Integrating resource selection into spatial capture ... · spatial capture-recapture (SCR) methods...

Integrating resource selection intospatial capture-recapture models for large carnivores

K. M. PROFFITT,1,� J. F. GOLDBERG,2 M. HEBBLEWHITE,2 R. RUSSELL,4 B. S. JIMENEZ,3 H. S. ROBINSON,5

K. PILGRIM,6 AND M. K. SCHWARTZ6

1Montana Fish, Wildlife and Parks, 1400 South 19th Street, Bozeman, Montana 59718 USA2Wildlife Biology Program, Department of Ecosystem and Conservation Sciences, College of Forestry and Conservation,

University of Montana, Missoula, Montana 59812 USA3Montana Fish, Wildlife and Parks, 3201 Spurgin Road, Missoula, Montana 59804 USA4US Geological Survey, National Wildlife Health Center, Madison, Wisconsin 53711 USA

5Panthera, 8 West 40th Street, 18th Floor, New York 10018 USA6USDA Forest Service, Rocky Mountain Research Station, Missoula, Montana 59801 USA

Citation: Proffitt, K. M., J. F. Goldberg, M. Hebblewhite, R. Russell, B. S. Jimenez, H. S. Robinson, K. Pilgrim, and M. K.

Schwartz. 2015. Integrating resource selection into spatial capture-recapture models for large carnivores. Ecosphere

6(11):239. http://dx.doi.org/10.1890/ES15-00001.1

Abstract. Wildlife managers need reliable methods to estimate large carnivore densities and population

trends; yet large carnivores are elusive, difficult to detect, and occur at low densities making traditional

approaches intractable. Recent advances in spatial capture-recapture (SCR) models have provided new

approaches for monitoring trends in wildlife abundance and these methods are particularly applicable to

large carnivores. We applied SCR models in a Bayesian framework to estimate mountain lion densities in

the Bitterroot Mountains of west central Montana. We incorporate an existing resource selection function

(RSF) as a density covariate to account for heterogeneity in habitat use across the study area and include

data collected from harvested lions. We identify individuals through DNA samples collected by (1) biopsy

darting mountain lions detected in systematic surveys of the study area, (2) opportunistically collecting

hair and scat samples, and (3) sampling all harvested mountain lions. We included 80 DNA samples

collected from 62 individuals in the analysis. Including information on predicted habitat use as a covariate

on the distribution of activity centers reduced the median estimated density by 44%, the standard deviation

by 7%, and the width of 95% credible intervals by 10% as compared to standard SCR models. Within the

two management units of interest, we estimated a median mountain lion density of 4.5 mountain lions/100

km2 (95% CI¼ 2.9, 7.7) and 5.2 mountain lions/100 km2 (95% CI¼ 3.4, 9.1). Including harvested individuals

(dead recovery) did not create a significant bias in the detection process by introducing individuals that

could not be detected after removal. However, the dead recovery component of the model did have a

substantial effect on results by increasing sample size. The ability to account for heterogeneity in habitat

use provides a useful extension to SCR models, and will enhance the ability of wildlife managers to reliably

and economically estimate density of wildlife populations, particularly large carnivores.

Key words: Bayesian; carnivore; mountain lion; non-invasive; population estimation; Puma concolor; SCR.

Received 2 January 2015; revised 16 June 2015; accepted 15 July 2015; published 20 November 2015. Corresponding

Editor: G. Chapron.

Copyright: � 2015 Proffitt et al. This is an open-access article distributed under the terms of the Creative Commons

Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the

original author and source are credited. http://creativecommons.org/licenses/by/3.0/

� E-mail: [email protected]

v www.esajournals.org 1 November 2015 v Volume 6(11) v Article 239

INTRODUCTION

Understanding patterns and drivers of abun-dance and density is a central tenant of ecologyand wildlife management (Andrewartha andBirch 1954), and the estimation of these param-eters has long challenged ecologists (Seber 1973,Jolly 1982). The ability to estimate the abundanceand density of wildlife is particularly importantin applied settings, where conservation or man-agement actions are often assessed by measuringtrends in these parameters. Capture-recapture(CR) methods for closed populations are thestandard methodology for the estimation ofanimal abundance from fixed arrays of traps orother sampling devices (Borchers and Buckland2002). However, some species such as largecarnivores introduce additional complexities forthe estimation of density because these speciesare wide ranging, occur at low densities, and aredifficult to detect. These species commonlyviolate assumptions about geographic closure inthe CR framework and make estimation of theeffective sampling area difficult (Royle et al.2013a). Additionally, individual heterogeneity inrecapture probability (detection probability) overfixed arrays due to behavioral differences ordifferences in space use challenges conventionalCR methods. Recent methodological advances inspatial capture-recapture (SCR) methods addressthese shortcomings of conventional CR methodsby incorporating the spatial organization ofindividuals through the estimation of trap-specific capture probabilities (Efford 2004, Effordet al. 2009, Gardner et al. 2010, Royle et al. 2013a).

SCR methods have recently been extended toaccommodate unstructured spatial sampling(Thompson et al. 2012) where effort is variableacross the study area and applied to theestimation of mountain lion density (Russell etal. 2012). Mountain lions (Puma concolor) in NorthAmerica have slowly increased in number andexpanded their range over the last severaldecades (Hornocker and Negri 2009). Wildlifemanagers need reliable methods to monitormountain lion population trends to manageharvest, minimize conflicts with humans andbalance mountain lion densities with ungulatemanagement objectives. Traditional approachesto estimate mountain lion abundance havefocused on marking and counting individual

lions, a method that is labor-intensive andexpensive, and often minimum counts of indi-viduals are treated as a true census for manage-ment purposes (Robinson et al. 2015). Theresources required by these traditional methodshave limited the spatial scope and utility of theresulting estimates for population management(Stoner et al. 2006, Quigley and Hornocker 2010),and minimum counts of known individualsunderestimate true population sizes. Therefore,the SCR approach provides managers with aneffective and economical alternative method toestimate mountain lion density.

Royle et al. (2013b) provided an approach toincorporating covariates on density includinginformation about habitat selection into SCR inthe Bayesian framework. Mountain lions havebeen shown to have strong selective preferencesfor areas that offer cover, forest edges, andmoderate slopes (Newby 2011). The assumptionthat all habitat within the study area will be usedequally is unlikely to be true for mountain lionsand most large carnivores. Therefore, we extendthe Russell et al. (2012) model for estimatingmountain lion density to include the integrationof a previously existing resource selection modelas a covariate to account for this differentialhabitat selection. For many studies, pre-existinginformation about habitat use could inform thedistribution of activity centers without requiringancillary data (e.g., GPS or telemetry data), or useof the methodologically intensive joint estimationframework. Here, we evaluate the effects ofintroducing an existing RSF into Bayesian SCRmodels by comparing models results with andwithout the RSF. Additionally, we incorporatethe ability to include information about harvest-ed animals (dead recoveries) into Bayesian SCRmodels, increasing the utility of the modellingapproach for species subject to harvest.

METHODS

Study areaThe 2,625 km2 study area was located in the

southern Bitterroot watershed in western Mon-tana, USA, primarily within Ravalli County andspanning portions of two mountain lion man-agement units (LMU 250 and LMU 270; Fig. 1).Elevations range from 1200 m to 2600 m, withmoderate to steep terrain. Precipitation ranges


PROFFITT ET AL.

annually from 40 cm in the valley bottoms to 88cm in the mountains, and primarily falls as snowduring winter (PRISM Climate Group 2013).Ungulate species in the study area include elk(Cervus elaphus), white-tailed deer (Odocoileusvirginianus), mule deer (O. hemionus), bighornsheep (Ovis candensis), mountain goat (Oreamnosamericanus) and moose (Alces alces). Large carni-vore species, in addition to mountain lions,include wolves (Canis lupus) and black bears(Ursus americanus). The mountain lion manage-ment units have had variable season structures,mountain lion harvest quotas, and presumablypopulation size, during the past 20 years. From1992 to 2000, harvest across both managementunits averaged 28.2 mountain lions per year (SD¼ 12.9). From 2000 to 2008, harvest across bothmanagement units declined to an average of 6.4mountain lions per year (SD¼ 2.3). From 2009 to2012, harvest across both management unitsaveraged 16.5 mountain lions per year (SD ¼7.6). During 2009–2012, harvest included an

average of 6.5 females and 10.0 males, and89.6% of the harvest was classified as adultanimals.

Data collectionWe overlaid a 5 3 5 km grid across the study

area and assigned each cell a grid identificationnumber. We randomly generated a list of gridcells and started search effort each day in therandomly assigned grid cell. We stratified sam-pling in this manner to ensure sampling wasallocated across both the high and low qualityhabitat. Mountain lion hair, scat, and musclesamples were collected by trackers and hounds-men for genetic analysis to identify individuals.When a fresh mountain lion track was located,the houndsmen would release trained hounds tolocate and tree the mountain lion. Tracks werebacktracked and inspected to determine if themountain lion was independent or associatedwith a family group, and group size wasrecorded. Sex was determined based on track

Fig. 1. The mountain lion study area in the Bitterroot Watershed of western Montana during winter 2012–2013

(A) showing the 53 5 km sampling grid and the underlying resource selection function (RSF) for mountain lions

during winter (B), the spatial distribution of effort (C; measured in km), and the spatial locations of recaptures

(D). The 53 5 km grid cells define the spatial capture-recapture model grid where the center point of grid serves

as a trap. The black lines denote mountain lion hunting district (HD) boundaries, with HD 250 and HD 270

denoted.


PROFFITT ET AL.

size and physical features of treed mountainlions. Sex was assigned by genetic analysis whensex could not be determined in the field or fieldstaff was uncertain of sex. Muscle samples werecollected from treed animals using biopsy dartsfired from a CO2-powered rifle (Palmer Cap-Chur brand model 1200c). When older mountainlion tracks were located, a tracker or houndsmenwould backtrack the tracks and collect any hairor scat samples along the tracks. All field crewsused a Global Positioning System to record thelength (in km) and location of their search effort.Harvest and management removals occurredduring the sampling period and we used samplescollected from harvested animals within thestudy area. In Montana, the hide and skull ofall mountain lions publically harvested must bepresented to Montana Department of Fish,Wildlife and Parks. During the mandatory check,officers collected a muscle sample from eachharvested animal. We also collected harvestsamples from all adjacent hunting districts todetermine if animals marked within the studyarea may have moved out of the study area.Adjacent districts had similar harvest manage-ment regulations as the study area.

To estimate the density of independent moun-tain lions in the study area, we censored thedataset to include only samples from indepen-dent animals or the adult female of a familygroup. This eliminated multiple samples fromwithin family groups, and eliminated all groupswhere only a subadult animal within the groupwas sampled. The average age that dependentoffspring disperse and become independent oftheir mother is approximately 15 months of age(Sweanor et al. 2000, Robinson and DeSimone2011), therefore our density estimates include allanimals .15 months of age. We estimated thenumber of independent mountain lions ratherthan density of all mountain lions becauseharvest management quotas are based on thenumber of independent, subadult or adult-agedanimals.

We performed genetic analysis of hair, scat,and muscle samples to identify the sex andindividual identity of sampled mountain lionsfollowing methods described in Russell et al.(2012). We genotyped tissue samples using 20variable microsatellite loci used previously inmountain lions (see Appendix A for details).

Spatial capture-recapture modellingWe followed the hierarchical model formula-

tion described by Royle et al. (2009) applied togenetic capture-recapture data from unstruc-tured spatial sampling. For our purposes wedecomposed the DNA observations of individu-als at particular sites during a sampling periodinto two components: a spatial point process thatdescribes the distribution of animals in space andan encounter process that describes the captureof individuals in grid cells given their activitycenter. The spatial point process model allows forthe spatial information from the locations ofindividual captures to be incorporated into theestimate of density or abundance. Within theSCR framework we assume that a populationconsists of n individuals, and that each individ-ual, i¼ 1, 2, . . . , n, in the population has a fixedactivity center representing the center of the areaoccupied by the individual during the studyperiod. Each individual moves about theseactivity centers, which are allowed to overlap,according to some distribution defined in theobservation model. In addition, we assume thatthe farther an observer is from the animal’sactivity center the less likely the animal is to bedetected.

For the encounter model, we constructedindividual, cell-specific encounter histories foreach time period of the study, yi,j,k for individuali; cells j¼ 1, 2, . . . , J; and sample periods k¼ 1, 2,. . . , K. In this study individual encounters didnot arise from discrete trap locations (e.g.,camera traps), but instead encounters couldoccur at any spatial location searched by trackersand houndsmen. To accommodate this unstruc-tured spatial sampling, we used the center ofsampling grid cells as conceptual traps followingRussell et al. (2012). Previous simulations dem-onstrated little effect of grid cell size on liondensity estimates using this design (Russell et al.2012), and, more generally in SCR models(Sollmann et al. 2012). Because animals werealso harvested and removed from the populationduring the sampling period, we defined 4sampling periods so that harvested individuals’detection probabilities could be adjusted in latersampling periods (see below for dead recoveries).We selected 4 sampling periods (December,January, February and March–April) that roughlycorresponded to monthly sampling intervals in


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efforts to adjust detection probabilities of har-vested animals and still allow for adequatesampling effort and detections per samplinginterval. We assumed that individuals couldhave been encountered in all traps for eachsampling period through search effort or harvest.We developed an encounter history for eachanimal during each sampling period where yi,j k; Binomial (K, pi,j) (Eq. 5.2.1, Royle et al. 2013a)and the value of yi,j,k ¼ 0 if the animal i was notencountered in the grid cell j on samplingoccasion k and yi,j,k ¼ 1 if the animal i wasencountered 1 or more times in the grid cell j onsampling occasion k. If an animal i was harvestedduring a previous sampling period, we set theencounter history to yi,j,k ¼ 0 for all grid cells forall subsequent sampling periods, and removedthe individual from likelihoods within theMarkov chain Monte Carlo estimation of param-eters (i.e., the detection probability for thatindividual after known harvest did not influencethe estimate of detection probability for theremaining live individuals).

Following Gardner et al. (2010) and Russell etal. (2012), we assume that cell-specific encounterprobabilities for each i individual and j cell ( pij)are related to the Euclidean distance between anindividual’s activity center (si ) and cell j, r is ascale parameter depending on the measurementunits, and h is a shape parameter of the activitydistribution (Gardner et al. 2010)

pij ¼ p0exp � 1

2r2jjxj � sijj2

� �

(Eq. 5.2.3, Royle et al. 2013a). When h ¼ 1, thismodel describes a bivariate-normal distributionof animal activity, and a value of h ¼ 0.5corresponds to an exponential activity distribu-tion. We used a prior distribution for h ; U(0.5,1). This model of detection probability

logitðp0;ijÞ ¼ }0 þ b 3 Xij

assumes a baseline encounter rate a0 which is theprobability of encounter at the animal’s center ofactivity (Royle et al. 2013a). We considered thefollowing covariates as potentially modifyingdetection probability: (1) sex, and (2) log-trans-formed search effort within a given samplingperiod (Thompson et al. 2012). We did not recordhunter search effort, so we assumed that huntersearch effort was equal to the mean of our search

effort during each sample period because bothhunters and researchers utilized the same roadnetwork to search for tracks. This allowed us toestimate the effects of search effort, given a smallnumber of samples were collected via harvest ingrid cells with no recorded search effort. Wefurther considered the interactive effects ofdistance and sex on detection probability, where-in capture probabilities differ by sex becausefemales are expected to have smaller activitydistributions than males (Hornocker and Negri2009).

In practice, the statespace is chosen to encom-pass the movements of all animals within thestudy area but the statespace does not determinethe extent of animal movements as part of thedensity estimate, as one-half mean maximumdistance moved (MMDM; Royle et al. 2013a) orsimilar measures do in traditional studies. Thestatespace is chosen to be larger than thetrapping grid such that the model accounts forindividuals with activity centers outside of thetrapping grid, but whose activity range extendsinto the trapping grid. The exact size of thetrapping grid buffer used to construct the states-pace does not strongly influence density esti-mates under the assumption of a uniformdistribution of activity centers (Russell et al.2012). When spatial covariates are included,however, the size of the buffer may influencedensity, as different values of spatial covariatesmay be included within the buffer. We choose abuffer size of 10 km around our study grid andidentified potential activity centers within thisarea every 2 km. Because our study grid was nota square, we applied the 10 km from the mostextreme edges of our grid in each cardinaldirection, such that the buffer exceeded 10 kmin some areas. In one area the buffer zone wasreduced to ,10 km to exclude areas that did notinclude wintering lion habitat. This resulted in a5912 km2 statespace.

Currently, methods exist in ‘‘secr’’ (Efford2014) to incorporate dead recoveries into spatialcapture-recapture models in the likelihoodframework. We developed a method to incorpo-rate information about harvested lions in aBayesian framework by including a matrix,indicating whether the animal was potentiallyalive in each sampling period and thereforeavailable to be captured or if the animal had


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been harvested during a previous session. Thismatrix was then used to censor when animalswere not available to be captured from thelikelihood, thus preventing a bias in detectionprobabilities from harvested individuals notavailable for detection post-harvest.

We included information about winter moun-tain lion habitat quality by incorporating predic-tions from an existing resource selection function(RSF) as a density covariate. We incorporatedvalues of the RSF into our estimate of densityusing the following equation:

log�lðs; bÞ

�¼ b0 þ bvCvðsÞ

(Eq. 11.2.1, Royle et al. 2013a); where l(s, b)returns the expected density of activity centers atlocation s given the covariate values C and theparameter estimates b. The RSF was developedstatewide in Montana using radiotelemetry (VHFand GPS) data from 1980 to 2012, using ageneralized linear mixed-effects model (Robin-son et al. 2015). The RSF was developedfollowing a used-available design at the second-order, home range scale (Johnson 1980), corre-sponding well to the ecological selection processfor individual activity distributions. The RSF wasestimated by comparing 18,695 GPS telemetrylocations from 85 individual lions to availabilityat the state-wide scale, and then validating itusing withheld data from 142 VHF and GPScollared lions, as well as harvest locations from1988 to 2011. Winter mountain lion habitat was apositive function of southerly aspects, intermedi-ate elevations and slopes, forested areas, andareas far from agriculture or human develop-ment (Robinson et al. 2015). The RSF modelvalidated very well using out-of-sample teleme-try data (Spearmans rho ¼ 0.95). In the studyarea, 218 mountain lion harvest locations wereused to validate the RSF model, and the modelvalidated well (Spearman rho ¼ 0.87; AppendixB). We used the logit of continuous predictionsrescaled from 0 to 1 from this RSF as a covariatein the SCR model.

We evaluated the effects of including harvestedanimals in the analyses in two ways. First, toevaluate potential effects of bias in the detectionprocess by introducing individuals that could notbe detected after removal, we compared densityand precision of estimates from a model that

masked harvested animals from sampling peri-ods post-harvest and a model that treatedharvested animals as live throughout the sam-pling period. Second, to evaluate the effects ofthe harvest samples on the density estimates, wecompared density estimates from a model thatincluded only the live animal samples with amodel that included both the live animal andharvest samples. In both these evaluations, weused the best model identified through ourmodel selection process for comparisons.

Bayesian analysis by MCMCWe used Bayesian MCMC methods in the

SCRbayes package for the R programming lan-guage to estimate the posterior distribution of themodel parameters (https://sites.google.com/site/spatialcapturerecapture/scrbayes-r-package; seeSupplement). This approach uses data augmenta-tion to add a sufficiently large number of all-zero(unencountered) capture histories to create adataset of M individuals. We determined the dataaugmentation to be large enough when finalposterior estimates of population size were notlimited by the number of augmented unencoun-tered individuals (see Royle et al. 2013a). Inessence, we assume a uniform prior distributionon N, population size, from 0 to M, where Mincludes the unencountered animals. Here, weaugmented with 1000 all-zero encounter histories.Following Russell et al. (2012), models were runfor 30,000 iterations with the first 10,000 iterationsdiscarded as burn-in, leaving 20,000 samples fromthe posterior distribution. Starting values forparameters were: r ¼ 1, h ¼ 0.75, ln(a0) ¼ 0, b ¼0, w ¼ 0, and wsex ¼ proportion of individualssampled that were male (0.40 for our sample). Weused improper priors (�‘, ‘) for a0 and all bparameters, (0, ‘) for r, (0.5, 1) for h, and (0, 1) forw and wsex. We assessed model convergence byexamining posterior parameter-wise trace plotsand histograms.

To estimate lion abundance (N) within thestatespace and within the two management unitsof interest, we counted the number of activitycenters within the statespace and within themanagement units. Since this estimate of abun-dance is linked explicitly to an area (either thestatespace or a management unit), we calculatedensity (D) by finding the quotient of the Nactivity centers and the area of the statespace or


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management unit.

Bayesian model selection and model goodness of fitWe evaluated 16 potential models (Appendix

C) that we fit to the data in a Bayesianframework. We conducted a form of modelselection by examining the posterior significanceof the parameters in each model weighted by ourprior knowledge of mountain lion biology. Forthe sex and effort effects on the detectionprobability, as well as RSF covariate on activitycenter distribution, 95% credible intervals thatexcluded zero would provide evidence of signif-icance. Similarly, for the sex effects on the scaleparameter of the activity distribution, we exam-ined whether male and female values hadsignificantly different 95% credible intervals. Wedid not, however, immediately exclude modelsthat included apparently non-significant param-eters, as many of these parameters derivesupport from previous ecological studies (i.e.,differences in male and female activity rangesizes). We evaluated the effects of introducing theRSF covariate by comparing models with with-out the RSF as a covariate on the distributions ofactivity centers. We compared the density andprecision of estimates of the best model with andwithout the RSF covariate.

We evaluated model goodness of fit for the topmodels following methods described by Russellet al. (2012) including a standard Bayesian P-value approach (Gelman and Shalizi 2011, Royleet al. 2013a). We tested the GOF of the encounterprocess separately from the GOF of the underly-ing spatial point process. For the encounterprocess, we calculated a discrepancy measurefor the cell-specific individual encounter frequen-cies to compare posterior samples and newrealizations of the data generated from theposterior distribution. We used the Freeman-Tukey statistic to construct a Bayesian P-value

D ¼XN

i¼1

ð ffiffiffiffinip � ffiffiffiffi

eip Þ2

where ni is the (observed or simulated) encounterfrequency conditional on si (activity center) and eiis the expected value under the model. The P-value is the proportion of time D(obs) .

D(posterior).For the point-process, we examined model

GOF by testing whether estimated activitycenters were independently and uniformly dis-tributed over the statespace. We calculated aBayesian P-value based on the statistic, I¼ (G – 1)3 s2/�n, where G is the total number of grid cells,and �n and s2 are the mean and variance of thenumber of activity centers per grid cell. Wecompare I from the estimated posterior distribu-tion of the point-process to simulations undercomplete spatial randomness. We did not applythe point-process GOF test to models with theRSF covariate on the distribution of activitycenters, because we would not expect activitycenters to be independently and uniformlydistributed across space for these models.

As a final metric of model goodness of fit, wecompared the observed and expected number ofindividuals captured for each model to holisti-cally examine both the point-process and detec-tion process. We calculated the expected numberof individuals captured with

EðncapÞ ¼X

S

Esi3 nsi

where Esirepresents the exposure probability of

an individual with an activity center at si and nsi

is the number of activity centers estimated at si.By computing these values for each MCMCiteration, we constructed a 95% confidenceinterval for the number of individuals capturedgiven the complete process described by themodel. An observed number of captures that felloutside this range would indicate poor model fit.

RESULTS

We searched for mountain lion sign over a totalof 8382 km during 98 person-days from Decem-ber 7, 2012 to April 2, 2013. Search effort wasdistributed across 85 of 105 grid cells, and 80% ofthe effort occurred before February 15, 2014(Appendix D). Hunter effort was unquantified,but there were only 8 grid cells in which aharvest but no live recapture occurred. Animalswere sampled in 35 grid cells, and individualgrid cells contained 0–6 samples (Fig. 1). A totalof 80 samples from independent animals wereincluded in the analysis, and 62 unique individ-uals were identified. Three individuals wereidentified from hair samples, 4 individuals wereidentified from scat samples, 43 individuals were


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identified from biopsy muscle samples, and 30individuals were identified from harvest sam-ples. There were 25 male mountain lions identi-fied and 37 female mountain lions identified.Fifteen individuals were recaptured 2–4 timesduring the sampling period (13 animals captured2 times, 1 animal captured 3 times, and 1 animalcaptured 4 times). Thirty of the 62 individualswere harvested (17 female, 13 male), and of these,10 (6 female, 4 male) were previously sampledand identified. The detection of new genotypesscaled linearly with search effort throughout theentire sampling period (Appendix D). No ani-mals detected within the study area were laterdetected in the harvest sampling conductedoutside the study area, suggesting limited move-ment occurred during the sampling period.

Model selection and goodness of fitWe evaluated 16 candidate models. Across all

models, the parameter estimates for effort andRSF were consistently positive with 95% credibleintervals that did not include zero (Appendix C).The 95% credible interval for the effect of sex ondetectability and the sex-specific scale parame-ters overlapped zero in all models, but the effectof sex and sex-specific scale parameters were inthe expected direction (Appendix C). The Bayes-ian P-value for the encounter process GOFproduced reasonable results for all models anddid not aid discrimination between models. Ourad hoc GOF measure of the predicted number ofcaptures showed all models plausibly describedthe combination of the underlying point processand capture of individuals because the number

of individuals captured (n ¼ 62) falls within theexpected range. Therefore, we present results ofall 4 models that included effort and RSF, and weselected the full model that included detectioncovariates for search effort and sex, RSF-drivendensities and sex-specific activity distributionsfor further evaluation (Table 1).

Estimates from the full model indicatedmonthly detection probabilities were higher ingrid cells with more search effort and mountainlion activity center densities were higher in areaswith larger RSF values (Table 2). Females hadhigher baseline detection probability. Males weremore likely to be detected farther from theiractivity center than females (e.g., males hadlarger observed movements; Appendix E). Usingthis best model, we estimated a median of 226mountain lions over the entire statespace of 5,912km2 (Fig. 2), corresponding to a median realizeddensity (D) of 3.8 (6 1.02 SD) mountain lions/100km2. We estimated the proportion of males in thepopulation was 0.41 (95% CI ¼ 0.26–0.61).Extracting estimates from the two managementunits of interest, in HD 250 we estimate a medianof 82 (95% CI ¼ 54, 141) mountain lions,corresponding to a median density of 4.5mountain lions/100 km2 and a median of 79(95% CI ¼ 51, 137) mountain lions in HD 270,corresponding to a median density of 5.2mountain lions/100 km2.

Effects of including habitat qualityon density estimates

Including the RSF as a covariate on thedistribution of activity centers reduced estimated

Table 1. Spatial capture-recapture model estimates for the total number (N ) and density of mountain lions/100

km2 in the 5912 km2 statespace in western Montana during winter 2012–2013. Sex and search effort (Effort) are

included as covariates on baseline detection probability and the parameter rsex allows for the scale of activity

ranges to vary by sex. An existing resource selection function (RSF) was included as a covariate on the density

of activity centers across the statespace. The 95% CI represent the Bayesian credible intervals. The goodness of

fit (GOF) p-value represents the GOF p-value for the encounter model with values between 0.05 and 0.95

indicate an adequate fit. EðncapÞ represents the 95% credible interval of the expected number of captured

individuals given the estimated point process and encounter process, and values including ncap¼ 62, indicate

adequate fit.

Model N Median density 95% CI GOF p-value E(ncap)

Effort þ RSF 201 3.4 2.4–5.7 0.64 56–84Effort þ RSF þ Sex 229 3.9 2.6–7.7 0.73 55–85Effort þ RSF þ rsex 214 3.6 2.5–5.8 0.66 56–84Effort þ RSF þ Sex þ rsex 226 3.8 2.6–6.5 0.73 50–81


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mountain lion densities across all models (Fig. 3,Table 3), and had mixed effects on extrapolateddensities in the two management units ofinterest. Comparing the best model with andwithout the RSF covariate, we found estimated

abundance and density was reduced and the

effective sampling area was similar (Fig. 4).

Median density was 44% less in models with

the RSF covariate (3.6 lions/100 km2; 95% CI ¼2.4, 7.4) compared to the average of models

Table 2. Median parameter estimates and 95% Bayesian credible intervals from spatial capture-recapture models

of mountain lion abundance in western Montana during winter 2012–2013. Sex and search effort (Effort) are

included as covariates on baseline detection probability and the parameter rsex allows for the scale of activity

ranges to vary by sex. Female r and Male r represent estimated values for female and male mountain lions. An

existing resource selection function (RSF) was included as a covariate on the density of activity centers across

the statespace.

Model Female r Male r beffort bsex bRSF

Effort þ RSF 0.71 (0.50, 1.00) 0.71 (0.50, 1.00) 0.91 (0.67, 1.15) . . . 0.84 (0.62, 1.00)Effort þ RSF þ Sex 0.68 (0.51, 1.00) 0.68 (0.51, 1.00) 0.89 (0.66, 1.13) �0.20 (�1.33, 0.48) 0.66 (0.51, 0.82)Effort þ RSF þ rsex 0.66 (0.50, 0.98) 0.67 (0.49, 1.02) 0.89 (0.65, 1.17) . . . 0.68 (0.43, 0.87)Effort þ RSF þ Sex þ rsex 0.62 (0.45, 0.93) 0.85 (0.53, 1.94) 0.90 (0.66, 1.19) �0.97 (�2.40, 0.18) 0.63 (0.45, 0.94)

Fig. 2. The spatial densities of mountain lions/4 km2

across the statespace in the Bitterroot Watershed of

western Montana estimated from the best model

assuming uniform distribution of activity centers

(Effortþ Sexþ rsex; A) and best model that estimated

the distribution of activity centers as a function of the

resource selection function (RSF, Effort þ Sex þ rsex þRSF; B) for sampling conducted during winter 2012–

2013.

Fig. 3. Effects of including a pre-existing mountain

lion resource selection function (RSF) as a covariate on

the distribution of activity centers on estimated

median mountain lion population density (mountain

lions/100 km2) the Bitterroot Watershed of western

Montana during winter 2012–2013 from 16 candidate

spatial capture-recapture models. The uniform model

estimates are based on a prior assumption of uniform

distribution of activity centers and did not include RSF

as a covariate on the distribution of activity centers.

Error bars represent 95% credible intervals.


PROFFITT ET AL.

without the RSF covariate (5.2 lions/100 km2; 95%CI¼ 3.4, 8.8). The inclusion of the RSF improvedprecision by decreasing the standard deviationby 7% and decreasing the width of 95% credibleintervals by 10%. Within the two managementunits of interest, median density was 17% less inthe best model with the RSF covariate (4.5; 95%CI ¼ 2.9, 7.7) as compared to the same modelwithout the RSF covariate (5.4; 95% CI¼ 3.4, 9.2)in lion management unit 250 and 4% greater inthe best model with the RSF covariate (5.2; 95%CI ¼ 3.4, 9.1) as compared to the same modelwithout the RSF covariate (5.0; 95% CI¼ 3.1, 9.0)in lion management unit 270.

Effects of including harvest on density estimatesTreating harvested individuals as live captures

did not create a significant bias in the detectionprocess by introducing individuals that could notbe detected after removal. When samples fromharvested individuals were treated as live cap-tures, we estimated a median density of 3.9 (95%CI¼ 2.6, 6.7) mountain lions/100 km2, which didnot represent a significant difference from themodel that masked these individuals fromsampling periods after they had been harvested(3.8, 95% CI¼ 2.6, 6.5). Similarly, we observed nosignificant differences in any of the parameterestimates from models fit with these twopermutations of the data.

The dead recovery component of the modeldid have a substantial effect on results byincreasing sample size. When captures fromharvested individuals were excluded from thesample, the data set had 50 total captures ofwhich 5 were recaptures. With this reduced data

set, we estimated a median density of 6.8 (95% CI¼ 2.7, 16.6) mountain lions/100 km2. This mediandensity represented a 78% increase over themodel fit with the complete data set (3.8, 95%CI ¼ 2.6, 6.5). Moreover, with a reduction insample size, the precision of the estimatedecreased substantially. The standard deviationincreased by 277% and the 95% credibilityinterval width increased by 251%. The effectson our estimate of density manifested throughpoor estimates of the sex-specific parameters onboth detection probability and the scale of theactivity distribution. Removing samples fromharvested individuals eliminated all recapturesof male individuals such that the sex-specificparameters could not be estimated.

DISCUSSION

Our results indicate that incorporating priorknowledge of animal habitat selection intospatial capture-recapture models may improvemodel fit and the precision of the abundanceestimates. In this case, the model where theprobability of an activity center being located in agrid cell was a positive function of an existingRSF reduced the overall estimate of abundanceby 44%, the SD by 7% and the CI width by 10%,an important improvement in both biologicalrealism (i.e., high quality habitats had higherdensity than lower quality habitats) as well asprecision of estimates. This approach to SCRmodelling that increases the precision of esti-mates may increase the applicability of SCRmodelling as an applied tool for monitoringtrends in population abundance and effects of

Table 3. Spatial capture-recapture model estimates of median mountain lion density/100 km2 in western Montana

during winter 2012–2013 for 8 models with a uniform prior distribution on activity centers and 8 models with a

resource selection function (RSF) included as a covariate on the density of activity centers across the statespace.

Sex and search effort (Effort) are included as covariates on baseline detection probability and the parameter

rsex allows for the scale of activity ranges to vary by sex. The 95% CI represent the Bayesian credible intervals.

Model Median density 95% CI Median density 95% CI

Distance 4.8 3.2–7.5 3.2 2.2–5.1Sex 5.1 3.3–8.6 3.8 2.4–16.4rsex 5.1 3.3–8.8 3.6 2.4–5.9Sex þ rsex 5.3 3.5–9.7 3.5 2.4–5.7Effort 5.1 3.3–7.9 3.4 2.4–5.7Effort þ Sex 5.6 3.7–10.4 3.9 2.6–7.7Effort þ rsex 5.2 3.4–8.5 3.6 2.5–5.8Effort þ Sex þ rsex 5.3 3.5–9.3 3.8 2.6–6.5


PROFFITT ET AL.

various management actions on these trends.The overall strength of the SCR approach is the

ability to explicitly estimate density over adefined area and account for animals whoseactivity ranges overlap the periphery of the areasurveyed. This is particularly important for largecarnivore species that tend to be wide-rangingand violate traditional capture-recapture geo-graphic closure assumptions. For example, weestimated the location of activity centers acrossthe statespace and calculated a statespace densi-ty, then estimate the density across two definedareas of interest (the hunting districts) as afunction of the number of activity centers withinthe area of the hunting districts. In this manner,animals whose activity ranges overlap theperiphery of the hunting districts are accountedfor. These strengths add ecological realism, andaddress the challenge of comparing estimatesacross studies. The differences in estimateddensity between the statespace and managementunits of interest highlight the fact that densityestimates are sensitive to the area over which thedensity estimates are generated. Thus, the abilityto generate spatially explicit spatial abundancesas a function of underlying habitat qualitythrough the SCR approach may improve appli-cability of extrapolated density estimates beyonda given study area, making the approach morerelevant to wildlife managers making decisionsfor larger landscapes rather than distinct studyareas. Further improvements and refinements toSCR methods, including pooling data acrossstudy areas (Howe et al. 2013) or data sources(Gopalaswamy et al. 2012) will continue toimprove rigor and reliability of SCR methodsfor monitoring trends in wildlife populationabundance.

Our methods provide a method of integratingharvest into Bayesian SCR models. Similarmethods exist within the likelihood framework(Borchers and Efford 2008, Efford 2014), howeverharvest has not been previously included withinthe Bayesian framework. SCR models have beenapplied to other species, for example, wolverines(Gulo gulo) and Lynx (Lynx lynx; Royle et al. 2011,Blanc et al. 2013) with potentially open harvestseasons without explicitly considering effects ofongoing harvest. Given that most large carnivorespecies are harvested or subject to managementremovals, our dead-recovery approach is likely to

Fig. 4. Comparison of SCR model parameters

estimating mountain lion density in the Bitterroot

Watershed of western Montana during winter 2012–

2013 that include RSF as a covariate on activity center

distributions (black line) and with uniform distribution

of activity centers (grey line). Panel (A) shows the

effects of the RSF covariate on posterior probability

densities of abundance over the entire statespace.

Panel (B) shows the effects on estimated population

density (mountain lions/400 km2) over the entire

statespace.


PROFFITT ET AL.

be very useful for future studies with openharvest seasons.

Our median estimates of 4.5 and 5.2 indepen-dent mountain lions/100 km2 in the managementunits of interest represent the estimated densityof a hunted population living sympatrically withwolves, and are higher than previously pub-lished estimates of mountain lion densities(Hornocker and Negri 2009). There could beimportant methodological as well as ecologicalreasons for our high estimates. Most publishedmountain lion density estimates are based onintensive, multi-year marking, radiocollaring andpopulation monitoring methodologies that gen-erate a mean minimum population densityestimate. These studies assume that all individ-uals within the study population are detected, anindividual’s presence in the population may bebackdated based on age to account for theirpresence prior to detection, and the study areaincludes the annual ranges of radiocollaredmountain lions (Hornocker and Negri 2009).However, even within these types of intensiveradiocollaring studies differences in samplingand estimation methodologies make compari-sons of mountain lion density across study areaschallenging. Specifically, the inclusion of differentsex-age classes and, crucially, differences in areaover which density is calculated (i.e., winterrange vs. annual range) differs between studiesand obviously challenges comparisons. UsingSCR methods, we do not assume perfect detec-tion and we include transient individuals in theestimate.

Additionally, two important ecological fac-tors may be contributing to a high mountainlion density in the study area. First, mountainlion harvest in the study area has beenconservative during the past decade and thepopulation has likely increased throughout thisperiod of conservative harvest management.Second, the abundance and diversity of prey inthis area, resulting partially from ungulatemanagement practices, likely sustains a higherthan average mountain lion population (Car-bone and Gittleman 2002, Karanth et al. 2004).The potential for individuals to move into thestudy area to occupy territories vacated byharvested individuals could result in overesti-mating mountain lion density, as our estimateis designed as an estimate of density pre-

harvest (i.e., on the first day of the samplingperiod). However, the study area was locatedwithin a watershed under uniform mountainlion harvest management, and source-sinkdynamics are unlikely in this scenario. Further,we designed our sampling plan to minimizethe potential for movement into the study areaby minimizing the duration of sampling and byconcentrating our search effort during theperiod prior to the hunting season opening tothe general public (see Appendix D). Althoughsubtle shifts in territory use may have occurredas nearby animals were harvested, this effectwould positively bias our estimates of activityrange and negatively bias our estimates ofpopulation density. Therefore, shifting territo-ries during the sampling period is not likely toexplain our high density estimates. Finally,while SCR models do not necessarily allowflexibility in violating the closure assumption(but there are open SCR models that can doso), the explicit integration of space combinedwith choice of effective study area boundariescan minimize potential problems with closurecompared to non-spatial capture-recapturemodels (Royle et al. 2013a).

The DNA sampling methodology used inthis study reduces the time and effort involvedin capturing and handling animals, but doesnot provide information about the age, bodycondition or other individual characteristics ofan animal. Additionally, the ability to distin-guish between transient and resident individu-als is limited. For some areas and speciestransients may constitute a major portion ofthe population, and methodological develop-ment may be required to adjust densityestimates for these areas. For many other largecarnivores, transient or dispersing individualscomprise a significant portion of the harvest-able population (e.g., wolves in Alaska where50% of the harvest were such animals; Adamset al. 2008). We suggest that for mountain lionsincluding transient animals in the populationestimate is appropriate because these animalsare present, likely affect the dynamics of localungulate populations, and are legally harvest-able during the hunting season. We also expectover the long-term the number of transientsmoving into and out of the study area areroughly equal, resulting in a consistent effect


PROFFITT ET AL.

on both mountain lion density and ungulatepopulations.

In our study, like many other studies of largecarnivores, detection probability was relativelylow, 0.09/month for males and 0.21/month forfemales with average effort at the center of thehome range of the lion. Despite being low, ourdetection rates were similar to other largecarnivore studies; for example, detection prob-ability in non-spatial capture-recapture rangedfrom 0.12 to 0.26 for grizzly bears in BritishColumbia (Boulanger et al. 2002), from 0.11 to0.26 for Bengal tigers in non-spatial models inIndia (Karanth and Nichols 1998), from 0.01 to0.04/night for tiger density estimated in aspatial capture-recapture model (Royle et al.2009), and from 0.05 to 0.09/period for jaguarsin Brazil (Sollmann et al. 2013). In our case,with mountain lions, our detection probabilitiesresulted in reduced precision of our parameterestimates, increased estimates of populationabundance well beyond the raw number ofindividuals identified, and emphasizes thecryptic nature of mountain lions. Future stud-ies of large carnivores could probably improveprecision of SCR estimates by incorporatingexisting information regarding habitat quality(or if unavailable, radiocollaring and estimatinga RSF or some other index of habitat suitabil-ity) or developing sampling plans that targetrecaptures of sampled individuals to improvethe estimation of the detection function (i.e.,deliberately resampling areas that have previ-ously been sampled).

We recommend that the decision to approachfuture large carnivore studies using the SCR ortraditional radiocollaring approach be madebased on the questions and applications ofinterest. For monitoring long-terms trends inanimal abundance, non-invasive sampling tech-niques for capture-recapture studies provide afast and economical method to estimate thenumber of individuals and monitor trends insegments of a population across time. The SCRmethod for the analysis of capture-recapturedata provides estimates of density using arepeatable methodology which makes compar-isons across time and space possible. Studiesseeking to estimate vital rates, assess space use,distinguish between residents and transients orunderstand cause–specific mortality may be

best approached using traditional trackingmethodologies or capture-recapture approach-es.

ACKNOWLEDGMENTS

Project funding and support was provided byRavalli County Fish and Wildlife Association, theMontana Outdoor Legacy Foundation, Western Mon-tana Chapter of the Safari Club International, SafariClub International Foundation, Rocky Mountain ElkFoundation, the University of Montana, U.S.D.A.Cooperative State Research, Education and ExtensionService Grant No. MONZ-1106, and by the sale ofhunting and fishing licenses in Montana and MontanaFish, Wildlife and Parks Federal Aid in WildlifeRestoration grants. We thank R. Beausoleil for adviceregarding field methodology, and J. A. Royle for expertadvice on SCR modelling. We thank the projecthoundsmen and field staff for their dedicated effortsand expertise. Any use of trade, product, or firmnames are for descriptive purposes only and do notimply endorsement by the U.S. Government.

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SUPPLEMENTAL MATERIAL

ECOLOGICAL ARCHIVES

Appendices A–E and the Supplement are available online: http://dx.doi.org/10.1890/ES15-00001.1.sm


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