Inferences about population dynamics from count data using multistate models: a comparison to capture–recapture approaches

Wildlife populations consist of individuals that contribute disproportionately to growth and viability. Understanding a population's spatial and temporal dynamics requires estimates of abundance and demographic rates that account for this heterogeneity. Estimating these quantities can be difficult, requiring years of intensive data collection. Often, this is accomplished through the capture and recapture of individual animals, which is generally only feasible at a limited number of locations. In contrast, N‐mixture models allow for the estimation of abundance, and spatial variation in abundance, from count data alone. We extend recently developed multistate, open population N‐mixture models, which can additionally estimate demographic rates based on an organism's life history characteristics. In our extension, we develop an approach to account for the case where not all individuals can be assigned to a state during sampling. Using only state‐specific count data, we show how our model can be used to estimate local population abundance, as well as density‐dependent recruitment rates and state‐specific survival. We apply our model to a population of black‐throated blue warblers (Setophaga caerulescens) that have been surveyed for 25 years on their breeding grounds at the Hubbard Brook Experimental Forest in New Hampshire, USA. The intensive data collection efforts allow us to compare our estimates to estimates derived from capture–recapture data. Our model performed well in estimating population abundance and density‐dependent rates of annual recruitment/immigration. Estimates of local carrying capacity and per capita recruitment of yearlings were consistent with those published in other studies. However, our model moderately underestimated annual survival probability of yearling and adult females and severely underestimates survival probabilities for both of these male stages. The most accurate and precise estimates will necessarily require some amount of intensive data collection efforts (such as capture–recapture). Integrated population models that combine data from both intensive and extensive sources are likely to be the most efficient approach for estimating demographic rates at large spatial and temporal scales.     

multimark: an R package for analysis of capture–recapture data consisting of multiple “noninvasive” marks

I describe an open‐source R package, multimark , for estimation of survival and abundance from capture–mark–recapture data consisting of multiple “noninvasive” marks. Noninvasive marks include natural pelt or skin patterns, scars, and genetic markers that enable individual identification in lieu of physical capture. multimark provides a means for combining and jointly analyzing encounter histories from multiple noninvasive sources that otherwise cannot be reliably matched (e.g., left‐ and right‐sided photographs of bilaterally asymmetrical individuals). The package is currently capable of fitting open population Cormack–Jolly–Seber (CJS) and closed population abundance models with up to two mark types using Bayesian Markov chain Monte Carlo (MCMC) methods. multimark can also be used for Bayesian analyses of conventional capture–recapture data consisting of a single‐mark type. Some package features include (1) general model specification using formulas already familiar to most R users, (2) ability to include temporal, behavioral, age, cohort, and individual heterogeneity effects in detection and survival probabilities, (3) improved MCMC algorithm that is computationally faster and more efficient than previously proposed methods, (4) Bayesian multimodel inference using reversible jump MCMC, and (5) data simulation capabilities for power analyses and assessing model performance. I demonstrate use of multimark using left‐ and right‐sided encounter histories for bobcats (Lynx rufus) collected from remote single‐camera stations in southern California. In this example, there is evidence of a behavioral effect (i.e., trap “happy” response) that is otherwise indiscernible using conventional single‐sided analyses. The package will be most useful to ecologists seeking stronger inferences by combining different sources of mark–recapture data that are difficult (or impossible) to reliably reconcile, particularly with the sparse datasets typical of rare or elusive species for which noninvasive sampling techniques are most commonly employed. Addressing deficiencies in currently available software, multimark also provides a user‐friendly interface for performing Bayesian multimodel inference using capture–recapture data consisting of a single conventional mark or multiple noninvasive marks.     

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.     

Combining capture–recapture data and known ages allows estimation of age‐dependent survival rates

In many animal populations, demographic parameters such as survival and recruitment vary markedly with age, as do parameters related to sampling, such as capture probability. Failing to account for such variation can result in biased estimates of population‐level rates. However, estimating age‐dependent survival rates can be challenging because ages of individuals are rarely known unless tagging is done at birth. For many species, it is possible to infer age based on size. In capture–recapture studies of such species, it is possible to use a growth model to infer the age at first capture of individuals. We show how to build estimates of age‐dependent survival into a capture–mark–recapture model based on data obtained in a capture–recapture study. We first show how estimates of age based on length increments closely match those based on definitive aging methods. In simulated analyses, we show that both individual ages and age‐dependent survival rates estimated from simulated data closely match true values. With our approach, we are able to estimate the age‐specific apparent survival rates of Murray and trout cod in the Murray River, Australia. Our model structure provides a flexible framework within which to investigate various aspects of how survival varies with age and will have extensions within a wide range of ecological studies of animals where age can be estimated based on size.     

Capture–recapture analysis with a latent class model allowing for local dependence and observed heterogeneity

In epidemiology, capture–recapture models are commonly used to estimate the size of an unknown population based on several incomplete lists of individuals. The method operates under two main assumptions: independence between the lists (local independence) and homogeneity of capture probabilities of individuals. In practice, these assumptions are rarely satisfied. We introduce a multinomial latent class model that can account for both list dependence and heterogeneity. Parameter estimation is performed by maximizing the conditional likelihood function with the use of the EM algorithm. In addition, a new approach for evaluating the standard errors of the parameter estimates is discussed, which considerably reduces the computational burden associated with the evaluation of the variance of the population size estimate.     

Estimability of migration survival rates from integrated breeding and winter capture–recapture data

Long‐distance migration is a common phenomenon across the animal kingdom but the scale of annual migratory movements has made it difficult for researchers to estimate survival rates during these periods of the annual cycle. Estimating migration survival is particularly challenging for small‐bodied species that cannot carry satellite tags, a group that includes the vast majority of migratory species. When capture–recapture data are available for linked breeding and non‐breeding populations, estimation of overall migration survival is possible but current methods do not allow separate estimation of spring and autumn survival rates. Recent development of a Bayesian integrated survival model has provided a method to separately estimate the latent spring and autumn survival rates using capture–recapture data, though the accuracy and precision of these estimates has not been formally tested. Here, I used simulated data to explore the estimability of migration survival rates using this model. Under a variety of biologically realistic scenarios, I demonstrate that spring and autumn migration survival can be estimated from the integrated survival model, though estimates are biased toward the overall migration survival probability. The direction and magnitude of this bias are influenced by the relative difference in spring and autumn survival rates as well as the degree of annual variation in these rates. The inclusion of covariates can improve the model's performance, especially when annual variation in migration survival rates is low. Migration survival rates can be estimated from relatively short time series (4–5 years), but bias and precision of estimates are improved when longer time series (10–12 years) are available. The ability to estimate seasonal survival rates of small, migratory organisms opens the door to advancing our understanding of the ecology and conservation of these species. Application of this method will enable researchers to better understand when mortality occurs across the annual cycle and how the migratory periods contribute to population dynamics. Integrating summer and winter capture data requires knowledge of the migratory connectivity of sampled populations and therefore efforts to simultaneously collect both survival and tracking data should be a high priority, especially for species of conservation concern.     

Using dynamic N‐mixture models to test cavity limitation on northern flying squirrel demographic parameters using experimental nest box supplementation

Dynamic N‐mixture models have been recently developed to estimate demographic parameters of unmarked individuals while accounting for imperfect detection. We propose an application of the Dail and Madsen ( 2011 : Biometrics, 67 , 577–587) dynamic N‐mixture model in a manipulative experiment using a before‐after control‐impact design (BACI). Specifically, we tested the hypothesis of cavity limitation of a cavity specialist species, the northern flying squirrel, using nest box supplementation on half of 56 trapping sites. Our main purpose was to evaluate the impact of an increase in cavity availability on flying squirrel population dynamics in deciduous stands in northwestern Québec with the dynamic N‐mixture model. We compared abundance estimates from this recent approach with those from classic capture–mark–recapture models and generalized linear models. We compared apparent survival estimates with those from Cormack–Jolly–Seber (CJS) models. Average recruitment rate was 6 individuals per site after 4 years. Nevertheless, we found no effect of cavity supplementation on apparent survival and recruitment rates of flying squirrels. Contrary to our expectations, initial abundance was not affected by conifer basal area (food availability) and was negatively affected by snag basal area (cavity availability). Northern flying squirrel population dynamics are not influenced by cavity availability at our deciduous sites. Consequently, we suggest that this species should not be considered an indicator of old forest attributes in our study area, especially in view of apparent wide population fluctuations across years. Abundance estimates from N‐mixture models were similar to those from capture–mark–recapture models, although the latter had greater precision. Generalized linear mixed models produced lower abundance estimates, but revealed the same relationship between abundance and snag basal area. Apparent survival estimates from N‐mixture models were higher and less precise than those from CJS models. However, N‐mixture models can be particularly useful to evaluate management effects on animal populations, especially for species that are difficult to detect in situations where individuals cannot be uniquely identified. They also allow investigating the effects of covariates at the site level, when low recapture rates would require restricting classic CMR analyses to a subset of sites with the most captures.     

Individual heterogeneity and capture–recapture models: what,why and how?

Variation between and within individuals in life history traits is ubiquitous in natural populations. When affecting fitness‐related traits such as survival or reproduction, individual heterogeneity plays a key role in population dynamics and life history evolution. However, it is only recently that properly accounting for individual heterogeneity when studying population dynamics of free‐ranging populations has been made possible through the development of appropriate statistical models. We aim here to review case studies of individual heterogeneity in the context of capture–recapture models for the estimation of population size and demographic parameters with imperfect detection. First, we define what individual heterogeneity means and clarify the terminology used in the literature. Second, we review the literature and illustrate why individual heterogeneity is used in capture–recapture studies by focusing on the detection of life‐history tradeoffs, including senescence. Third, we explain how to model individual heterogeneity in capture–recapture models and provide the code to fit these models ( https://github.com/oliviergimenez/indhet_in_CRmodels ). The distinction is made between situations in which heterogeneity is actually measured and situations in which part of the heterogeneity remains unobserved. Regarding the latter, we outline recent developments of random‐effect models and finite‐mixture models. Finally, we discuss several avenues for future research.     

Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture–recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture–recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi‐likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture–recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods.     

Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension

Summary Reversible jump Markov chain Monte Carlo (RJMCMC) methods are used to fit Bayesian capture–recapture models incorporating heterogeneity in individuals and samples. Heterogeneity in capture probabilities comes from finite mixtures and/or fixed sample effects allowing for interactions. Estimation by RJMCMC allows automatic model selection and/or model averaging. Priors on the parameters stabilize the estimates and produce realistic credible intervals for population size for overparameterized models, in contrast to likelihood‐based methods. To demonstrate the approach we analyze the standard Snowshoe hare and Cottontail rabbit data sets from ecology, a reliability testing data set.     

Inferring causal factors for a declining population of bottlenose dolphins via temporal symmetry capture–recapture modeling

We applied temporal symmetry capture–recapture (TSCR) models to assess the strength of evidence for factors potentially responsible for population decline in bottlenose dolphins (Tursiops truncatus) in Doubtful Sound, New Zealand from 1995 to 2008. Model selection was conducted to estimate recruitment and population growth rates. There were similar levels of support for three different models, each reflecting distinct trends in recruitment. Modeling yielded low overall estimates of recruitment (0.0249, 95% CI: 0.0174–0.0324) and population growth rate (0.9642, 95% CI: 0.9546–0.9737). The TSCR rate of population decline was consistent with an estimate derived from trends in abundance (lambda = 0.9632, 95% CI: 0.9599–0.9665). The TSCR model selection confirmed the influence of a decline in the survival of calves (<1 yr old) since 2002 for population trends. However, TSCR population growth rates did not exceed 1 in any year between 1995 and 2008, indicating the population was declining prior to 2002. A separate reduction in juvenile survival (1–3 yr old) prior to 2002 was identified as a likely contributing factor in the population decline. Thus, TSCR modeling indicated the potential cause of the population decline in Doubtful Sound: cumulative impacts on individuals <3 yr old resulting in a reduced recruitment.     

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Species richness estimation and determinants of species detectability in butterfly monitoring programmes

Abstract 1. Species richness is the most widely used biodiversity index, but can be hard to measure. Many species remain undetected, hence raw species counts will often underestimate true species richness. In contrast, capture–recapture methods estimate true species richness and correct for imperfect and varying detectability. 2. Detectability is a crucial quantity that provides the link between a species count and true species richness. For insects, it has hardly ever been estimated, although this is required for the interpretation of species counts. 3. In the Swiss butterfly monitoring programme about 100 transect routes are surveyed seven times a year using a highly standardised protocol. In July 2003, control observers made two additional surveys on 38 transects. Data from these 38 quadrats were analysed to see whether currently available capture–recapture models can provide quadrat‐specific estimates of species richness, and to estimate species detectability in relation to transect, observer, survey, region, and abundance. 4. Species richness over the entire season cannot be estimated using current capture–recapture methods. The species pool was open, preventing use of closed population models, and detectability varied by species, preventing use of current open population models. Assuming a closed species pool during two mid‐season (July) surveys, a Jackknife capture–recapture method was used that accounts for heterogeneity to estimate mean detectability and species richness. 5. In every case, more species were present than were counted. Mean species detectability was 0.61 (SE 0.01) with significant differences between observers (range 0.37–0.83). Species‐specific detection at time t+ 1 was then modelled for those species seen at t for three mid‐season surveys. Detectability averaged 0.50 (range 0.17–0.81) for individual species and 0.65, 0.44, and 0.42 for surveys. Abundant species were detected more easily, although this relationship explained only 5% of variation in species detectability. 6. These are important, although not entirely unexpected, results for species richness estimation of short‐lived animals. Raw counts of species may be misleading species richness indicators unless many surveys are conducted. Monitoring programmes should be calibrated, i.e. the assumption of constant detectability over dimensions of interest needs to be tested. The development of capture–recapture or similar models that can cope with both open populations and heterogeneous species detectability to estimate species richness should be a research priority.     

Capture–recapture models with heterogeneity to study survival senescence in the wild

Detecting senescence in wild populations and estimating its strength raise three challenges. First, in the presence of individual heterogeneity in survival probability, the proportion of high‐survival individuals increases with age. This increase can mask a senescence‐related decrease in survival probability when the probability is estimated at the population level. To accommodate individual heterogeneity we use a mixture model structure (discrete classes of individuals). Second, the study individuals can elude the observers in the field, and their detection rate can be heterogeneous. To account for detectability issues we use capture–mark–recapture (CMR) methodology, mixture models and data that provide information on individuals’ detectability. Last, emigration to non‐monitored sites can bias survival estimates, because it can occur at the end of the individuals’ histories and mimic earlier death. To model emigration we use Markovian transitions to and from an unobservable state. These different model structures are merged together using hidden Markov chain CMR models, or multievent models. Simulation studies illustrate that reliable evidence for survival senescence can be obtained using highly heterogeneous data from non site‐faithful individuals. We then design a tailored application for a dataset from a colony of black‐headed gull Chroicocephalus ridibundus. Survival probabilities do not appear individually variable, but evidence for survival senescence becomes significant only when accounting for other sources of heterogeneity. This result suggests that not accounting for heterogeneity leads to flawed inference and/or that emigration heterogeneity mimics survival heterogeneity and biases senescence estimates.     

Survival estimation of a cryptic antelope via photographic capture–recapture

Adult survival is a primary determinant of abundance and dynamics of large herbivore populations. For species that are inconspicuous, however, accurate survival estimation depends on accommodating low detection probability. For species with individually recognizable markings, photographic capture–recapture (CR) provides an approach to estimate population parameters while accounting for imperfect detection. I investigated the use of photographic CR for a cryptic large herbivore, the nyala, in a region of Hluhluwe–iMfolozi Park, South Africa. I conducted photographic sampling based on the closed robust design, with 5–6 daily sampling occasions nested within three week‐long sampling periods, which delineated one dry and one wet season. Detection differed between sexes: encounter probability of female adults depended on whether individuals fell into high‐encounter (seasonal range: 0.61–0.71) or low‐encounter (seasonal range: 0.29–0.40) groups, whereas male adults had a constant encounter probability of 0.39 per day. For both sexes, monthly survival probability was ≥0.93 and did not differ appreciably between seasons or sexes. Given the role of survival in population dynamics, photographic CR has the potential to provide survival estimates for cryptic large herbivores that lack such information.     

Demographic estimation methods for plants with unobservable life-states

Demographic estimation of vital parameters in plants with an unobservable dormant state is complicated, because time of death is not known. Conventional methods assume that death occurs at a particular time after a plant has last been seen aboveground but the consequences of assuming a particular duration of dormancy have never been tested. Capture–recapture methods do not make assumptions about time of death; however, problems with parameter estimability have not yet been resolved. To date, a critical comparative assessment of these methods is lacking. We analysed data from a 10 year study of Cleistes bifaria, a terrestrial orchid with frequent dormancy, and compared demographic estimates obtained by five varieties of the conventional methods, and two capture–recapture methods. All conventional methods produced spurious unity survival estimates for some years or for some states, and estimates of demographic rates sensitive to the time of death assumption. In contrast, capture–recapture methods are more parsimonious in terms of assumptions, are based on well founded theory and did not produce spurious estimates. In Cleistes, dormant episodes lasted for 1–4 years (mean 1.4, SD 0.74). The capture–recapture models estimated ramet survival rate at 0.86 (SE～0.01), ranging from 0.77–0.94 (SEs≤0.1) in any one year. The average fraction dormant was estimated at 30% (SE 1.5), ranging 16–47% (SEs≤5.1) in any one year. Multistate capture–recapture models showed that survival rates were positively related to precipitation in the current year, but transition rates were more strongly related to precipitation in the previous than in the current year, with more ramets going dormant following dry years. Not all capture–recapture models of interest have estimable parameters; for instance, without excavating plants in years when they do not appear aboveground, it is not possible to obtain independent time‐specific survival estimates for dormant plants. We introduce rigorous computer algebra methods to identify the parameters that are estimable in principle. As life‐states are a prominent feature in plant life cycles, multistate capture–recapture models are a natural framework for analysing population dynamics of plants with dormancy.     

Recommendations for photo‐identification methods used in capture‐recapture models with cetaceans

Capture‐recapture methods are frequently employed to estimate abundance of cetaceans using photographic techniques and a variety of statistical models. However, there are many unresolved issues regarding the selection and manipulation of images that can potentially impose bias on resulting estimates. To examine the potential impact of these issues we circulated a test data set of dorsal fin images from bottlenose dolphins to several independent research groups. Photo‐identification methods were generally similar, but the selection, scoring, and matching of images varied greatly amongst groups. Based on these results we make the following recommendations. Researchers should: (1) determine the degree of marking, or level of distinctiveness, and use images of sufficient quality to recognize animals of that level of distinctiveness; (2) ensure that markings are sufficiently distinct to eliminate the potential for “twins” to occur; (3) stratify data sets by distinctiveness and generate a series of abundance estimates to investigate the influence of including animals of varying degrees of markings; and (4) strive to examine and incorporate variability among analysts into capture‐recapture estimation. In this paper we summarize these potential sources of bias and provide recommendations for best practices for using natural markings in a capture‐recapture framework.     

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.     

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.     

Estimating population size by spatially explicit capture–recapture

The number of animals in a population is conventionally estimated by capture–recapture without modelling the spatial relationships between animals and detectors. Problems arise with non‐spatial estimators when individuals differ in their exposure to traps or the target population is poorly defined. Spatially explicit capture–recapture (SECR) methods devised recently to estimate population density largely avoid these problems. Some applications require estimates of population size rather than density, and population size in a defined area may be obtained as a derived parameter from SECR models. While this use of SECR has potential benefits over conventional capture–recapture, including reduced bias, it is unfamiliar to field biologists and no study has examined the precision and robustness of the estimates. We used simulation to compare the performance of SECR and conventional estimators of population size with respect to bias and confidence interval coverage for several spatial scenarios. Three possible estimators for the sampling variance of realised population size all performed well. The precision of SECR estimates was nearly the same as that of the null‐model conventional population estimator. SECR estimates of population size were nearly unbiased (relative bias 0–10%) in all scenarios, including surveys in randomly generated patchy landscapes. Confidence interval coverage was near the nominal level. We used SECR to estimate the population of a species of skink Oligosoma infrapunctatum from pitfall trapping. The estimated number in the area bounded by the outermost traps differed little between a homogeneous density model and models with a quadratic trend in density or a habitat effect on density, despite evidence that the latter models fitted better. Extrapolation of trend models to a larger plot may be misleading. To avoid extrapolation, a large region of interest should be sampled throughout, either with one continuous trapping grid or with clusters of traps dispersed widely according to a probability‐based and spatially representative sampling design.