Abundance of rare and elusive species: Empirical investigation of closed versus spatially explicit capture–recapture models with lynx as a case study

Effective conservation and management require reliable monitoring methods and estimates of abundance to prioritize human and financial investments. Camera trapping is a non-invasive sampling method allowing the use of capture–recapture (CR) models to estimate abundance while accounting for the difficulty of detecting individuals in the wild. We investigated the relative performance of standard closed CR models and spatially explicit CR models (SECR) that incorporate spatial information in the data. Using simulations, we considered 4 scenarios comparing low versus high detection probability and small versus large populations and contrasted abundance estimates obtained from both approaches. Standard CR and SECR models both provided minimally biased abundance estimates, but precision was improved when using SECR models. The associated confidence intervals also provided better coverage than their non-spatial counterpart. We concluded SECR models exhibit better statistical performance than standard closed CR models and allow for sound management strategies based on density maps of activity centers. To illustrate the comparison, we considered the Eurasian lynx (Lynx lynx) as a case study that provided the first abundance estimates of a local population in France. © 2012 The Wildlife Society.     

A spatially explicit capture–recapture estimator for single‐catch traps

Single‐catch traps are frequently used in live‐trapping studies of small mammals. Thus far, a likelihood for single‐catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture–recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous‐time model for SECR to derive a likelihood for single‐catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single‐catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single‐catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single‐catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single‐catch likelihood with unknown capture times remains intractable for now, researchers using single‐catch traps should aim to incorporate timing devices with their traps.     

Leopard density in post-conflict landscape,Cambodia: Evidence from spatially explicit capture–recapture

Effective conservation of large carnivores requires reliable estimates of population density, often obtained through capture–recapture analysis, in order to prioritize investments and assess conservation intervention effectiveness. Recent statistical advances and development of user-friendly software for spatially explicit capture–recapture (SECR) circumvent the difficulties in estimating effective survey area, and hence density, from capture–recapture data. We conducted a camera-trapping study on leopards (Panthera pardus) in Mondulkiri Protected Forest, Cambodia. We compared density estimates using SECR with those obtained from conventional approaches in which the effective survey area is estimated using a boundary strip width based on observed animal movements. Density estimates from Chao heterogeneity models (3.8 ± SE 1.9 individuals/100 km²) and Pledger heterogeneity models and models accounting for gender-specific capture and recapture rates (model-averaged density 3.9 ± SE 2.9 individuals/100 km²) were similar to those from SECR in program DENSITY (3.6 ± SE 1.0/100 km²) but higher than estimates from Jack-knife heterogeneity models (2.9 ± SE 0.9 individuals/100 km²). Capture probabilities differed between male and female leopards probably resulting from differences in the use of human-made trails between sexes. Given that there are a number of biologically plausible reasons to expect gender-specific variation in capture probabilities of large carnivores, we recommend exploratory analysis of data using models in which gender can be included as a covariate affecting capture probabilities particularly given the demographic importance of breeding females for population recovery of threatened carnivores. © 2011 The Wildlife Society.     

Evaluating the potential biases in carnivore capture–recapture studies associated with the use of lure and varying density estimation techniques using photographic-sampling data of the Malagasy civet

Estimating density of elusive carnivores with capture–recapture analyses is increasingly common. However, providing unbiased and precise estimates is still a challenge due to uncertainties arising from the use of (1) bait or lure to attract animals to the detection device and (2) ad hoc boundary-strip methods to compensate for edge effects in area estimation. We used photographic-sampling data of the Malagasy civet Fossa fossana collected with and without lure to assess the effects of lure and to compare the use of four density estimators which varied in methods of area estimation. The use of lure did not affect permanent immigration or emigration, abundance and density estimation, maximum movement distances, or temporal activity patterns of Malagasy civets, but did provide more precise population estimates by increasing the number of recaptures. The spatially-explicit capture–recapture (SECR) model density estimates ±SE were the least precise as they incorporate spatial variation, but consistent with each other (Maximum likelihood-SECR = 1.38 ± 0.18, Bayesian-SECR = 1.24 ± 0.17 civets/km²), whereas estimates relying on boundary-strip methods to estimate effective trapping area did not incorporate spatial variation, varied greatly and were generally larger than SECR model estimates. Estimating carnivore density with ad hoc boundary-strip methods can lead to overestimation and/or increased uncertainty as they do not incorporate spatial variation. This may lead to inaction or poor management decisions which may jeopardize at-risk populations. In contrast, SECR models free researchers from making subjective decisions associated with boundary-strip methods and they estimate density directly, providing more comparable and valuable population estimates.     

Density estimation in a wolverine population using spatial capture–recapture models

Classical closed-population capture–recapture models do not accommodate the spatial information inherent in encounter history data obtained from camera-trapping studies. As a result, individual heterogeneity in encounter probability is induced, and it is not possible to estimate density objectively because trap arrays do not have a well-defined sample area. We applied newly-developed, capture–recapture models that accommodate the spatial attribute inherent in capture–recapture data to a population of wolverines (Gulo gulo) in Southeast Alaska in 2008. We used camera-trapping data collected from 37 cameras in a 2,140-km² area of forested and open habitats largely enclosed by ocean and glacial icefields. We detected 21 unique individuals 115 times. Wolverines exhibited a strong positive trap response, with an increased tendency to revisit previously visited traps. Under the trap-response model, we estimated wolverine density at 9.7 individuals/1,000 km² (95% Bayesian CI: 5.9–15.0). Our model provides a formal statistical framework for estimating density from wolverine camera-trapping studies that accounts for a behavioral response due to baited traps. Further, our model-based estimator does not have strict requirements about the spatial configuration of traps or length of trapping sessions, providing considerable operational flexibility in the development of field studies. © 2011 The Wildlife Society.     

Effective sociodemographic population assessment of elusive species in ecology and conservation management

Wildlife managers are urgently searching for improved sociodemographic population assessment methods to evaluate the effectiveness of implemented conservation activities. These need to be inexpensive, appropriate for a wide spectrum of species and straightforward to apply by local staff members with minimal training. Furthermore, conservation management would benefit from single approaches which cover many aspects of population assessment beyond only density estimates, to include for instance social and demographic structure, movement patterns, or species interactions. Remote camera traps have traditionally been used to measure species richness. Currently, there is a rapid move toward using remote camera trapping in density estimation, community ecology, and conservation management. Here, we demonstrate such comprehensive population assessment by linking remote video trapping, spatially explicit capture–recapture (SECR) techniques, and other methods. We apply it to three species: chimpanzees Pan troglodytes troglodytes, gorillas Gorilla gorilla gorilla, and forest elephants Loxodonta cyclotis in Loango National Park, Gabon. All three species exhibited considerable heterogeneity in capture probability at the sex or group level and density was estimated at 1.72, 1.2, and 1.37 individuals per km² and male to female sex ratios were 1:2.1, 1:3.2, and 1:2 for chimpanzees, gorillas, and elephants, respectively. Association patterns revealed four, eight, and 18 independent social groups of chimpanzees, gorillas, and elephants, respectively: key information for both conservation management and studies on the species' ecology. Additionally, there was evidence of resident and nonresident elephants within the study area and intersexual variation in home range size among elephants but not chimpanzees. Our study highlights the potential of combining camera trapping and SECR methods in conducting detailed population assessments that go far beyond documenting species diversity patterns or estimating single species population size. Our study design is widely applicable to other species and spatial scales, and moderately trained staff members can collect and process the required data. Furthermore, assessments using the same method can be extended to include several other ecological, behavioral, and demographic aspects: fission and fusion dynamics and intergroup transfers, birth and mortality rates, species interactions, and ranging patterns.     

Density estimation in live-trapping studies

Unbiased estimation of population density is a major and unsolved problem in animal trapping studies. This paper describes a new and general method for estimating density from closed-population capture–recapture data. Many estimators exist for the size (N) and mean capture probability ( p ) of a closed population. These statistics suffer from an unknown bias due to edge effect that varies with trap layout and home range size. The mean distance between successive captures of an individual (     ) provides information on the scale of individual movements, but is itself a function of trap spacing and grid size. Our aim is to define and estimate parameters that do not depend on the trap layout. In the new method, simulation and inverse prediction are used to estimate jointly the population density (D) and two parameters of individual capture probability, magnitude (g₀) and spatial scale (σ), from the information in     , p and     . The method uses any configuration of traps (e.g. grid, web or line) and any choice of closed-population estimator. It is assumed that home ranges have a stationary distribution in two dimensions, and that capture events may be simulated as the outcome of competing Poisson processes in time. The method is applied to simulated and field data. The estimator appears unusually robust and free from bias.     

Estimating multiple years,tributary-specific,and overall Atlantic salmon smolt abundance in a large Canadian catchment using capture–mark–recapture experiments

Population monitoring of Atlantic salmon (Salmo salar L.) abundance is an essential element to understand annual stock variability and inform fisheries management processes. Smolts are the life stage marking the transition from the freshwater to the marine phase of anadromous Atlantic salmon. Estimating smolt abundance allows for subsequent inferences on freshwater and marine survival rates. Annual abundances of out-migrating Atlantic salmon smolts were estimated using Bayesian models and an 18-year capture–mark–recapture time series from two to five trapping locations within the Restigouche River (Canada) catchment. Some of the trapping locations were at the outlet of large upstream tributaries, and these sampled a portion of the total out-migrating population of smolts for the watershed, whereas others were located just above the head of tide of the Restigouche River and sampled the entire run of salmon smolts. Due to logistic and environmental conditions, not all trapping locations were operational each year. Additionally, recapture rates were relatively low (<5%), and the absolute number of recaptures was relatively few (most often a few dozen), leading to incoherent and highly uncertain estimates of tributary-specific and whole catchment abundance estimates when the data were modeled independently among trapping locations and years. Several models of increasing complexity were tested using simulated data, and the best-performing model in terms of bias and precision incorporated a hierarchical structure among years on the catchability parameters and included an explicit spatial structure to account for the annual variations in the number of sampled locations within the watershed. When the best model was applied to the Restigouche River catchment dataset, the annual smolt abundance estimates varied from 250,000 to 1 million smolts, and the subbasin estimates of abundance were consistent with the spatial structure of the monitoring programme. Ultimately, increasing the probabilities of capture and the absolute number of recaptures at the different traps will be required to improve the precision and reduce the bias of the estimates of smolt abundance for the entire basin and within subbasins of the watershed. The model and approach provide a significant improvement in the models used to date based on independent estimates of abundance by trapping location and year. Total abundance and relative production in discrete spawning, nesting, or rearing areas provide critical information to appropriately understand and manage the threats to species that can occur at subpopulation spatial scales.     

Assessing the performance of index calibration survey methods to monitor populations of wide‐ranging low‐density carnivores

Apex carnivores are wide‐ranging, low‐density, hard to detect, and declining throughout most of their range, making population monitoring both critical and challenging. Rapid and inexpensive index calibration survey (ICS) methods have been developed to monitor large African carnivores. ICS methods assume constant detection probability and a predictable relationship between the index and the actual population of interest. The precision and utility of the resulting estimates from ICS methods have been questioned. We assessed the performance of one ICS method for large carnivores—track counts—with data from two long‐term studies of African lion populations. We conducted Monte Carlo simulation of intersections between transects (road segments) and lion movement paths (from GPS collar data) at varying survey intensities. Then, using the track count method we estimated population size and its confidence limits. We found that estimates either overstate precision or are too imprecise to be meaningful. Overstated precision stemmed from discarding the variance from population estimates when developing the method and from treating the conversion from tracks counts to population density as a back‐transformation, rather than applying the equation for the variance of a linear function. To effectively assess the status of species, the IUCN has set guidelines, and these should be integrated in survey designs. We propose reporting the half relative confidence interval width (HRCIW) as an easily calculable and interpretable measure of precision. We show that track counts do not adhere to IUCN criteria, and we argue that ICS methods for wide‐ranging low‐density species are unlikely to meet those criteria. Established, intensive methods lead to precise estimates, but some new approaches, like short, intensive, (spatial) capture–mark–recapture (CMR/SECR) studies, aided by camera trapping and/or genetic identification of individuals, hold promise. A handbook of best practices in monitoring populations of apex carnivores is strongly recommended.     

Estimating local population size of the European Nightjar Caprimulgus europaeus using territory capture–recapture models

Capsule The capture–recapture model M(o) is an efficient way to estimate local population size.

Aims To test if a single capture–recapture modelling approach, combined with a simple survey method, can produce estimates of local population size from a dataset involving large‐scale multi‐observer surveys

Methods We sampled the presence of Nightjars in three separate sessions at three forests. Territory numbers were estimated using conventional territory‐mapping criteria. We ran different capture–recapture models to analyse the detection histories of territories obtained across the three sampling sessions and in the three different forests, using either only registrations of churring birds or all contacts.

Results The capture–recapture model M(o), assuming a constant detection probability, was the most efficient one to produce estimates of local population size. Using only two of the three sampling sessions gave less precise, though quite similar, estimates of the number of territories, with standard deviations representing 5–10% of the estimate values. However, this was reduced to 0.7–3.5%, i.e. three to seven times lower, when using the three sessions.

Conclusion Repeated sampling sessions to map territories can be efficiently used within the capture–recapture model M(o) to estimate detection probability and produce precise estimates of local population size.     

Open population maximum likelihood spatial capture‐recapture

Open population capture‐recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modeling with spatial capture‐recapture (SCR), allowing for estimation of the effective area sampled and population density. Here, open population SCR is formulated as a hidden Markov model (HMM), allowing inference by maximum likelihood for both Cormack‐Jolly‐Seber and Jolly‐Seber models, with and without activity center movement. The method is applied to a 12‐year survey of male jaguars (Panthera onca) in the Cockscomb Basin Wildlife Sanctuary, Belize, to estimate survival probability and population abundance over time. For this application, inference is shown to be biased when assuming activity centers are fixed over time, while including a model for activity center movement provides negligible bias and nominal confidence interval coverage, as demonstrated by a simulation study. The HMM approach is compared with Bayesian data augmentation and closed population models for this application. The method is substantially more computationally efficient than the Bayesian approach and provides a lower root‐mean‐square error in predicting population density compared to closed population models.     

Genetic sampling for estimating density of common species

Understanding population dynamics requires reliable estimates of population density, yet this basic information is often surprisingly difficult to obtain. With rare or difficult‐to‐capture species, genetic surveys from noninvasive collection of hair or scat has proved cost‐efficient for estimating densities. Here, we explored whether noninvasive genetic sampling (NGS) also offers promise for sampling a relatively common species, the snowshoe hare (Lepus americanus Erxleben, 1777), in comparison with traditional live trapping. We optimized a protocol for single‐session NGS sampling of hares. We compared spatial capture–recapture population estimates from live trapping to estimates derived from NGS, and assessed NGS costs. NGS provided population estimates similar to those derived from live trapping, but a higher density of sampling plots was required for NGS. The optimal NGS protocol for our study entailed deploying 160 sampling plots for 4 days and genotyping one pellet per plot. NGS laboratory costs ranged from approximately $670 to $3000 USD per field site. While live trapping does not incur laboratory costs, its field costs can be considerably higher than for NGS, especially when study sites are difficult to access. We conclude that NGS can work for common species, but that it will require field and laboratory pilot testing to develop cost‐effective sampling protocols.     

Trap Array Configuration Influences Estimates and Precision of Black Bear Density and Abundance

Spatial capture-recapture (SCR) models have advanced our ability to estimate population density for wide ranging animals by explicitly incorporating individual movement. Though these models are more robust to various spatial sampling designs, few studies have empirically tested different large-scale trap configurations using SCR models. We investigated how extent of trap coverage and trap spacing affects precision and accuracy of SCR parameters, implementing models using the R package secr. We tested two trapping scenarios, one spatially extensive and one intensive, using black bear (Ursus americanus) DNA data from hair snare arrays in south-central Missouri, USA. We also examined the influence that adding a second, lower barbed-wire strand to snares had on quantity and spatial distribution of detections. We simulated trapping data to test bias in density estimates of each configuration under a range of density and detection parameter values. Field data showed that using multiple arrays with intensive snare coverage produced more detections of more individuals than extensive coverage. Consequently, density and detection parameters were more precise for the intensive design. Density was estimated as 1.7 bears per 100 km² and was 5.5 times greater than that under extensive sampling. Abundance was 279 (95% CI = 193–406) bears in the 16,812 km² study area. Excluding detections from the lower strand resulted in the loss of 35 detections, 14 unique bears, and the largest recorded movement between snares. All simulations showed low bias for density under both configurations. Results demonstrated that in low density populations with non-uniform distribution of population density, optimizing the tradeoff among snare spacing, coverage, and sample size is of critical importance to estimating parameters with high precision and accuracy. With limited resources, allocating available traps to multiple arrays with intensive trap spacing increased the amount of information needed to inform parameters with high precision.     

Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model

Summary Estimation of abundance is important in both open and closed population capture–recapture analysis, but unmodeled heterogeneity of capture probability leads to negative bias in abundance estimates. This article defines and develops a suite of open population capture–recapture models using finite mixtures to model heterogeneity of capture and survival probabilities. Model comparisons and parameter estimation use likelihood‐based methods. A real example is analyzed, and simulations are used to check the main features of the heterogeneous models, especially the quality of estimation of abundance, survival, recruitment, and turnover. The two major advances in this article are the provision of realistic abundance estimates that take account of heterogenetiy of capture, and an appraisal of the amount of overestimation of survival arising from conditioning on the first capture when heterogeneity of survival is present.     

Spatial capture–recapture models allowing Markovian transience or dispersal

Spatial capture–recapture (SCR) models are a relatively recent development in quantitative ecology, and they are becoming widely used to model density in studies of animal populations using camera traps, DNA sampling and other methods which produce spatially explicit individual encounter information. One of the core assumptions of SCR models is that individuals possess home ranges that are spatially stationary during the sampling period. For many species, this assumption is unlikely to be met and, even for species that are typically territorial, individuals may disperse or exhibit transience at some life stages. In this paper we first conduct a simulation study to evaluate the robustness of estimators of density under ordinary SCR models when dispersal or transience is present in the population. Then, using both simulated and real data, we demonstrate that such models can easily be described in the BUGS language providing a practical framework for their analysis, which allows us to evaluate movement dynamics of species using capture–recapture data. We find that while estimators of density are extremely robust, even to pathological levels of movement (e.g., complete transience), the estimator of the spatial scale parameter of the encounter probability model is confounded with the dispersal/transience scale parameter. Thus, use of ordinary SCR models to make inferences about density is feasible, but interpretation of SCR model parameters in relation to movement should be avoided. Instead, when movement dynamics are of interest, such dynamics should be parameterized explicitly in the model.     

Application of Spatial and Closed Capture-Recapture Models on Known Population of the Western Derby Eland (Taurotragus derbianus derbianus) in Senegal

Camera trapping with capture-recapture analyses has provided estimates of the abundances of elusive species over the last two decades. Closed capture-recapture models (CR) based on the recognition of individuals and incorporating natural heterogeneity in capture probabilities are considered robust tools; however, closure assumption is often questionable and the use of an M_h jackknife estimator may fail in estimations of real abundance when the heterogeneity is high and data is sparse. A novel, spatially explicit capture-recapture (SECR) approach based on the location-specific capture histories of individuals overcomes the limitations of closed models. We applied both methods on a closed population of 16 critically endangered Western Derby elands in the fenced 1,060-ha Fathala reserve, Senegal. We analyzed the data from 30 cameras operating during a 66-day sampling period deployed in two densities in grid and line arrays. We captured and identified all 16 individuals in 962 trap-days. Abundances were estimated in the programs CAPTURE (models M₀, M_h and M_h Chao) and R, package secr (basic Null and Finite mixture models), and compared with the true population size. We specified 66 days as a threshold in which SECR provides an accurate estimate in all trapping designs within the 7-times divergent density from 0.004 to 0.028 camera trap/ha. Both SECR models showed uniform tendency to overestimate abundance when sampling lasted shorter with no major differences between their outputs. Unlike the closed models, SECR performed well in the line patterns, which indicates promising potential for linear sampling of properly defined habitats of non-territorial and identifiable herbivores in dense wooded savanna conditions. The CR models provided reliable estimates in the grid and we confirmed the advantage of M_h Chao estimator over M_h jackknife when data appeared sparse. We also demonstrated the pooling of trapping occasions with an increase in the capture probabilities, avoiding violation of results.     

Spatially explicit maximum likelihood methods for capture-recapture studies

Live-trapping capture-recapture studies of animal populations with fixed trap locations inevitably have a spatial component: animals close to traps are more likely to be caught than those far away. This is not addressed in conventional closed-population estimates of abundance and without the spatial component, rigorous estimates of density cannot be obtained. We propose new, flexible capture-recapture models that use the capture locations to estimate animal locations and spatially referenced capture probability. The models are likelihood-based and hence allow use of Akaike's information criterion or other likelihood-based methods of model selection. Density is an explicit parameter, and the evaluation of its dependence on spatial or temporal covariates is therefore straightforward. Additional (nonspatial) variation in capture probability may be modeled as in conventional capture-recapture. The method is tested by simulation, using a model in which capture probability depends only on location relative to traps. Point estimators are found to be unbiased and standard error estimators almost unbiased. The method is used to estimate the density of Red-eyed Vireos (Vireo olivaceus) from mist-netting data from the Patuxent Research Refuge, Maryland, U.S.A. Estimates agree well with those from an existing spatially explicit method based on inverse prediction. A variety of additional spatially explicit models are fitted; these include models with temporal stratification, behavioral response, and heterogeneous animal home ranges.     

Estimating abundance of mountain lions from unstructured spatial sampling

Mountain lions (Puma concolor) are often difficult to monitor because of their low capture probabilities, extensive movements, and large territories. Methods for estimating the abundance of this species are needed to assess population status, determine harvest levels, evaluate the impacts of management actions on populations, and derive conservation and management strategies. Traditional mark–recapture methods do not explicitly account for differences in individual capture probabilities due to the spatial distribution of individuals in relation to survey effort (or trap locations). However, recent advances in the analysis of capture–recapture data have produced methods estimating abundance and density of animals from spatially explicit capture–recapture data that account for heterogeneity in capture probabilities due to the spatial organization of individuals and traps. We adapt recently developed spatial capture–recapture models to estimate density and abundance of mountain lions in western Montana. Volunteers and state agency personnel collected mountain lion DNA samples in portions of the Blackfoot drainage (7,908 km²) in west-central Montana using 2 methods: snow back-tracking mountain lion tracks to collect hair samples and biopsy darting treed mountain lions to obtain tissue samples. Overall, we recorded 72 individual capture events, including captures both with and without tissue sample collection and hair samples resulting in the identification of 50 individual mountain lions (30 females, 19 males, and 1 unknown sex individual). We estimated lion densities from 8 models containing effects of distance, sex, and survey effort on detection probability. Our population density estimates ranged from a minimum of 3.7 mountain lions/100 km² (95% CI 2.3–5.7) under the distance only model (including only an effect of distance on detection probability) to 6.7 (95% CI 3.1–11.0) under the full model (including effects of distance, sex, survey effort, and distance × sex on detection probability). These numbers translate to a total estimate of 293 mountain lions (95% CI 182–451) to 529 (95% CI 245–870) within the Blackfoot drainage. Results from the distance model are similar to previous estimates of 3.6 mountain lions/100 km² for the study area; however, results from all other models indicated greater numbers of mountain lions. Our results indicate that unstructured spatial sampling combined with spatial capture–recapture analysis can be an effective method for estimating large carnivore densities. Published 2012. This article is a U.S. Government work and is in the public domain in the USA.