Pairing field methods to improve inference in wildlife ... · Pairing ﬁeld methods to improve inference in wildlife surveys while accommodating detection covariance JOHN CLARE,

Pairing field methods to improve inference in wildlife surveyswhile accommodating detection covariance

JOHN CLARE,1,5 SHAWN T. MCKINNEY,2 JOHN E. DEPUE,3,4 AND CYNTHIA S. LOFTIN2

1Department of Wildlife, Fisheries, and Conservation Biology, University of Maine, Orono, Maine 04469-5755 USA2Maine Cooperative Fish and Wildlife Research Unit, U.S. Geological Survey, Orono, Maine 04469-5755 USA

3Maine Department of Inland Fisheries and Wildlife, Bangor, Maine 04401-5654 USA4Michigan Department of Natural Resources, Baraga, Michigan 49908 USA

Abstract. It is common to use multiple field sampling methods when implementing wildlifesurveys to compare method efficacy or cost efficiency, integrate distinct pieces of informationprovided by separate methods, or evaluate method-specific biases and misclassification error.Existing models that combine information from multiple field methods or sampling devicespermit rigorous comparison of method-specific detection parameters, enable estimation ofadditional parameters such as false-positive detection probability, and improve occurrence orabundance estimates, but with the assumption that the separate sampling methods producedetections independently of one another. This assumption is tenuous if methods are paired ordeployed in close proximity simultaneously, a common practice that reduces the additionaleffort required to implement multiple methods and reduces the risk that differences betweenmethod-specific detection parameters are confounded by other environmental factors. Wedevelop occupancy and spatial capture–recapture models that permit covariance between thedetections produced by different methods, use simulation to compare estimator performanceof the new models to models assuming independence, and provide an empirical applicationbased on American marten (Martes americana) surveys using paired remote cameras, haircatches, and snow tracking. Simulation results indicate existing models that assume that meth-ods independently detect organisms produce biased parameter estimates and substantiallyunderstate estimate uncertainty when this assumption is violated, while our reformulated mod-els are robust to either methodological independence or covariance. Empirical results sug-gested that remote cameras and snow tracking had comparable probability of detectingpresent martens, but that snow tracking also produced false-positive marten detections thatcould potentially substantially bias distribution estimates if not corrected for. Remote camerasdetected marten individuals more readily than passive hair catches. Inability to photographi-cally distinguish individual sex did not appear to induce negative bias in camera density esti-mates; instead, hair catches appeared to produce detection competition between individualsthat may have been a source of negative bias. Our model reformulations broaden the range ofcircumstances in which analyses incorporating multiple sources of information can be robustlyused, and our empirical results demonstrate that using multiple field-methods can enhanceinferences regarding ecological parameters of interest and improve understanding of how reli-ably survey methods sample these parameters.

Key words: American marten; density; false positive detection; Martes americana; monitoring; multi-method dependence; noninvasive methods; occupancy; spatial capture–recapture methods; survey design.

INTRODUCTION

Species distribution and abundance are the canonicalparameters for applied ecologists (K�ery and Royle 2016),and estimates of distribution and abundance are oftenused to justify resource management decisions (e.g.,Fuller et al. 2016). Robust decision making is improvedby reliable information, and there have been three majormethodological branches of recent applied ecological

research aimed at improving the information used toinform decision making. One branch has focused ondeveloping statistical models to reduce the bias of distri-bution or abundance estimates and properly characterizeestimate uncertainty (e.g., MacKenzie et al. 2006, Royleet al. 2014). A second has focused on optimizing studydesign in order to maximize the statistical power or esti-mate precision of statistical models, given that limitedresources are available to devote to data collection (e.g.,MacKenzie and Royle 2005). Finally, a third branch hasfocused on developing field methods that ensure the req-uisite data needed to fit statistical models are collected asefficiently as possible without violating estimator assump-tions (e.g., Long et al. 2007a, Pauli et al. 2008).

Manuscript received 11 November 2016; revised 8 March2017; accepted 10 May 2017. Corresponding Editor: DavidA. W. Miller.

5 E-mail: [email protected]

2031

Ecological Applications, 27(7), 2017, pp. 2031–2047© 2017 by the Ecological Society of America

The causes of bias and uncertainty in distribution orabundance estimates are increasingly well described.Few survey efforts detect all animals in a population orall species present at a location, and statistical methodsto account for false absences associated with observeddistribution or abundance are now widely used (K�eryand Royle 2016). The precision of distribution or abun-dance estimates that account for imperfect detection isimproved by either increasing the spatial or temporalsampling effort (greater sample size) or increasing sam-pling efficiency (increasing the probability of detection;MacKenzie and Royle 2005). Other causes of bias haveonly more recently received attention: survey efforts sub-ject to even a small number of false-positive detectionsor that non-representatively sample a subset of the targetpopulation can produce estimate bias (e.g., Miller et al.2011, Graves et al. 2012). Although field method com-parisons often seek to find methods that allow stronginference at reduced cost, selecting a single method oftenrequires practitioners to weigh trade-offs between finan-cial or logistical constraints to data collection vs. the riskof biased or uncertain inference (Gompper et al. 2006,Long et al. 2007b, Chambert et al. 2015).Field method comparisons and state parameter infer-

ence can be greatly enhanced by models that explicitlyincorporate multiple survey methods (multi-methodmodels). Multi-method models permit direct compar-ison of method-specific detection probabilities, allow theestimation of false-positive detection probabilities andevaluation of method-specific sampling biases, providemore precise estimates of distribution or abundance,enable estimation of additional parameters such as avail-ability for detection, and permit practitioners to for-mally combine different pieces of method-specificinformation into an integrated model (Nichols et al.2008, Miller et al. 2011, Gopalaswamy et al. 2012, Soll-man et al. 2013, Fisher and Bradbury 2014). Becausemulti-method models allow simultaneous field-methodcomparison, bias correction, and improved estimationof state parameters, they represent very powerful toolsfor a variety of applied objectives if correctly imple-mented. However, a critical assumption of existing mul-ti-method models is that different methods produceindependent detections.Meeting this assumption can present logistical and

inferential challenges. Maintaining independence betweenthe detections produced by different methods means thatthe methods must operate in different places or at differ-ent times. Because methodological comparisons or multi-method inferences are often most critical for species suchas carnivores that are inherently difficult to detect andexpensive to effectively survey because they exist at lowdensity over broad spatial extents, maintaining indepen-dence between methods can require substantial additionalfield effort or sampling duration. Indeed, many carni-vore-sampling efforts specifically pair multiple detectionmethods at the same location to reduce logistical costs,and because pairing methods provides ancillary benefits

like laboratory cost-savings associated with culling geneticsamples deposited by non-target species (Maguoun et al.2011). Furthermore, maintaining independence betweendifferent detection methods can induce additional causesof bias. Prolonging a survey duration to maintain tempo-ral independence (sensu Gopalaswamy et al. 2012,Sollman et al. 2013) increases the likelihood that popula-tion size or distribution changes over the survey dura-tion, while staggering detection methods in space caninduce additional detection variance associated with localhabitat conditions or the location of individuals withrespect to specific methods (Graves et al. 2012). Thus, itis unsurprising that many multi-method survey effortscollocate methods (e.g., Maguoun et al. 2011, Fisheret al. 2016).The assumption that different methods provide inde-

pendent detections is tenuous when methods are collo-cated, because two paired methods should jointly detectindividuals or species more often than expected underthe assumption of independence. Treating positivelycovarying detections as independent may not effect rela-tive estimates of detection probability or estimates ofdetection bias, but is expected to overstate the overallprobability of detecting a species or individual, and con-sequently lead to negative bias in state parameters. Thus,developing models that can allow covariance betweenthe detections produced by different field methods is animportant research need for preserving the benefits asso-ciated with multi-method models without biasing esti-mates of the parameters of primary managerial interest.Below, we formally describe occupancy and spatial cap-ture–recapture models (MacKenzie et al. 2006, Royleet al. 2014) that can accommodate observation covari-ance between separate survey methods.Our motivation for developing these models was

based on a need to evaluate survey methods for Ameri-can marten (Martes americana) in order to inform effec-tive survey designs for providing baseline estimates ofpopulation density at specific localities of managerialinterest and for monitoring changes in distribution overbroader extents in Maine, USA. Martens are predictedto have undergone recent state-wide decline due to habi-tat loss (Simons 2009), and mitigating this decline mayrequire making changes to existing fur-harvest or forestmanagement practices. Because physically capturingmarten requires tremendous field effort (Buskirk andRuggiero 1994), passive detection techniques such assnow tracking, non-invasive genetic sampling, andremote cameras are common survey methods used foroccupancy or capture–recapture efforts (Williams et al.2009, Moriarty et al. 2011, Siren et al. 2016). Thesemethods incur different costs and carry different poten-tial shortcomings. We were concerned that tracks of theclosely related fisher (Pekania pennanti) could be mis-classified as marten due to overlap in track and gaitmeasurements (Halfpenny et al. 1995). Although inde-pendent observers appear capable of distinguishing indi-vidual martens in remote-camera photograph for

2032 JOHN CLARE ET AL.Ecological Applications

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capture–recapture analysis using remote cameras (Sirenet al. 2016), the technique is still relatively untested.Hair collection and subsequent genetic analysis pro-duces reliable detections, but can be inefficient due toincreased expense and lower probabilities of detection(Fisher and Bradbury 2014). Our goal was to generaterobust estimates of marten state parameters and com-pare alternative methods to inform future designs whileworking under logistical constraints that made collocat-ing survey methods most feasible.

METHODS

Model descriptions

We use a hierarchical Bayesian framework to describemodels to estimate animal occurrence or density whenmultiple methods produce correlated detections, but themodels could also be fit by maximizing the likelihoodafter marginalizing out latent variables. Throughout, weindex individual animals i, spatial replicates (sites or sta-tions) j, and temporal replicates corresponding to sam-pling occasions k. We consider a sampling situation inwhich there are two collocated methods that may detecta species or individual organism. We consider theobserved data y (yj,k or yi,j,k, depending on whether spe-cies or individual-level detections are considered) as acategorical random variable to reflect four possibledetection outcomes that can occur at a station during aspecific occasion: detection by method 1 but not method2, detection by method 2 but not method 1, detection byboth methods, and detection by neither method. Thevector p denotes the probability of each outcome.Following MacKenzie et al. (2006), we assume that the

latent occupancy state at site j, zj, is distributed as Ber-noulli (wj), where wj is the expected occupancy at site j andmay vary across space in relation to environmental covari-ates as logit (wj) = b0 + b1Xj. Under a standard single-method design, detections during repeated visits to sitesare Bernoulli outcomes with probability (zj 9 pj,k), wherepj,k is the probability of detecting a species present at site jduring interval k and may vary across spatial and/or tem-poral replicates: for example, logit (pj,k) =b0 + b1Xj + b2Xk + b3Xj,k. Our reformulation considersyj,k ~ Categorical (p), and if methods are assumed to beindependent, the vector p can be described using twoparameters corresponding to the probabilities of detectionwith method 1 and method 2 (Table 1). To accommodatecovariance, we estimate four real parameters (the vectorφp) associated with the probabilities of all outcomes yj,k|zj = 1 (Table 1): if a species is present, there are distinctprobabilities associated with detecting the species usingmethod 1 but not method 2, detection with method 2 butnot method 1, detection with both methods, and detectionwith neither. Thus the elements of p, the probability vectorthat describes the distribution of yj,k, are equal to[{zj 9 φ1} {zj 9 φ2} {zj 9 φ3} {zj 9 φ4 + (1 � zj)}]. Wedefine φp ~ Dirichlet (a1,. . . a4), where the subscript p TABLE1.

Categorical

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October 2017 PAIRINGMETHODS TO IMPROVE INFERENCE 2033

indexes a particular detection outcome (out of total possi-ble outcomes P) that occurs with probability φp. FollowingRoyle and Dorazio (2008), we induce the Dirichlet priordistribution for φp by treating each ap ~ Gamma (1, 1)and calculating each probability within up ¼ ap=

PPp¼1ap.

Method-specific probabilities of detection p1 and p2can be respectively derived as p1 ¼ u1 þ u3 and p2 ¼u2 þ u3. The additional real parameters allow the covari-ance between derived quantities p1 and p2 to take on val-ues other than 0, as according to probability theory,^Covðp1; p2Þ ¼ u3 � ðu1 þ u3Þ � ðu2 þ u3Þ. The vector φp

can vary in relation to covariates, for example, a categori-cal covariate with two levels (A, B) can be accommodatedby defining two different vectors for φp: φp,A ~ Dirichlet(a1,A,. . . a4,A), and φp,B ~ Dirichlet (a1,B,. . . a4,B). Estimatesof p1 and p2 for each categorical level can be derivedthe same as when there are no covariates (e.g., p1;B ¼u1;B þ u3;B), and the effect of the categorical covariate ona specific method can be estimated by calculating the dif-ference between the posterior distributions of p1;A andp1;B. Alternatively, both continuous or categorical vari-ables can be accommodated by using a multinomial logis-tic link function such that ap = b0,p + b1,pXj, whereup ¼ eap=ð1þPP�1

p¼1 eapÞ and one value of φp is treated as

a reference and equal to 1=ð1þPP�1p¼1 e

apÞ. Modeling φp

as varying in relation to covariates implicitly allows thecovariance between derived method-specific detectionprobabilities to vary as well.The model can be easily extended to estimate false-

positive detection probability within a site-confirmationdesign (Miller et al. 2011, Chambert et al. 2015,Table 1). We assume that one of the two methods pro-duces uncertain detections of the focal species of inter-est, and that the species is truly absent from a site, false-positive detections occur with probability pfp. The othermethod is assumed to produce certain detections thatprovide auxiliary information about species presence.For example, if method 2 is prone to false positives andmethods are not assumed to be independent, thenp = [{zj 9 φ1} {zj 9 φ2 + (1 � zj) 9 pfp} {zj 9 φ3}{zj 9 φ4 + (1 � zi) 9 (1 � pfp)}]. The probability offalsely detecting a species can be allowed to vary in rela-tion to predictors as logit (pfp,j) = b0,fp + b1,fpXj.Alternatively, φp can be considered conditional on

detection rather than conditional on the state parameter,and defined as a vector of length three corresponding tothe probability of detecting a species in a certain mannergiven that it was detected at all. Under this formulation,φ1, φ2, and φ3 are equivalent to the probability that agiven detection occurs with method 1 only, method 2only, or both methods. The vector φp ~ Dirichlet (a1. . .a3), and yj,k ~ Categorical (p), with p = [{φ1 9 p 9 zj}{φ2 9 p 9 zj} {φ3 9 p 9 zj} {(1 � p) 9 zj + (1 � zj)}].In essence, φp is reformulated to represent the expectedproportional probability of specific positive detection out-comes conditional on a single pooled detection model,and p now represents the probability of detection in anyfashion. Outcome-specific detection probabilities can be

derived as φp 9 p, and covariance between derivedmethod-specific detection probabilities can be furtherderived as ^Covðp1; p2Þ ¼ u3 � p� ððu1 � pÞ þ ðu3�pÞÞ � ððu2 � pÞ þ ðu3 � pÞÞ. This formulation precludesestimation of additional parameters such as false-positivedetection probability or multi-scale occurrence becausethere is a single detection process. However, it can drasti-cally reduce the number of parameters that need to beestimated if there are several methods in operation or sev-eral detection covariates, as it makes it possible to modelvariation in the overall probability of detection withoutneeding to also model variation in or covariance betweenthe probability of specific detection outcomes.We adopt this formulation for implementation of mul-

ti-method spatial capture–recapture models (SCR;Borchers and Efford 2008, Royle et al. 2014) when meth-ods produce covarying detections. In describing SCR,we reuse certain variable names used in the occupancydescription above to retain consistency with publisheddescriptions. SCR models assume that an individual ihas a latent activity center si where its detection proba-bility during a specific sampling occasion is equal toparameter p0. Individual detection probability at specificlocations j during specific intervals k decreases as a func-tion of distance (di,j) between location j and si, such thatpi,j,k = f(di,j). The decay function is commonly consid-ered bivariate normal, with pi,j,k = p0 9 exp(�d2

i;j=2r2),

and r describes the rate of detection decay given dis-tance from the activity center and relates to the spatialarea that an individual uses (Royle et al. 2014). Varia-tion in p0 and r can be modeled using individual, trap,or temporal covariates: e.g., logit (p0) = b0 + b1X1,j, orlog (r) = b0 + b1X1,i. Bayesian implementation of SCRmodels requires supplementing the observed individualdetection histories with a number of all-zero detectionhistories such that there are M observed and augmentedindividuals (Royle et al. 2014). The crux of the model isto estimate the total number of the M individuals thathave an activity center within a user-defined space (||S||):the existence of individual animals zi ~ Bernoulli(w),and abundance (N) is estimated as

PMi¼1 z. With a single

survey method, individual detections at specific stationsand specific times yi,j,k ~ Bernoulli (pi,j,k 9 zi).Following our occupancy description above, our mul-

ti-method reformulation instead considers yi,j,k ~ Cate-gorical (p), with four potential outcomes: y

i,j,k= 1

indicates an individual has been detected by the firstmethod but not the second, yi,j,k = 2 indicates an indi-vidual has been detected by the second method but notthe first, yi,j,k = 3 indicates detection by both methods,and yi,j,k = 4 indicates no detection. If methods areassumed to produce independent detections, p can beformulated using method-specific parameters for p0, andr can either be considered fixed or method specific(Gopalaswamy et al. 2012, Table 2). To accommodatecovariance between methods, we define p = [{φ1 9 pi,j,k 9 zi} {φ2 9 pi,j,k 9 zi} {φ3 9 pi,j,k 9 zi} {(1 � pi,j,k) 9 zi + 1 � zi}], where φ1, φ2, and φ3 are equivalent


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to the probability that an individual was detected withmethod 1 only, method 2 only, or both methods giventhat it was detected at all, the vector φp ~ Dirichlet(a1. . .a3), and pi,j,k, = p0 9 exp (�d2

i; j/2r2). Under this formu-

lation, p0 is equivalent to individual detection by anypossible means given that a set of detection devices areplaced at the activity center, and r describes the declinein detection probability in any fashion as distance fromthe activity center increases. We adopt the formulationof φp as conditional on detection and state parametersrather than as a detection probability vector conditionalon individual existence and location because we considerit unlikely that the relative probability of a specific detec-tion outcome given detection at all changes across space.However, method-specific p0 estimates can be derivedfor comparison or subsequent power analysis, e.g.p0;1 ¼ ðu1 þ u3Þ � p0, and the covariance betweenmethod specific detection probabilities can be esti-mated as Covðpi;j;k;1; pi;j;k;2Þ ¼ u3 � pi;j;k � ððu1 � pi;j;kÞþðu3 � pi;j;kÞÞ � ððu2 � pi;j;kÞ þ ðu3 � pi;j;kÞÞ. Modelingvariation in the covariance between methods can beaccommodated by incorporating additional dimensionsof φp or using log-linear models for ap within a multino-mial logistic link function.

Simulation study

We used simulation to evaluate the influence ofbetween-method detection covariance on multi-methodoccupancy and SCR estimators assuming methods oper-ated independently, and we evaluated the ability of differ-ent posterior predictive checks (Gelman et al. 1996) todetect departures from model assumptions (Appendix S1contains details). We considered an occupancy designwith 100 sites, three visits, and two methods. We simu-lated 500 data sets for each of 18 scenarios correspondingto different values for occupancy probability, overalldetection probability, and covariance between detectionmethods. Our simulation for SCR models was more lim-ited because the models are highly dimensional and com-putationally more intensive. We considered a design with36 detectors placed in a 6 9 6 square with one unit spac-ing, and five sampling occasions. We fixed r = 0.5 and

p0 = 0.3, with N = Binomial (100, 0.3), and φp varying aseither [{0.1} {0.1} {0.8}], or [{0.2} {0.2} {0.6}], becausewe could not imagine that individual identification couldbe reconciled across methods if they did not stronglypositively covary. We simulated 150 data sets for each sce-nario. We fit models assuming between-method indepen-dence and accommodating between-method covarianceusing Markov chain Monte Carlo simulation in JAGS(Plummer 2003) via the R Library jagsUI (R Develop-ment Core Team 2014, Kellner 2015). We evaluated rela-tive bias of point estimates (posterior mean or mode) andfrequentist coverage of the 95% credible intervals in orderto evaluate sensitivity to violation of observation indepen-dence. Simulation convergence was assessed by visualiz-ing trace plots and considering a value of 1.05 for theGelman-Rubin statistic (Gelman and Rubin 1992) as athreshold for convergence.We assessed the ability of three posterior predictive

checks (Gelman et al. 1996) to correctly reject a modelassuming independence between method-specific detec-tions: one based on the marginal log-likelihood of theobservations, one based on the log-likelihood of theobservations conditional on the latent occupancyparameters, and one based on the distribution of jointand method-specific detections (Appendix S1). Wereport average Bayesian P values across simulations as adescription of how powerful the checks were to detectdeparture from assumptions. For SCR models, we onlyused the third posterior predictive check because itera-tively tracing the log-likelihood required an enormousamount of computer memory.

Empirical study

We surveyed martens in north-central Maine, USA(adjacent townships T5R11, T6R10, T6R11, T7R10 cen-tered at 46.149° N, 69.124° W; Fig. 1). The region ishumid (mean annual precipitation 105 cm; NOAA2015a) and characterized by cold winters and mild sum-mers (mean temperature, January �11°C, July 17°C;NOAA 2015a). Forest composition in the study area wastypified by red and white spruce (Picea rubens andP. glauca), balsam fir (Abies balsama), American beech

TABLE 2. Categorical observation probabilities for spatial capture–recapture models when two separate detection methods areconsidered independent or covarying.

Pr(yi,j,k)

yi,j,k Description Independent Covarying

1 detection method 1 only (zi)(pi,j,k,1)(1 � pi,j,k,2) (zi)(φ1)(pi,j,k)2 detection method 2 only (zi)(pi,j,k,2)(1 � pi,j,k,1) (zi)(φ2)(pi,j,k)3 detection both methods (zi)(pi,j,k,1)(pi,j,k,2) (zi)(φ3)(pi,j,k)4 not detected (zi)(1 � pi,j,k,1)(1 � pi,j,k,2) + (1 � zi) (zi)(1 � pi,j,k) + (1 � zi)

Notes: All values of pi,j,k = p0 9 exp(�d2i;j /2r

2), where p0 is equivalent to detection probability if a detector is placed directly atan individual’s activity center, and r represents the rate of detection decay given distance from the activity center; zi indicates thebinary occurrence state of an individual animal, and φ is a vector of probabilities associated with each specific observation outcomeconditional on it being detected.


(Fagus grandifolia), and sugar maple (Acer saccharum)managed for industrial or mixed-use purposes.During 7 January–4 April 2015, we deployed 238

detection stations with multiple detection methods(Fig. 1). We used Monte Carlo simulation to evaluatehow different station spacing and deployment time influ-enced spatial capture–recapture estimators in order tooptimize survey design with the R library secr (R Devel-opment Core Team 2014, Efford 2014) and simulatedmarten detection parameters drawn from the results ofSiren (2013). Simulations suggested that 750-m spacingand 15-d deployment time produced satisfactory estima-tion, and our planned design was to rotate stationsacross the study area every 15 d. In reality, stations weresampled for 9–31 consecutive 24-h periods (x ¼ 19)owing to an abrupt loss of snowpack at the end of theseason, and because we extended one rotation to evalu-ate whether we had dramatically underestimated latencyto detection. Mean nearest neighbor distance betweenstations was 602 m, and the minimum convex polygonsurrounding the outer camera stations was 306 km2.Each station consisted of a bait platform built out of

2.5 9 10 cm boards screwed or zip tied to a standingtree 50–100 cm above snow level, and baited with anopen sardine can (Fig. 2). Following the designs ofMaguoun et al. (2011) and Siren et al. (2016), we wiredan access ramp (downed wood with >7 cm diameter) tothe bait station to provide access from the snow level.We set a single camera (Bushnell Trophy Cam, Overland

Park, Kansas, USA) facing the bait station 50–100 cmopposite the bait to capture images of unique ventralmarkings (Fig. 2). We collected hair samples on twopieces of glue-board (Tomcat Indoor Rodent Trap,Madison, Wisconsin, USA) cut into 2.5 9 10 cm stripsand stapled below the sardine tin on the platform. Allstations were located between 50 and 100 m from unp-lowed roads or snowmobile trails, and we deployed a calllure made out of skunk quill mixed into liquefied petro-leum jelly (ratio of quill to petroleum jelly 1:12 ounces).Although the proximity to roads creates the risk of abiased sample, because sites were baited, nearly allpotential marten home ranges within the study area con-tain roads, and martens exhibit only extremely fine-scaleavoidance of roads, we expect our design did not seri-ously compromise estimates of marten occurrence ordensity (Chapin et al. 1998, Robataille and Aubry 2000,Zielinski et al. 2008).We visited the detection stations every 3–4 d

(�x ¼ 3:18d) to replace bait, camera batteries, and gluestrips as needed. If hair was deposited, glue strips werereplaced. We collected hair samples if we could notexclude marten deposition (e.g., deposition by anotherspecies was observed on camera). We stored samples incoin envelopes with silica desiccant. During each visit,we recorded any marten tracks encountered along thefoot trail to the station or underneath the station. Wemarked tracks when observed to avoid subsequent dou-ble counting.

FIG. 1. Location of stations used to sample American marten during winter 2015, and recorded detections by sampling methodin northern Maine, USA relative to existing tree cover derived from LANDFIRE. Detections by method are aggregated across visits(e.g., camera and track indicates that both methods produced detections, not necessarily that both methods produced a simultane-ous detection).


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We identified individual martens detected by camerasand hair catches. Two independent observers identifiedindividual martens from photographs based on the pres-ence of unique ventral markings (Siren et al. 2016).When both observers agreed, we treated this as a specificindividual encounter, and when observers were eitherambiguous regarding individual assignment or dis-agreed, we discarded the image sequence from analysis.Hair samples were confirmed as marten using standardmtDNA protocols (Riddle et al. 2003) and individuallyassigned based on genotypes from nine microsatelliteloci and sex-specific markers (Appendix S2). A primarydifference between the methods was that although hairsamples could only possibly detect one individual visit-ing a station during a check, a camera could detect mul-tiple individuals visiting the station.We cross-compared marten images with the detection

histories produced by genotypes to evaluate the accuracyof our photo-identification. The evaluation was imper-fect, because there were several possible comparativeoutcomes: (1) a marten was identified on camera anddirectly observed depositing hair during the encounter,(2) a single marten was identified on camera during aspecific check and a genotype was available for thatcheck, (3) multiple martens were identified on cameraduring a specific check, and a genotype was available, (4)a genotype was available without a photographic identi-fication, and (5) a photographic identification was avail-able without a genotype. We treated outcomes one andtwo as absolute matches, and first evaluated any incon-sistency between detection histories. We cross-checkedthe third outcome by assessing if an individual withlinked photographic and genotypic signatures wasobserved during the check. Ultimately, we found nounambiguous disagreements between individual assign-ments (see Appendix S3 for outcomes).

Fitting occupancy models

We considered six distinct models for estimating mar-ten occupancy based on the combination of cameraimages and snow tracks: three models consideredmethod-specific observations to be independent, andthree models allowed methods to produce covaryingdetections. Within each model, we considered variance inoccupancy as logit (wi) = b0 + b1 9 FORESTj, whereFORESTj represents average vertically projected treecanopy cover (LANDFIRE 2015) within a 1-km circularbuffer around a specific station. Martens select againstusing landscapes with limited forest regionally (e.g., Cha-pin et al. 1998), and the extent of this buffer was selectedbased on previous studies of marten habitat associations(e.g., Simons 2009, Wasserman et al. 2012). Whenmethods were assumed to be independent, variance indetection probability conditional on presence (pj,k,m,where m indexes method) was modeled as logit (pj,k,m) =b0,m + b1,m 9 EARLYj + b2,m 9 Cj,k,m. EARLYj was asite-specific binary variable distinguishing sites sampledduring early winter (January and February) and late win-ter (March and April) to account for temperature-specificchanges in marten activity, seasonal effects with regard todetecting active marten such as changes in snow com-paction, temperature effects on the stickiness of glue trapsand camera triggering, and real changes in marten behav-ior associated with females giving birth in March andearly April (Powell et al. 2003). We used this binary vari-able to capture numerous correlated continuous variables(snow depth and compaction, temperature) for which welacked data: February 2015 was a historically cold monthin the study area, after which the temperature increasedrapidly (NOAA 2015b), and initial assessment suggestedthat detection rates were better reflected by two distinctaverages than a linear or quadratic trend. Cj,k,m was atime- and site-specific binary indicator of whether a speci-fic method had previously detected marten, included toaccommodate potential trap-happy responses to the bait.When methods were considered to have covariance, wedefined four probability vectors φ to describe the fourpossible detection outcomes for each possible covariatecombination of Cj,k and EARLYj. Because we wereexplicitly concerned about the potential for track-basedfalse positive detections, four models (two assuming inde-pendence, two allowing covariance) included a track-spe-cific false positive probability. In two models, pfp wasconsidered constant. In two other models, pfp,i,j varied asa logit-linear model based on whether a fisher was pho-tographed at the station during the same occasion. Forgeneral comparison, we also fit single-method models(which could not incorporate false-positive probability)based on track and photographic detections; we makecomparisons based on estimates of finite-sample occu-pancy (i.e., the proportion of detection stations within thesample estimated as occupied; Royle and K�ery 2007).We fit all models using JAGS through the R Library

jagsUI (R Core Team 2014, Kellner 2015). Prior

FIG. 2. Detection station design used to sample Americanmarten in northern Maine during winter 2015. On right, amarten visiting a detection station and depositing hair on a gluestrip.


distributions for the inverse-logit of the intercept param-eters were set as Uniform (0, 1), and prior distributionsfor effects on the logit scale were defined as Uniform(�5, 5) to reflect the limited range of plausible effectsizes (Gelman et al. 2008). Simulation settings includedthree chains of 25,000 iterations, with the first 15,000iterations discarded as burn-in and the last 10,000 itera-tions thinned by five. Thus, 6,000 posterior samples wereused for inference, and model convergence was assessedby visual inspection of the chain trace-plots and withestimates of the potential scale reduction factor (Gelmanand Rubin 1992).We first evaluated the suitability of different model

structures (independent vs. covarying methods), using theresults of our simulation study and posterior predictivechecks to assess whether assuming independence betweenmethod-specific detections was a reasonable assumption.Once a model structure was selected, we compared thethree candidate models with indicator variable selectionmethods (Kuo and Mallick 1998). Indicator variableselection typically associates a model coefficient termwith a latent indicator variable g that has a prior distribu-tion of Bernoulli (0.5) that determines whether the predic-tor is included within the model likelihood. We modifiedthe formulation to treat g2 (the indicator associated witha fisher effect on false-positive probability) as conditionalon g1 (the indicator associated with there being any false-positive probability at all): when the iterative sample forg1 = 1, g2 ~ Bernoulli (0.5), but was otherwise fixed asequal to zero. Thus, an intercept-only false-positive prob-ability entered the model likelihood when g1 = 1 andg2 = 0, and when both g1 and g2 = 1, false-positive prob-ability was modeled as varying in relation to visit-specificfisher photographs. The posterior mean of the indicatorvariables is used to evaluate model support (Kuo andMallick 1998, Royle and Dorazio 2008): the proportionof simulations in which g1 = 0 is equivalent to the sup-port for a model lacking a false-positive component, theproportion of iterations in which both g = 1 is equivalentto the support for a false-positive model and a term forfisher, and the remainder is the support for an intercept-only false-positive model. Because there were three mod-els under consideration, we used a Bernoulli (0.67) priorfor g1 and a Bernoulli (0.5) prior for g2 to represent uni-form prior support for each specific model. Post-hoc refit-ting suggested little sensitivity to the prior distributionsused for g.

Comparing method-specific density estimates

We attempted to fit two spatial capture–recapturemodels: one assuming independence between geneticand photographic detections and one allowing methodsto produce covarying detections. The model thatassumed independence between genetic and photo-graphic detections exhibited poor mixing even afterextending chain length, and we consequently make infer-ence with the single model incorporating method-

specific detection covariance. We considered the samesources of detection variation used for occupancy model-ing, trap-specific behavioral responses and a detector-specific factor coding for whether it was deployed duringearly or late winter. We also modeled sex-specific differ-ences in p0 and r to account for differences betweenmale and female marten space use (Katnik et al. 1994),treating the sex of individual marten as a random vari-able following Sollman et al. (2011). Thus, the model forindividual detection probability was pi,j,k = p0,i,j,k 9 exp(�d2

i;j/2r2sex½i�), where logit (p0,i,j,k) = b0,sex[i] + b1,sex[i] 9

EARLYj + b2,sex[i] 9 Ci,j,k. Observed data yi,j,k ~Categorical (p), with p = [{φ1 9 pi,j,k 9 zi} {φ2 9 pi,j,k 9 zi} {φ3 9 pi,j,k 9 zi} {(1 � pi,j,k) 9 zi + 1 � zi}].The prior distribution for r was defined as Uniform (0,10). MCMC settings, assessments of convergence, andprior distributions for probability or beta parameterswere identical to those used for occupancy modelingexcept that all 30,000 samples after the burn-in wereused for inference. For comparison, we also fit SCRmodels using exclusively camera or hair detections. Thesingle-method model based on hair detections incorpo-rated the same covariate structure for pi,j,k, but the sin-gle-method camera model did include sex-specificparameters because we could not distinguish sex photo-graphically and were specifically interested in under-standing whether failure to do so might bias estimates.We considered φp as a constant vector because earliermodel fitting attempts suggested that there were too fewdetections during earlier winter to effectively identifyseparate levels of φp, and that φp exhibited little changeafter a marten was initially detected. Code for fittingoccupancy and SCR models with empirical data is pro-vided in the supporting information.

RESULTS

Simulation results

As we hypothesized, multi-method occupancy andspatial capture–recapture estimators that assume meth-ods produce independent detections performed poorlywhen this assumption was violated. Occupancy modelsthat assume methodological independence and thataccommodate inter-method detection covariance per-formed similarly when the simulated covariance betweeninter-method detections was small. When simulatedcovariance was large, models that assumed methodologi-cal independence tended to underestimate occupancyand overestimate detection probability, although theeffect of inter-method covariance did not seem to com-promise model performance when the overall probabilityof detection was large enough that few occupied siteslacked detections (Appendix S1: Fig. S3). Modelsaccommodating inter-method detection covarianceexhibited approximately nominal coverage and muchless bias across the high-covariance simulations,although estimates of method-specific detection


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probability were positively biased when the number ofobservations within the simulated data was very sparse(i.e., p = 0.3, w = 0.3; Fig. 3). Spatial capture–recapturemodels that assumed methodological independencewhen the models featured positive observation covari-ance also exhibited permissive coverage, negativelybiased estimates of both population size and r, and pos-itively biased estimates of p0 (Table 3). Models accom-modating detection covariance methods exhibitedapproximately nominal coverage and minimal bias.None of the posterior predictive checks we considered

were perfect tools for determining when assumption

violations led to estimator bias (Appendix S1). The checkbased on a chi-square discrepancy between the sums ofobserved and simulated detections by method rejected theoccupancy models assuming independence when methodsproduced strongly positively covarying detections regard-less of whether inter-method covariance led to estimatorbias, but exhibited limited power to reject improperlystructured SCR models (Appendix S1). The other poste-rior predictive checks based on model deviance exhibitedlimited power to reject models that incorrectly assumedmethods produced independent detections, althoughpower to detect poor goodness-of-fit tended to increase as

FIG. 3. (A) Relative bias of occupancy and method-specific detection probability point estimates and (B) frequentist coverageof 95% credible intervals when multi-method occupancy models assumed independence between methods or allowed covariancebetween methods. Axes correspond to simulated occupancy probability and the combined detection probability of the two simu-lated methods per occasion.


estimator bias increased (Appendix S1). Although this wasinitially surprising, such checks would be better suited fordetecting a misspecification of the variability in occupancyor detection probability, and our simulations consideredall parameters constant across sites and occasions. Thus,the most robust way to ensure assumptions were not beingviolated in ways that hindered inference appeared to be fit-ting both models to evaluate estimate similarity.

Empirical study

Occupancy.—Total sampling effort was 4,112 nights,corresponding to 1,296 individual station visits. Camerasrecorded martens during 52 (4%) station visits, trackswere recorded on 76 (6%) visits, and verified marten hairwas collected on 39 (3%) visits. In total, martens weredetected at 49 (21%) out of the 238 stations, althoughdetection outcomes were variable by method (cam-eras = 24, hair = 20, tracks = 47; Fig. 1). Of the threepositive detection outcomes we considered within multi-method camera and track occupancy models, camera-only detections were recorded 13 times, track-only detec-tions were recorded 37 times, and joint camera and trackdetections were recorded 39 times. Fishers were detectedon camera at 18 stations during 21 check intervals.Estimates of marten occupancy using multiple methods

were ubiquitously smaller and more precise than those

based on single-method observations, but they varied con-siderably depending on assumptions of methodologicalindependence and false-positive detections (Fig. 4). Modelsassuming independence between methods provided moreprecise estimates of marten occupancy than models allow-ing methodological covariance, but also provided muchlower estimates of occupancy (Fig. 5), a strong indicationthat the assumption of methodological independence wasinducing bias. Furthermore, the model assuming method-ological independence and no false-positive detectionsappeared to be producing more joint-method detectionsthan iteratively simulated data (Bayesian P value < 0.01),while exhibiting poorer fit for the detection sub-model thaniteratively simulated data (Bayesian P value = 0.88,Table 4). Consequently, we further considered only modelsallowing methodological covariance.Indicator variable selection suggested there was extre-

mely little support for assuming that snow tracking didnot produce false-positive detections (posterior modelprobability = 0.01), with relatively equitable support formodels that assumed snow tracks resulted in false-posi-tive marten detections at a constant rate (posteriormodel probability = 0.50) or that the likelihood of false-positive track detections increased during check inter-vals when fishers were observed on camera (posteriormodel probability = 0.49). We use the averaged modelproduced by indicator variable selection when presenting

TABLE 3. The relative bias and coverage of spatial capture–recapture models that either assume multiple methods produceindependent observations or allow method-specific observations to covary.

Relative bias

Detection vector (φ), model type, and, parameter Posterior mean (%) Posterior mode (%) 95% CRI coverage (%) BPV

[{0.1} {0.1}{0.8}]Independent methodsp0 75.44 — 30.67 0.204r �16.44 — 34.00N �14.14 �16.90 56.00

Covarying methodsp0 6.04 — 96.00 —

r 0.95 — 94.00N 6.17 �0.75 93.30

[{0.2} {0.2}{0.6}]Independent methodsp0 57 — 44.00 0.201r �13.39 — 45.30N �11.59 �14.37 70.00

Covarying methodsp0 5.51 — 93.30 —r 0.97 — 97.30N 3.43 �1.50 92.70

Notes: Simulated models include three potential successful detection outcomes that make up specific proportions of the observeddetections (φ): the first two values represent the proportion of detections that are exclusively achieved with a specific method, andthe third value represents the proportion of detections in which both methods detect an individual. Parameters p0, r, and N corre-spond to method-specific detection probability of an individual when a method is located directly at its activity center, the half-nor-mal decay of individual detection probability as distance between an individual and detector increases, and the number ofindividuals. BPV corresponds to the average value of a posterior predictive check based on a comparison of the empirical chi-squarediscrepancy between the number of methods detecting an individual at a specific trap and occasion vs. iteratively simulated data.CRI, credible interval. Dashes represent values that were not estimated.


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estimates of detection and state parameters. Realizedmarten occupancy within the sampling area was low(finite sample occupancy = 0.26, 95% credible interval[CRI] 0.15–0.42), but positively associated with sur-rounding forest canopy cover (b ¼ 1:51, 95% CRI0.50–2.77). Cameras and snow tracks had comparableprobabilities of detecting present martens: both methodswere more likely to detect present martens in late winterand after initial marten detection (Fig. 5). The overallprobability of detecting a present marten by any meansduring a specific visit ranged from 0.08 (95% CRI0.02–0.17) in early winter for initial detections to 0.57 (95%CRI 0.43–0.70) in late winter after a marten had beenpreviously detected. The constant probability of falselydetecting marten tracks during a check at a site where thespecies was absent was estimated as 0.02 (95% CRI0.01–0.03); when the additional term associated with con-current fisher photographs was included within the model,there was weak indication that this probability increased tonearly 0.08 (b ¼ 1:30, 95% CRI�1.61–3.68; Fig. 5).

Density.—Individual martens were detected at specificstations during specific checks 55 times (24 camera only,4 hair only, 27 combined). We identified 15 individualmartens visiting camera stations based on photographs,with 75% observer agreement on individual assignmentacross all photographic events. A substantial proportion(66%) of the unassigned photographic events containedno individual markings or were too blurry to be useful,with the remaining events subject to observer disagree-ment. Based on the patterns of assigned individuals (i.e.,several successive visits over a single occasion), weexpect that few data were lost, because most of the unas-signed photographic events were flanked by identifiableevents within the same occasion and the average timebetween inter-individual visits has been reported as>24 h (Siren et al. 2016). Genetic assignments based onhair distinguished eight individuals with an equal sexratio (4:4), with one individual we assume was distinctand not identified photographically given that nearby

martens identified photographically were linked to geno-types (Appendix S3).We estimated marten density using a multi-method

model as 7.7 or 8.0 individuals/100 km2 (respectively,the mode and mean of the posterior distribution; 95%CRI 4.4–13.1). Camera-only estimates of marten densitywere comparable (posterior mode = 6.0, posteriormean = 6.8, 95% CRI 3.8–11.1), while hair-only esti-mates were lower (posterior mode = 2.9, posteriormean = 3.5, 95% CRI 1.50–6.60; 95% CRI for differ-ences between posterior density samples using hair-onlyand or multi-method models did not overlap 0).Although male martens appeared to use more spacethan female martens (rmale > rfemale), they were typi-cally less detectable at any specific point within the areathey used (p0,male > p0,female; Table 5). Both sexes weredetected less frequently during early winter and detectedmore frequently at specific detectors after initial encoun-ter, and we could not detect whether the sex ratio of mar-tens within the study area was different than 1:1(Table 5). Individual martens were more likely to bedetected photographically than genetically, althoughcombined genetic and photographic detections were aslikely as photographic detections alone (Table 5).

DISCUSSION

Using multiple survey methods and multi-methodanalysis can enhance the rigor of wildlife survey infer-ence by strengthening state parameter estimates, incor-porating information that may be provided only byspecific methods such as individual sex, and correctingfor specific methodological shortcomings such as false-positive detections (Nichols et al. 2008, Miller et al.2011, Sollman et al. 2013, Fisher and Bradbury 2014).Additionally, multi-method models serve as valuabletools for evaluating the strengths and weaknesses of dif-ferent field methods, allowing practitioners to moreeffectively design and efficiently implement survey ormonitoring efforts. Our reformulations relax the need

TABLE 4. Model selection and goodness of fit results for the six multi-method occupancy models fit considering method-specificdetection to be either independent or covarying.

Model MethodsBPV

(detections)BPV

(marginal log L)BPV

(conditional log L)Modelweight

w(forest), p(early + C) independent <0.01 0.54 0.88 —w(forest), p(early + C), fp(.) independent 0.44 0.52 0.65 —

w(forest), p(early + C), fp(fisher) independent 0.48 0.53 0.26 —w(forest), p(early + C) covarying — 0.26 0.25 0.01w(forest), p(early + C), fp(.) covarying — 0.45 0.36 0.50w(forest), p(early + C), fp(fisher) covarying — 0.46 0.37 0.49

Notes: BPV represents the proportion of Markhov chain Monte Carlo (MCMC) iterations in which the data set produced a lessextreme chi-square statistic based on cell-specific detections than a simulated data set (Detections), a smaller log likelihood thansimulated data based on iterative parameter values (BPV Marginal Log L), and a smaller log-likelihood given iterative parametervalues and the latent occurrence states of specific sites (BPV Conditional Log L). Model weight represents the proportion of poste-rior MCMC iterations in which that model was used for estimation. Dashes indicate no values were estimated. C is an indicator ofwhether a marten had been detected previously at a specific trap location, and fp represents false-positive detection probability.


for methods to operate independently, providing practi-tioners considerably more flexibility to take advantageof existing models. Furthermore, our application high-lights the broader value of using multiple field-methodswhen implementing wildlife surveys.Relaxing the assumption of methodological indepen-

dence when using multi-method analysis provides twoprimary benefits. First, our simulations suggest that

violation of this assumption can result in precisely biasedestimates of state and detection parameters using previ-ously described model structures, meaning that practi-tioners using these analyses without consideration for theassumptions may gain the pyrrhic ability to estimate newparameters or compare relative method-specific detectionparameters while losing the ability to robustly estimatethe state or detection parameter values motivating the

FIG. 4. Posterior distributions of finite-sample occupancy (proportion of sites occupied, or ^PAO) for American martens sam-pled using multiple methods in Maine during winter 2015. Vertical lines correspond to observed occupancy by method (snow tracksor remote camera detections), or 95% credible intervals (CRI). Top panels depict estimates derived from a single method, middlepanels depict estimates derived from multi-method models incorporating methodological covariance, and bottom panels depict esti-mates derived from multi-method models assuming methodological independence. Multi-method models either assumed no falsepositive detections (left), constant probability of false positive detections using tracks (middle), or that false positive detections wereassociated with observed fishers (right).


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survey effort. Simulation results suggest that modelsassuming independence produce robust parameter esti-mates when there is not strong inter-method covarianceor when overall detectability is high. Unfortunately, theseparameters are difficult to accurately guess a priori (Guil-lera-Arroita et al. 2014), and thus the biased estimatesproduced by models assuming independence cannot nec-essarily be used to diagnose whether one operates in aproblematic part of the parameter space. This may beparticularly problematic for efforts like our own that seek

to use initial parameter estimates to inform subsequentsurvey or monitoring designs. The combination of nega-tive bias and permissive coverage increases the likelihoodof overstating population vulnerability and survey abilityto detect changes in population parameters across time orspace. As many changes in management or policy aretriggered when specific population objectives areachieved, this precise bias increases the risk of using sur-vey or monitoring designs that may both fail to detect theachievement of a positive distribution or abundance

FIG. 5. Posterior distributions of method-specific detection and false-positive detection parameters drawn from a model-selected multi-method occupancy model estimated for American martens in Maine during winter 2015. Panels depict (A) initialdetection probability during early winter, (B) detection probability after initial detection during early winter, (C) initial detectionprobability during late winter, (D) detection probability after initial detection during late winter, (E) probability of falsely detectinga marten when not present at a station, and (F) the effect of a fisher being photographed at a station on false-positive probability.


objective as well as misconstrue random sampling varia-tion with negative distribution or abundance trends (e.g.,Gibbs et al. 1999). These risks are pointed within ourown study system, as our estimates corroborate previouspredictions of local marten population decline (Payer1999, Simons 2009), increasing the urgency of implement-ing monitoring practices and considering alterations tomanagement practices.Of course, such bias would be a non-issue if there were

no justification for pairing different survey methods orpractical constraints precluding maintaining inter-method independence, the second advantage providedby our reformulation. We had distinct motivations forpairing cameras and hair catches: a desire to limit costsassociated with laboratory processing of non-target hairsamples, and a desire to externally evaluate whetherrobust photographic identification of marten individualswas possible. Cameras allowed us to remove more than50% of hair samples from lab analysis, and the savingsessentially recouped our initial camera investment. Inturn, the observed agreement between genetic and pho-tographic identifications provided additional assurancethat martens could be reliably photographically distin-guished, an external validation that is largely absentfrom the vast majority of photographic capture–

recapture efforts (Foster and Harmsen 2012). We alsohad distinct constraints that limited our ability to main-tain spatial or temporal independence between the dif-ferent candidate field methods we deployed: mostpertinently, financial constraints required us to reducesampling extent, intensity, or duration. Even withoutthese considerations, maintaining methodological inde-pendence may have increased the risk that differences insampling efficacy would have been confounded with eco-logical differences (e.g., Graves et al. 2012). We expectthat our use of bait would have limited the risk of localspatial environmental heterogeneity confoundingmethod efficacy, as martens will willingly use manyotherwise risky or low quality habitats if there is a foodreward (Moriarty et al. 2016). On the other hand, hadwe operated distinct methods during different time inter-vals, our interpretation of the relative sampling efficacyof different methods may have been strongly compro-mised by the strong seasonal changes in detection proba-bility we observed. Lengthening our survey duration toachieve the same spatial coverage may have further exac-erbated confounding of method-specific sampling effi-cacy with marten population or behavioral changes,because our sampling period would then have over-lapped with either commercial fur-harvest or parturition(Powell et al. 2003). In essence, had we maintained inde-pendence between our field methods, our survey effortmay have been both more expensive and less effective atevaluating field methods and estimating populationparameters.The benefits associated with implementing multi-

method models in any fashion depend on there beingmeasurable value in using or considering multiple sam-pling methods. External constraints often motivate prac-titioners to evaluate trade-offs between the costs andefficacy of different field techniques (e.g., Long et al.2007a), and this was one objective of our field effort. Onthe basis of cost-efficiency alone, we may have identifiedsnow tracking as the most efficient means for monitor-ing changes in marten occupancy, and remote camerasas the most efficient means for estimating marten den-sity. But more broadly, different field methods providedifferent lenses through which ecological patterns areimperfectly sampled, and method-specific foibles canlead to distinct biases that can be difficult to evaluatewithout using multiple methods, and can change the cal-culus associated with survey design. We leveraged ourmulti-method approach to evaluate a priori concernsthat snow tracking could produce false-positive martendetections, that inability to distinguish marten sex pho-tographically could negatively bias camera-based densityestimates, and, as discussed above, that photographicmarten identification could be prone to misclassifica-tion. This more nuanced evaluation paid strong divi-dends. Despite the affordability of snow tracking,evidence that many snow-track detections were falsepositives reinforces previous warnings that exclusive reli-ance on inexpensive ephemeral detection methods to

TABLE 5. Parameter estimates (presented as effects) and 95%credible intervals (upper, UCRI; lower, LCRI) for male andfemale (M, F) American marten derived from multi-methodspatial capture–recapture models considering hair andcamera detections in northern Maine, USA.

Parameter Posterior mean LCRI UCRI

p0, intercept (M)† �1.93 �2.62 �1.12p0, intercept (F)† �1.34 �2.31 �0.27p0, early winter (M)† �1.51 �3.20 0.63p0, early Winter (F)† �1.50 �2.97 �0.11p0, previously detected (M)† 1.99 0.93 3.01p0, previously detected (F)† 1.37 0.18 2.61r (M)‡,§ 1.31 0.88 1.81r (F) 0.66 0.43 0.91Proportion female 0.68 0.32 0.94φ1, camera only 0.43 0.31 0.56φ2, hair only 0.09 0.02 0.16φ3, both camera and hair 0.48 0.35 0.61Proportion camera detections 0.91 0.84 0.98Proportion genetic detections 0.57 0.45 0.69Density¶ 8.00 4.40 13.10

Notes: Early winter indicates sampling during January andFebruary rather than March and April, previously detectedindexes the effect of being previously detected at a specificdetection station, p0 represents the probability of detecting anindividual at its activity center, r represents detection probabil-ity decay with distance, and φ represents the probability of aspecific detection type occurring conditional on any detectionat all.†Estimates are presented as effects on the logit scale.‡95% credible intervals for differences in sex-specific parame-

ters do not overlap 0.§r is estimated on the real scale in kilometer units.¶Individuals per 100 km2.


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survey organisms sympatric to very similar species cancarry substantial risk of overestimating distribution ormischaracterizing trends (Miller et al. 2015). Robust useof snow tracking or other ephemeral sign as exclusivesurvey techniques may generally be contingent on imple-menting more conservative protocols to avoid misclassi-fication, or using model frameworks that can accountfor false-positive error by leveraging additional informa-tion such as experimental assessments of observer erroror ancillary validation of plastered or photographedtracks (Halfpenny et al. 1995, Chambert et al. 2015,Ruiz-Gutierrez et al. 2016).In contrast, cameras provided a greater probability of

detecting individual martens than hair snares withreduced long-term cost, and similarity between densityestimates derived from camera detections only and acombination of genetic and photographic detectionssuggests photographic inability to distinguish martensex was not severely biasing density estimates. This maybe because, although male martens used more overallspace than female martens, they were detected less fre-quently at specific locations, a compensatory hetero-geneity in detection that is not expected to lead toserious bias in density estimates (Efford and Mowat2014). Consequently, using exclusively cameras for mar-ten capture–recapture studies (Siren et al. 2016) may bea cost-effective alternative to more prevalent genetic cap-ture–recapture techniques.Other benefits provided by using multiple field meth-

ods may be serendipitous. The ability to observe hairdeposition on camera revealed potential limitations ofour hair-catch implementation. The first marten todeposit hair while visiting a station often appeared to ripthe staple holding one part of the glue-strip off of thebait structure, precluding deposition by subsequent mar-tens. This limits individual cross-contamination (Pauliet al. 2008), however, it is problematic because it impliesa type of detection competition between individuals rec-ognized as leading to underestimating density usingSCR in live-trapping studies (Distiller and Borchers2015). In fact, this potential bias might be stronger whensampling with single-catch hair detectors rather thansingle-catch live traps because one individual can pre-vent the detection of other individuals at multiple loca-tions, and our hair-based estimates of marten densitywere notably smaller than estimates produced by cam-eras only or multiple methods. Consequently, we cautionthat density estimates derived from exclusive use of sin-gle-catch hair detectors may not be robust. To a lesserdegree, cameras delivered an additional unanticipatedbenefit by providing direct information about stationvisitation by fishers, a strongly suspected cause of mis-classification error. The effect of fisher detection by cam-era on track false-positive probability was not preciselyestimated, perhaps due to infrequent fisher detection,but modeling variation in false-positive detection proba-bility can improve occupancy estimates (Miller et al.2015). Observing fishers on camera, and not martens,

when marten tracks were detected also provided strongevidence of false-positive error independent of parame-ter estimates.However, the method-specific concerns we identified

should not over-shadow the value of the informationeach technique provided. For example, although somesnow-tracks appeared to be false-positive detection,many detections were true positive, providing additionalinformation regarding marten occurrence that improvedthe precision of occupancy estimates and required negli-gible additional cost or effort. Many surveys for differ-ent taxa may permit the collection of opportunistic butpotentially unreliable detection information such astracks or calls, and the framework we describe explicitlyenables practitioners to include this information withinmodels while accounting for the risk that this oppor-tunistic information is unreliable. We can think of fewmeans by which a survey effort can increase the proba-bility of detecting target species and improve the preci-sion of state parameter estimates that requires lessexpenditure. Similarly, hair catches were less likely todetect martens than cameras and there was no com-pelling evidence that ignoring sex-specific differences inmarten space use biased density estimates. Yet, contin-ued validation of photographic identification of individ-ual martens could prove extremely useful if theanalyzing observers changed, and the genetic and iso-topic information contained in hair samples providesconsiderable potential to evaluate more targeted reasonsfor variability in marten population parameters (e.g.,Schwartz et al. 2007). Our paired-method designappears to allow this information to be collected withsubstantial cost savings.Instead, a broader epiphany provided by this analysis

was that there was no compelling inferential or logisticalreason to monitor martens using only cameras or snowtracks, or estimate marten density using only either cam-eras or hair snares. Admittedly, the synergistic benefitsof using different field methods may not always out-weigh the financial costs of doing so. However, pairingmultiple methods and using models that appropriatelyaccommodate covariance between these methods pro-vides practitioners the potential to improve understand-ing of ecological parameters and how well theseparameters are sampled while simultaneously limitingthe investment that could be lost. No information comesfor free in wildlife sampling, but collocating methods isa practical approach to providing additional informationfor limited expenditure.

ACKNOWLEDGMENTS

Funding was provided by the Maine Department of InlandFisheries and Wildlife (MDIFW) through the Federal Aid inWildlife Restoration Act (award # 3013311); at the time of thispublication, the data have not been published by MDIFW. Addi-tional support was provided by the University of Maine andMDIFW through the Cooperative Agreement with the U.S.Geological Survey, Maine Cooperative Fish and Wildlife


Research Unit, and J. Clare was partially supported by NESSF#NNX16AO61H during manuscript preparation. This researchwas approved by University of Maine Institutional Animal andCare Use Committee (protocol #A2014-01-03). Mention of tradenames and commercial products does not constitute endorsementor recommendation for use by the U.S. Government. R. Canarr,J. Eddy, B. Peterson, and L. Skora provided field assistance;W. Jakubas assisted with logistics, improved research focus, andprovided helpful review; A. Siren provided insight into detectionstation design; J. Hoekwater, J. Bissell, R. Morrell, E. Sypitowski,B. Burgason, A. Cowperwaite, and M. McKeague graciouslyassisted with logistics and land access. M. Schwartz and K. Pil-grim graciously implemented laboratory methods to determinemarten genotypes. D. Linden, D. Miller, and three anonymousreviewers provided helpful commentary on previous drafts.

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SUPPORTING INFORMATION

Additional supporting information may be found online at: http://onlinelibrary.wiley.com/doi/10.1002/eap.1587/full

DATA AVAILABILITY

Data available from the Dryad Digital Repository: https://doi.org/10.5061/dryad.4mt00


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