Estimating population size by spatially explicit capture–recapture

Animal density is a parameter of basic interest to field biologists. But owing to logistical and analytical constraints, estimating animal density has been very challenging. Spatially explicit capture–recapture (SECR) models were developed to address this particular, long‐standing problem. In this article, some of the important “milestones” in the SECR literature are discussed. The basic idea in SECR models is to include information about locations of animal captures into the modeling so that density is estimated directly. The early SECR type of approach involved estimation of density via simulations and inverse prediction. The first direct SECR estimator was likelihood‐based, which was more flexible and allowed for inclusion of covariates. In parallel began the development of Bayesian versions of the SECR models. These allowed for greater flexibility and for extensions which could, in addition, also estimate population vital rates. SECR models have witnessed several applications, ranging from analysis of camera‐trap data on large cats to acoustic signal data from birds. The future of SECR models is expected to go far beyond density estimation. It has great potential to answer some long‐standing questions about how behavioral processes drive population dynamics in wild animals.

A fundamental problem in wildlife ecology and management is estimation of population size or density. The two dominant methods in this area are capture–recapture (CR) and distance sampling (DS), each with its own largely separate literature. We develop a class of models that synthesizes them. It accommodates a spectrum of models ranging from nonspatial CR models (with no information on animal locations) through to DS and mark-recapture distance sampling (MRDS) models, in which animal locations are observed without error. Between these lie spatially explicit capture–recapture (SECR) models that include only capture locations, and a variety of models with less location data than are typical of DS surveys but more than are normally used on SECR surveys. In addition to unifying CR and DS models, the class provides a means of improving inference from SECR models by adding supplementary location data, and a means of incorporating measurement error into DS and MRDS models. We illustrate their utility by comparing inference on acoustic surveys of gibbons and frogs using only capture locations, using estimated angles (gibbons) and combinations of received signal strength and time-of-arrival data (frogs), and on a visual MRDS survey of whales, comparing estimates with exact and estimated distances. Supplementary materials for this article are available online.

ABSTRACTInformed management of wildlife populations requires the accurate estimation of abundance, sex ratio, and other population parameters. For deer (Odocoileus spp.), the use of closed‐population, capture‐recapture (CR) methods, in conjunction with noninvasive DNA sampling, has become increasingly practical, but, up to now, these methods have been used in a non‐spatial modeling framework, which has limited their utility for population‐level inferences. In particular, extrapolation of plot‐level CR abundance estimates to the population required the use of multipliers of unknown reliability and potential bias. Spatially explicit capture‐recapture (SCR) models provide an integrated framework for directly estimating density as a function of spatial and habitat variables at landscape scales. We used fecal DNA samples in conjunction with SCR to estimate density, sex ratio, and habitat correlates to density for a mule deer (O. hemionus) population across a large (∼500 km2) area in the central Sierra Nevada Range, California, USA during 2013 and 2014. We surveyed 24 random transects within 4 30‐km2 sites representative of the study area. Based on 411 samples genotyped at a sex marker and 8–10 microsatellite loci, the sex‐ratio for the study area was 62 (95% CI = 41–93) males/100 females in 2013 and 65 (95% CI = 45–94) males/100 females in 2014. Using SCR, we estimated density at 5.0 (95% CI = 2.3–7.8) deer/km2 in 2013 and 5.1 (95% CI = 3.1–7.2) deer/km2 in 2014. In comparison, non‐spatial CR analysis produced density estimates on average 60% higher, likely reflecting bias resulting from use of the commonly employed mean maximum recapture distance (MMRD) to estimate effective sampling area. The SCR models indicated that density was effectively homogeneous throughout the study area, with no strong relationship to habitat correlates. Altogether, these results demonstrate the utility of noninvasive fecal DNA methods in a SCR framework for estimation of abundance and density in deer populations at landscape scales. © 2017 The Wildlife Society

Animal density is a parameter of basic interest to field biologists. But owing to logistical and analytical constraints, estimating animal density has been very challenging. Spatially explicit capture–recapture (SECR) models were developed to address this particular, long‐standing problem. In this article, some of the important “milestones” in the SECR literature are discussed. The basic idea in SECR models is to include information about locations of animal captures into the modeling so that density is estimated directly. The early SECR type of approach involved estimation of density via simulations and inverse prediction. The first direct SECR estimator was likelihood‐based, which was more flexible and allowed for inclusion of covariates. In parallel began the development of Bayesian versions of the SECR models. These allowed for greater flexibility and for extensions which could, in addition, also estimate population vital rates. SECR models have witnessed several applications, ranging from analysis of camera‐trap data on large cats to acoustic signal data from birds. The future of SECR models is expected to go far beyond density estimation. It has great potential to answer some long‐standing questions about how behavioral processes drive population dynamics in wild animals.

Population size is one of the basic demographic parameters for species management and conservation. Among different estimation methods, spatially explicit capture–recapture (SCR) models allow the estimation of population density in a framework that has been greatly developed in recent years. The use of automated detection devices, such as camera traps, has impressively extended SCR studies for individually identifiable species. However, its application to unmarked/partially marked species remains challenging, and no specific method has been widely used. We fitted an SCR‐integrated model (SCR‐IM) to stone marten Martes foina data, a species for which only some individuals are individually recognizable by natural marks, and estimate population size based on integration of three submodels: (1) individual capture histories from live capture and transponder tagging; (2) detection/nondetection or “occupancy” data using camera traps in a bigger area to extend the geographic scope of capture–recapture data; and (3) telemetry data from a set of tagged individuals. We estimated a stone marten density of 0.352 (SD: 0.081) individuals/km2. We simulated four dilution scenarios of occupancy data to study the variation in the coefficient of variation in population size estimates. We also used simulations with similar characteristics as the stone marten case study, comparing the accuracy and precision obtained from SCR‐IM and SCR, to understand how submodels' integration affects the posterior distributions of estimated parameters. Based on our simulations, we found that population size estimates using SCR‐IM are more accurate and precise. In our stone marten case study, the SCR‐IM density estimation increased the precision by 37% when compared to the standard SCR model as regards to the coefficient of variation. This model has high potential to be used for species in which individual recognition by natural markings is not possible, therefore limiting the need to rely on invasive sampling procedures.

Summary 1. Population density is a critical ecological parameter informing effective wildlife management and conservation decisions. Density is often estimated by dividing capture–recapture (C–R) estimates of abundance () by size of the study area, but this relies on the assumption of geographic closure – a situation rarely achieved in studies of large carnivores. For geographically open populations is overestimated relative to the size of the study area because animals with only part of their home range on the study area are available for capture. This bias (‘edge effect’) is more severe when animals such as large carnivores range widely. To compensate for edge effect, a boundary strip around the trap array is commonly included when estimating the effective trap area (). Various methods for estimating the width of the boundary strip are proposed, but / estimates of large carnivore density are generally mistrusted unless concurrent telemetry data are available to define. Remote sampling by cameras or hair snags may reduce study costs and duration, yet without telemetry data inflated density estimates remain problematic. 2. We evaluated recently developed spatially explicit capture–recapture (SECR) models using data from a common large carnivore, the American black bear Ursus americanus, obtained by remote sampling of 11 geographically open populations. These models permit direct estimation of population density from C–R data without assuming geographic closure. We compared estimates derived using this approach to those derived using conventional approaches that estimate density as /. 3. Spatially explicit C–R estimates were 20–200% lower than densities estimated as /. AICc supported individual heterogeneity in capture probabilities and home range sizes. Variable home range size could not be accounted for when estimating density as /. 4. Synthesis and applications. We conclude that the higher densities estimated as / compared to estimates from SECR models are consistent with positive bias due to edge effects in the former. Inflated density estimates could lead to management decisions placing threatened or endangered large carnivores at greater risk. Such decisions could be avoided by estimating density by SECR when bias due to geographic closure violation cannot be minimized by study design.

Spatially explicit capture–recapture (SECR) models have gained enormous popularity to solve abundance estimation problems in ecology. In this study, we develop a novel Bayesian SECR model that disentangles two processes: one is the process of animal arrival within a detection region, and the other is the process of recording this arrival by a given set of detectors. We integrate this complexity into an advanced version of a recent SECR model involving partially identified individuals (Royle JA. Spatial capture-recapture with partial identity. arXiv preprint arXiv:1503.06873, 2015). We assess the performance of our model over a range of realistic simulation scenarios and demonstrate that estimates of population size N improve when we utilize the proposed model relative to the model that does not explicitly estimate trap detection probability (Royle JA. Spatial capture-recapture with partial identity. arXiv preprint arXiv:1503.06873, 2015). We confront and investigate the proposed model with a spatial capture–recapture dataset from a camera trapping survey of tigers (Panthera tigris) in Nagarahole study area of southern India. Detection probability is estimated at 0.489 (with 95% credible interval (CI) [0.430, 0.543]) which implies that the camera traps are performing imperfectly and thus justifying the use of our model in real world applications. We discuss possible extensions, future work and relevance of our model to other statistical applications beyond ecology. AMS classification codes: 62F15, 92D40

Many species that occur at low densities are not accurately estimated using capture–recapture methods as such techniques assume that populations are well–defined in space. To solve this bias, spatially explicit capture–recapture (SECR) models have recently been developed. These models incorporate movement and can identify areas where it is more likely for individuals to concentrate their activity. In this study, we used data from camera–trap surveys of common genets (Genetta genetta) in Serra da Malcata (Portugal), designed to compare abundance estimates produced by SECR models with traditional closed–capture models. Using the SECR models, we observed spatial heterogeneity in genet distribution and density estimates were approximately two times lower than those obtained from the closed population models. The non–spatial model estimates were constrained to sampling grid size and likely underestimated movements, thereby overestimating density. Future research should consider the incorporation of cost–weighed models that can include explicit hypothesis on how environmental variables influence the distance metric.

SummaryRoyleet al. (Methods in Ecology and Evolution,,4, 520) proposed a spatially explicit capture–recapture (SECR) model in which an animal's usage of a site, and hence its probability of detection, depends on a function of site‐specific covariates normalized using a weighted sum of such values across the animal's home range.From simulations supposedly based on the model, they drew the conclusion that existing methods will produce ‘extremely biased’ estimates of population size when animals use space selectively. This conclusion is faulty because they simulated data from a different model, omitting the normalization needed to represent selection of resources at the home‐range level.New simulations show that the null SECR estimator of population size is nearly unbiased for low to moderate levels of selective space use when the generating model includes normalization. Including detector‐level covariates of detection, as allowed in standard software, nearly eliminates bias due to strongly selective space use, whether or not the generating model includes normalization.

Some deer species are of conservation concern; others are officially managed as a food source or for their trophies, whereas in many regions, deer are regarded as overabundant or even as a nuisance causing damages. Regardless of local management issues, in most cases, reliable data on deer population sizes and sex ratios are lacking. Non-invasive genetic approaches are promising tools for the estimation of population size and structure. We developed and tested a non-invasive genetic approach for red deer (Cervus elaphus) population size and density estimation based on faeces collected from three free-ranging red deer populations in south-western Germany. Altogether, we genotyped 2762 faecal samples, representing 1431 different individuals. We estimated population density for both sexes separately using two different approaches: spatially explicit capture-recapture (SECR) approach and a single-session urn model (CAPWIRE). The estimated densities of both approaches were similar for all three study areas, ranging between total densities of 3.3 (2.5–4.4) and 8.5 (6.4–11.3) red deer/km2. The estimated sex ratios differed significantly between the studied populations (ranging between 1:1.1 and 1:1.7), resulting in considerable consequences for management. In further research, the issues of population closure and approximation of the effectively sampled area for density estimation should be addressed. The presented approach can serve as a valuable tool for the management of deer populations, and to our knowledge, it represents the only sex-specific approach for estimation of red deer population size and density.

Simple SummaryThe objective of our study was to evaluate the mention of uncertainty (i.e., variance) associated with population size estimates within U.S. recovery plans for endangered animals. To do this we reviewed all finalized recovery plans for listed terrestrial vertebrate species. We found that more recent recovery plans reported more estimates of population size and uncertainty. Also, bird and mammal recovery plans reported more estimates of population size and uncertainty. We recommend that updated recovery plans combine uncertainty of population size estimates with a minimum detectable difference to aid in successful recovery. United States recovery plans contain biological information for a species listed under the Endangered Species Act and specify recovery criteria to provide basis for species recovery. The objective of our study was to evaluate whether recovery plans provide uncertainty (e.g., variance) with estimates of population size. We reviewed all finalized recovery plans for listed terrestrial vertebrate species to record the following data: (1) if a current population size was given, (2) if a measure of uncertainty or variance was associated with current estimates of population size and (3) if population size was stipulated for recovery. We found that 59% of completed recovery plans specified a current population size, 14.5% specified a variance for the current population size estimate and 43% specified population size as a recovery criterion. More recent recovery plans reported more estimates of current population size, uncertainty and population size as a recovery criterion. Also, bird and mammal recovery plans reported more estimates of population size and uncertainty compared to reptiles and amphibians. We suggest the use of calculating minimum detectable differences to improve confidence when delisting endangered animals and we identified incentives for individuals to get involved in recovery planning to improve access to quantitative data.

ABSTRACTMany large carnivores are recolonizing range as a result of improved management and conservation policy, habitat restoration, and reintroduction programs. American black bears (Ursus americanus) are projected to recolonize portions of the United States, but few studies have characterized or provided practical methods for monitoring this process. We used noninvasive hair sampling at 4 proximal study areas along the Kentucky–Virginia, USA, border during 2012–2013 to estimate demographics and population genetics, and investigate recolonization patterns of an American black bear population that was founded by 55 bears reintroduced to a fragmented mountainous landscape during the 1990s and subjected to harvest 6 years post‐reintroduction. Using spatially explicit capture–recapture (SECR) models, we estimated a density of 0.26 bear/km2, or minimum abundance of 482 bears, distributed among 2 primary core areas previously identified by occupancy analysis: a southern and northern core area. The southern core area was established by a founder adult female that exhibited post‐release dispersal, but moderate asymmetrical gene flow (Nm = 6 bears) from the northern core area mitigated deleterious genetic consequences typical of such founder events. Effective number of breeders (NB = 62 bears) was similar to the number of founders, suggesting that genetically, the population remains mostly the product of reintroduction. Despite limited connectivity with other populations in the region, genetic diversity (HE = 0.78) was retained because of rapid population growth during the 16 years post‐reintroduction (λ = 1.14/year). This bear population exhibited demographic characteristics indicative of continued recolonization, including a significantly female‐biased sex ratio (0.53M:1.00F) and female density decreasing with increasing distance from the reintroduction release areas in the northern core. Few bear detections at 2 peripheral study areas and results from SECR model detection function transformation suggested recolonization may continue to the southwest and northeast along prominent linear mountain ridges. Although the population has grown and is genetically stable, because of relatively low population density and recolonization direction, we suggest monitoring demographic vital rates to evaluate harvest sustainability and population viability. Our study demonstrates the utility of noninvasive genetic sampling in conjunction with SECR models to characterize and monitor recolonizing bear populations, which may also be useful for management of expanding populations of other large carnivores. © 2016 The Wildlife Society.

Camera‐trapping data analyzed with spatially explicit capture–recapture (SCR) models can provide a rigorous method for estimating density of small populations of elusive carnivore species. We sought to develop and evaluate the efficacy of SCR models for estimating density of a presumed low‐density bobcat ( Lynx rufus ) population in fragmented landscapes of west‐central Illinois, USA. We analyzed camera‐trapping data from 49 camera stations in a 1,458‐km 2 area deployed over a 77‐day period from 1 February to 18 April 2017. Mean operational time of cameras was 52 days (range = 32–67 days). We captured 23 uniquely identifiable bobcats 113 times and recaptured these same individuals 90 times; 15 of 23 (65.2%) individuals were recaptured at ≥2 camera traps. Total number of bobcat capture events was 139, of which 26 (18.7%) were discarded from analyses because of poor image quality or capture of only a part of an animal in photographs. Of 113 capture events used in analyses, 106 (93.8%) and 7 (6.2%) were classified as positive and tentative identifications, respectively; agreement on tentative identifications of bobcats was high (71.4%) among 3 observers. We photographed bobcats at 36 of 49 (73.5%) camera stations, of which 34 stations were used in analyses. We estimated bobcat density at 1.40 individuals (range = 1.00–2.02)/100 km 2 . Our modeled bobcat density estimates are considerably below previously reported densities (30.5 individuals/100 km 2 ) within the state, and among the lowest yet recorded for the species. Nevertheless, use of remote cameras and SCR models was a viable technique for reliably estimating bobcat density across west‐central Illinois. Our research establishes ecological benchmarks for understanding potential effects of colonization, habitat fragmentation, and exploitation on future assessments of bobcat density using standardized methodologies that can be compared directly over time. Further application of SCR models that quantify specific costs of animal movements (i.e., least‐cost path models) while accounting for landscape connectivity has great utility and relevance for conservation and management of bobcat populations across fragmented Midwestern landscapes. © 2019 The Wildlife Society.

Context Eld’s deer (Rucervus eldii) was once widely distributed across Southeast Asia but is now endangered. The strong hold of the subspecies R. e. siamensis is largely restricted to north and east Cambodia, with only small, spatially isolated populations known to occur. Aims To assess if camera traps and spatial capture–recapture methodology can estimate population size of Eld’s deer in Siem Pang Wildlife Sanctuary (SMWS). Methods Infra-red and white flash camera traps were set at 83 grid-point locations (83 km2) over a 5-month sampling period and used a Spatially Explicit Capture Recapture (SECR) model to estimate population size, relying on natural markings to identify males and using sex ratios to extrapolate a population estimate. Key results We estimated the number of Eld’s deer in SMWS to be 272 (95% CI: 169–435). We affirmed that white flash camera traps are advantageous in identifying individuals without significantly affecting detection probability. Conclusions Monitoring the small and difficult to detect subpopulations of R. e. siamensis is challenging. Camera traps can be used although there are challenges to resolve when using the SECR model that can be improved by using white flash cameras to improve the identification of individuals, and assisted with sex and age determination. Implications The SPWS population may potentially be the largest of the R. e. siamensis subspecies in Southeast Asia and it is therefore of critical conservation importance that long term camera trap monitoring is established.

Estimating the size of animal populations is essential for understanding the demography and conservation status of species. Genetic Non-Invasive Sampling (gNIS) combined with Spatially Explicit Capture-Recapture (SECR) modelling may provide a practical tool to obtain such estimates. Here, we evaluate for the first time the potential and limitations of this approach to estimate population densities for small mammals inhabiting patchily distributed habitats, focusing on the endemic Iberian Cabrera vole (Microtus cabrerae). Using 11 highly polymorphic microsatellites and two sex-linked introns, we compared population estimates in November/December 2011 based on live-trapping and gNIS and assessed the impact of distinct consensus criteria to differentiate unique genotypes. Live-trapping over 21 days captured 31 individuals, while gNIS over 5 days recorded 65–69 individuals. SECR models indicated that individual detectability was positively affected by live-trapping capture success on the previous occasion, while for gNIS, it was mainly affected by genotyping success rates and patch size. Live-trapping produced the lowest density estimates (mean ± SE) of 16.6 ± 3.2 individuals per hectare of suitable habitat (ind/ha). Estimates based on gNIS were higher and varied slightly between 25.2 ± 4.0 and 28.8 ± 4.5 ind/ha depending on assuming one or two genotyping errors, respectively, when differentiating individual genetic profiles. Results suggest that live-trapping underestimated the vole population, while the larger number of individuals detected through gNIS allowed better estimates with lower field effort. Overall, we suggest that gNIS combined with SECR models provides an effective tool to estimate small mammal population densities in fragmented habitats.