country 2 Þ; lp.year k Normal(, sd.lp.year 2 Þ f i;k Normalð; sd.lp.eps residual 2 Þ Thus, we estimated effects of five habitat covariates in all four processes: elevation, elevation squared, forest cover, human density and human density squared. These three factors were identified previously to influence lynx habitat selection (Zimmermann, 24). We were not able to include prey availability as a covariate because comparable data on prey density throughout the Alps and over 2 years are not available. Lynx in the Alps were re-introduced and there are likely historic effects of this that persist, hence we fitted an effect of the distance to the nearest release site into the parameters of the sub-models for the initial state and state dynamics. We had four factors in our analysis: winter has 21 levels, country has 6 and network and season have both 3 and the former 2 were modelled as random effects. Neighbourhood density is the estimated proportion of occupied cells in the preceding winter, using all eight contiguous cells around a focal cell. This autocovariate accounts for the fact that a cell is more likely to become colonized and a lynx presence to persist when it is surrounded by more cells that were occupied during the previous winter, since colonists and rescue animals (preventing local extinction; Brown & Kodric-Brown, 1977) are most likely to come from neighbouring cells. We computed the values of the autocovariate directly inside of our model, that is, based on the estimated value of the latent presence absence z i;k. Therefore, our autocovariate is corrected for imperfect detection, as did Bled, Royle & Cam (211), Bled, Nichols & Altweg (213) and Broms, Hooten & Fitzpatrick (216). As is customary for batches of similar parameters, we treated country and winter effects in detection probability as random. In addition to these and the environmental covariate effects, detection probability was modelled with effects of network, season and a random site-by-winter effect, or residual, which accommodated unexplained variation in detection probability among every combination of site and winter. We used the Bayesian general-purpose modelling software JAGS (Plummer, 23) to fit our model, using vague priors for all the parameters (see the Appendix S1 for a description of the model, including the priors used, in the BUGS language). We ran two Markov chains for 2k iterations, discarded the first 15k as a burn-in and thinned by 1, resulting in 1 samples from the joint posterior distribution. This took 28 days on a 2.4-GHz Windows machine with 16 cores and 32 GB RAM and was sufficiently long that values of the Brooks Gelman Rubin statistic <1.1 (Brooks & Gelman, 1998; Gelman & Hill, 27) and visual inspection of the traceplots suggested that convergence had been reached. We assessed the goodness of fit of our model using posterior predictive checks and a Bayesian P value (Gelman, Meng & Stern, 1996) for a chi-squared test statistic computed on a summary of the observed data: the total number of occasions per quadrat and winter (Kery & Schaub, 212; Kery & Royle, 216). This yielded a Bayesian P-value of.43, which suggested that the fit of our model could be improved, since ill-fitting models have values of the statistic near or 1. However, the magnitude of the lack of fit was extremely small, since the ratio of the test statistic for the observed and the expected datasets (c.hat) was 1.11. In maximum likelihood analyses of capture recapture and related models (e.g. Johnson, Laake & ver Hoef, 21 for a hierarchical distance sampling model), it is customary to assume that such small values of lack of fit represent simple overdispersion (i.e. unstructured noise rather than a structural breakdown of the model) and then to adjust uncertainty measures and AIC scores by the c.hat pvalue. ffiffiffiffiffiffiffiffiffi In our case, SEs would have to be inflated by c.hat, which is about 5%. This is such a small correction that we simply chose to ignore it. We consider as significant effects those whose 95% credible interval (CRI) does not cover. Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London 171

Occupancy modelling of lynx range dynamics Results Factors affecting occupancy, distribution dynamics and detection parameters of Alpine lynx 1994 214 Initial occupancy (w) in 1994 was higher for quadrats with extensive forest cover and located nearer to a release site (Table 1.1). Occupancy was estimated at.1% in tree-less habitats and at 3% in an entirely forested quadrat and at 2% in a quadrat right at a release site, declining to essentially % 25 km away (Fig. 1, row 1). Persistence probability was higher in more forested quadrats (Table 1.2), increasing from about 69 to 92% along a gradient from a treeless to a totally forested quadrat (Fig. 1, row 2 left). Neighbourhood density had a strong positive effect on persistence, which increased Table 1 Estimates of hyperparameters in the dynamic species distribution model of Alpine lynx in 6 countries during 21 winters (1994 214), with posterior means and standard deviations and the lower and upper bound of a percentile-based 95% Bayesian credible interval (CRI) given. Probability denotes the proportion of the posterior mass on the same side of zero as is the mean, that is, of the probability that an effect is greater or less than zero. Effects whose 95% CRI does not contain zero are printed in bold. All effects are on the logit scale. Parameter names are similar to those in the BUGS model description in Supporting Information Appendix S1, but slight changes were made to make them self-explanatory Parameter Mean SD 2.5% 97.5% Probability 1. Submodel for initial occupancy probability (w) alpha.lpsi1 4.32.55 5.25 3.45 1. beta.lpsi1[elev].536.361.129 1.279.931 beta.lpsi1[elev^2].137.275.737.343.681 beta.lpsi1[forest].632.315.33 1.257.981 beta.lpsi1[hdens].74 3.256 6.386 6.267.58 beta.lpsi1[hdens^2].267 3.21 6.584 6.58.536 beta.lpsi1[dist.release] 1.58.397 2.427.98 1. 2. Submodel for persistence probability (φ) alpha.lphi.528.32 1.159.11.95 sd.lphi.year.373.24.26.914 1. beta.lphi[elev].12.19.367.354.532 beta.lphi[elev^2].123.151.28.43.81 beta.lphi[forest].372.167.46.76.989 beta.lphi[hdens] 2.399 2.378 2.327 7.58.837 beta.lphi[hdens^2] 2.66 2.758 3.344 7.58.767 beta.lphi[dist.release].61.216.337.525.63 beta.lphi[neig.density] 4.275.64 3.171 5.722 1. 3. Submodel for colonization probability (c) alpha.lgamma 4.781.21 5.154 4.378 1. sd.lgamma.year.359.157.64.76 1. beta.lgamma[elev].231.113.45..975 beta.lgamma[elev^2].12.1.182.2.551 beta.lgamma[forest].88.12.13.297.82 beta.lgamma[hdens] 3.296 1.913 7.386.12.972 beta.lgamma[hdens^2] 1.62 3.53 5.77 6.335.667 beta.lgamma[dist.release].752.117.987.527 1. beta.lgamma[neig.density] 6.6.56 4.97 6.979 1. 4. Submodel for detection probability (P) alpha.lp 3.812.514 4.756 2.716 1. sd.lp.country 1.45.378.478 1.865 1. sd.lp.year.192.65.8.339 1. beta.lp[elev].196.77.348.52.996 beta.lp[elev^2].2.54.84.126.637 beta.lp[forest].541.79.391.695 1. beta.lp[hdens] 2.937 1.57 5.752.36.971 beta.lp[hdens^2].916 2.392 3.661 5.89.637 beta.lp[season2].274.68.138.41 1. beta.lp[season3].432.7.297.571 1. beta.lp[network2] 1.65.213 1.227 2.75 1. beta.lp[network3] 2.788.222 2.343 3.232 1. sd.lp.eps_residual.77.7.557.846 1. 172 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

.1. Occ. (psi1).2 Occupancy modelling of lynx range dynamics..1.2.3.4 Occ. (psi1) 2 4 6 8 1 5 1 15 2 25 3 Dist. to nearest release site (km) 2 4 6 8 1.2.1 Colo. (gamma)..9.8.7.6 Pers. (phi) 1. Forest cover (%) 5 2 3 4 5 Detection (p) 15 2 25 3 5 1 15 2 25 3 35 Elevation (m a.s.l.)..1.2.3.4.5.4.3.2 Detection (p).1 1 3 35 Dist. to nearest rel. site (km). 5 25.8 6 Human pop. density (per 1 km2) 2.4 Colo. (gamma) 1 15..8.4 1 Elevation (m a.s.l.). Colo. (gamma) Forest cover (%) 2 4 6 8 1 Forest cover (%) Figure 1 Spaghetti plots of the predicted marginal relationships for the significant terms in Table 1. Effects of all other covariates are averaged over, except for neighbourhood density, which was set at zero. Grey lines show the posterior distribution of the prediction (for a random subsample of 25 MCMC draws) and black lines show the posterior mean prediction. from an estimated 84 to 1% for the gradient from an isolated presence to an occupied quadrat surrounded by eight occupied quadrats (Fig. 2). Colonization probability declined with increasing elevation, human density (linear) and distance to the nearest release site (Table 1.3, Fig. 1, row 2 right and row 3). Neighbourhood density had again a strong positive effect, and colonization probability increased from essentially to 33% when none or all of the surrounding quadrats were occupied (Fig. 2). Detection probability per 2-month period was influenced by elevation, forest cover, season and network (Table 1.4). Detection probability was lower at increasing Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London elevation and higher in more forested quadrats (Fig. 1, bottom row). Moreover, it increased over the three winter seasons from 13 to 19% and also from 1 to 6% and 17% for network levels, 1 and 2 (Fig. 3). Overall, the efficiency of the lynx surveys varied greatly by winter and country (Table 2). The average per-winter detection probability was.45, but the average varied by country between.16 (Slovenia) and.58 (Switzerland) and by year between.25 (214) and.56 (212 and 213). Since in the last year of the study only one season was available (November/December 214), detection probability is lower than in previous years. 173

Occupancy modelling of lynx range dynamics Figure 2 Spaghetti plots of the predicted marginal relationships between neighbourhood density and the covariates and probabilities of persistence (left) and colonization (right). Effects of all other covariates were averaged over. Grey lines show the full posterior distribution of the prediction and black lines the posterior mean prediction. Density..5.1.15.2.25 Nov Dec Density 5 1 15 Density 5 1 15 2 25..5.1.15.2.25 Network = Density 1 3..5.1.15.2.25 Network = 1..5.1.15.2.25 Jan Feb Density 5 1 15 Density 5 1 15 1 2 3 4 5..5.1.15.2.25 Network = 2..5.1.15.2.25 Mar Apr Figure 3 Estimates of lynx detection probability in the Alps for the categories of the network factor and for the 2-month seasons. Effects of country, winter, per cent forest and season or network, respectively, were averaged over. The black bars show posterior means. Distribution dynamics Throughout the Alps, accounting for imperfect detection yielded an estimated number of occupied quadrats about twice the observed number of quadrats with records in a given winter (Fig. 4; Table 2). During the past 2 years, the Alpine lynx population has expanded by about 4% per year and these positive range dynamics are mainly due to the developments in Switzerland (Fig. 4). Our model yields statistical distribution maps that are corrected for imperfect detection and for the patterns in detection probability due to country, winter, per cent forest cover and season (see Fig. 5 for winter 213/214). Most of the quadrats with high predicted probability of lynx occurrence in a given winter, but where no lynx records were available during that winter, are situated close to quadrats with observed occurrences. France and Austria were a bit of an exception, with some quadrats predicted to have a high chance of lynx occurrence, despite being fairly distant from current observed occurrences. This is due to lynx detections in previous and/or subsequent winters, which inform the estimates for occurrence in a Markovian model such as ours. For the distribution map, 174 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

Occupancy modelling of lynx range dynamics Table 2 Mean overall finite-sample detection probability per country and winter estimated as the ratio of the observed and the estimated number of occupied quadrats. Liechtenstein was subsumed under Switzerland. In the German part of the study area, no lynx was ever detected during 1994 214, hence, no detection probability can be computed. Country abbreviations are F, France; I, Italy; CH, Switzerland; A, Austria; SLO, Slovenia. The average of.45 means that raw data underestimate the lynx distribution by 55% Year F I CH A SLO Overall 1994..35.36.5..26 1995..24.55.5..35 1996.39.34.68.14.15.48 1997..4.68..14.46 1998.45.25.6.13.11.42 1999.14.53.59.18.49.48 2.45.4.51.27.16.42 21.27.33.53.19.8.39 22.48.38.51.13.23.4 23.49.63.61.32..51 24.45.4.63.24.3.5 25.41.48.55.18.15.44 26..32.55.2..41 27.13.26.66.12.36.51 28.48.31.65.12.36.52 29.39.41.69.24.29.55 21.52.44.61.15.9.5 211.26.58.61.15..5 212.23.51.72.16.9.56 213.55.43.66.32.27.56 214.15.7.31.16.17.25 Mean.3.38.58.17.16.45 we also produced the associated uncertainty map, which gives the posterior standard deviation of the latent occurrence state z (Figs 5c and 6c). Uncertainty is higher close to occupied quadrats or quadrats that have been occupied in the previous year. To show the rate of change of lynx distribution in the Alps over a 2-year period, we present in Fig. 6 the distribution map for winter 1995/1996 showing the na ıve distribution, the conditional occupancy probability, which is the estimated occupancy probability given the observed data (i.e. the posterior mean of the latent occurrence state z in the model in the Appendix S1) and the associated uncertainty map. Compared with the distribution map of 213/214 (Fig. 5), an expansion of the north-western Alpine occurrence and a new presence of lynx in north-eastern Switzerland that was founded through translocation of 12 individuals between 21 and 28 are evident. Discussion We demonstrate the ability to assess range dynamics of secretive animals occurring at low densities using opportunistic data at a very large spatial and temporal scale. In our case, the spatial extent covered c. 2 km 2 and seven countries, which all have adopted a common standardized protocol for the interpretation of lynx monitoring data (Molinari-Jobin et al., 212). Our approach to distribution modelling and analysing time trends at the population level can be applied retrospectively and should be useful in many cases where a network of trained people is established to report presence of target species. In fact, the use of citizen science for monitoring programmes is becoming more and more common (e.g. Dolrenry, Hazzah & Frank, 216). Large carnivore monitoring programmes that are 25 2 15 1 5 5 4 3 2 1 All 7 countries 1995 2 25 21 215 Italy 1995 2 25 21 215 5 4 3 2 1 15 1 5 France 1995 2 25 21 215 Switzerland 1995 2 25 21 215 5 4 3 2 1 Austria 1995 2 25 21 215 Year 5 4 3 2 1 Slovenia 1995 2 25 21 215 Figure 4 Observed (dashed line) and estimated (solid line) number of occupied 1 km 2 quadrats in six Alpine countries. Liechtenstein with a single cell was lumped with Switzerland and Germany never had any lynx record during the study period. Uncertainty lines are 95% Bayesian credible intervals (CRI). Year Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London 175

Occupancy modelling of lynx range dynamics (a) Germany Austria Switzerland France Slovenia Italy 255 1 km (b) Occupancy probability Posterior mean. -.25.25 -.5.5 -.75.75 -.99 1. 255 1 km (c) Occupancy probability Posterior SD. -.1.1 -.2.2 -.3.3 -.4.4 -.5 255 1 km Figure 5 Distribution of lynx in the Alps for the winter 213/214, (a) based on na ıve estimate derived from the traditional presence detection approach, (b) based on dynamic occupancy model, distribution map corrected for imperfect detection and for the patterns in detection probability due to country, winter, per cent forest cover, network and season, (c) associated uncertainty map, which gives the posterior standard deviation of the latent occurrence state z. 176 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

Occupancy modelling of lynx range dynamics (a) Germany Austria Switzerland France Slovenia Italy 255 1 km (b) Occupancy probability Posterior mean. -.25.25 -.5.5 -.75.75 -.99 1. 255 1 km (c) Occupancy probability Posterior SD. -.1.1 -.2.2 -.3.3 -.4.4 -.5 255 1 km Figure 6 Alpine lynx distribution for the winter 1995/1996, (a) based on na ıve estimate derived from the traditional presence detection approach, (b) corrected for imperfect detection and for the patterns in detection probability due to country, winter, per cent forest cover, network and season, (c) associated uncertainty map, which gives the posterior standard deviation of the latent occurrence state z. Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London 177

Occupancy modelling of lynx range dynamics based to a large degree on citizen science are already established in northern, western and central Europe and are being built up in eastern Europe as well, as member states of the European Union have to report status and distribution of species of special conservation concern (Ozinga & Schaminee, 25) where compilation of information from citizen science is crucial at national and population scales. Through the use of camera trap data the quality of citizen science programmes can be greatly improved, as pictures can be retrospectively verified (e.g. Meek & Zimmermann, 216). The establishment of web portals, which allow uploading photos taken by citizens will ease data collection by a great deal, representing ideal datasets for occupancy modelling. The combination of citizen science and dynamic site-occupancy models provide an excellent framework to evaluate distributional change at large spatiotemporal scales. A distribution map that shows not only observed presence but includes also the probability of having missed the target species in a given area has clear advantages. It allows improving the network and hence the surveys. More generally, our analyses demonstrated the importance of dealing with detection probability: The inference about distribution of the raw data underestimates the occupancy of quadrats in any given winter by about 55% on average, depending on country and winter (Table 2). Therefore, we recommend that analyses of distribution surveys should try to account for imperfect detection whenever possible, to correct this potentially serious downward bias. We found some support for effects of all covariates that we considered a priori. Per cent forest cover was previously identified as positively influencing lynx distribution (Schadt et al., 22; Zimmermann & Breitenmoser, 27). In our study, it was found to be important for initial occupancy, persistence and detection (Table 1, Fig. 1). Colonization probability decreased with increasing distance to release sites, reaching % 25 km away. This needs to be considered when planning further reinforcement projects for the Alpine lynx population. Creating stepping stones (local lynx population nuclei) with a small number of lynx would help the population to expand and eventually to connect isolated occurrences (Kramer-Schadt et al., 211). The number of occupied cells in the neighbourhood of the focal cell, expressed by the autocovariate, had a very strong effect on the parameters governing the dynamics of the distribution, that is, on persistence and colonization rates. With the longest recorded dispersal distance of 27 km for a male (KORA, unpubl. data), lynx from the extent nuclei have the potential to reach about every site in the Alps. However, population spread depends on the dispersal pattern of females who seem to be much more conservative. In contrast to wolves who are able to establish in new areas which are quite distant from the source populations (Kojola et al., 26; Razen et al., 216), lynx have the tendency to establish their home range adjacent to other resident lynx (Zimmermann et al., 25). Individuals in solitary territorial species define their home-range borders in relation to the spatial distribution of conspecifics. This propensity combined with a low ability of sub-adults to cross unfamiliar land and barriers (Zimmermann, Breitenmoser-W ursten & Breitenmoser, 27) appears to hamper or at least greatly slow down the further expansion of lynx populations in the Alps. The conservation goal for Eurasian lynx in the European Union is to maintain or restore the populations at a FCS. Favourable conservation status is a central concept of the European Union (EU) s strategy for the conservation and recovery of species and habitats (Habitat Directive 92/43/ EEC). With regard to the lynx in the Alps, FCS may require a total of 1 mature individuals (or 13 independent individuals) widely distributed across the Alps (Schnidrig et al., 216). However, reliable abundance estimates at population level are difficult to achieve. Another variable that can be used to quantify the current status of a population is the proportion of area occupied by a species (MacKenzie et al., 26). Dynamic occupancy models permit direct trend analysis and yield statistical distribution maps (Figs 5 and 6) showing the conditional occupancy probability of each quadrat. For lynx in the Alps, this knowledge directly ties back into conservation efforts: The Alpine lynx population of 1995/1996 was split into two subpopulations, the north-western Alpine subpopulation and the south-eastern Alpine subpopulation (Fig. 6). Twenty years later, four subpopulations are identified: (1) The area occupied by lynx in the northwestern Alps has doubled in size. (2) A new subpopulation was founded in north-eastern Switzerland with the translocation of 12 lynx between 21 and 28. These two subpopulations are expected to merge in the near future. (3) With the release of five lynx in 211 217, a new occurrence was formed in the north-eastern Alps. (4) The south-eastern Alpine subpopulation has decreased continuously since 2. Based on these observations a reinforcement project was launched in 214 with the aim to add at least 7 lynx to the south-eastern Alps to save this occurrence from extinction. The most important contribution to lynx range expansion was due to lynx translocations and a natural spread in the north-western Alps. In future modelling efforts, additional variables such as frequency of lynx observations, the presence of reproducing females and interactions between lynx presence and habitat connectivity may be used as covariates for first-year occupancy and/or for the colonization and persistence parameters. This will improve our understanding of biological traits influencing the expansion potential of lynx. Hence, dynamic occupancy models are a very useful framework for inference of occurrence dynamics of rare species based on data produced by citizen science. Acknowledgements We thank all the governmental and non-governmental organizations, universities and people who have collaborated with the Status and Conservation of the Alpine Lynx Population programme to monitor the lynx in the Alps (for a complete list of partners see http://www.kora.ch/en/proj/scalp/publi cations.html). Hubert Potocnik provided assistance with GIS analysis. We gratefully acknowledge the comments of two anonymous reviewers which have led to an enriched final product. In recent years the Status and Conservation of the Alpine Lynx Population programme has been financially 178 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London

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Importance of dispersal for the expansion of a Eurasian lynx Lynx lynx population in a fragmented landscape. Oryx 41, 358 368. Supporting information Additional Supporting Information may be found in the online version of this article at the publisher s web-site: Appendix S1. Description of our model in the BUGS language. Parameter names are as analogous as possible to those in Table 1, except that there, for clarity, we replaced, say, beta.lphi[1] by beta.lphi[elev] and so forth. 18 Animal Conservation 21 (218) 168 18 ª 217 The Zoological Society of London