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.     

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.     

Does your species have memory? Analyzing capture–recapture data with memory models

We examine memory models for multisite capture–recapture data. This is an important topic, as animals may exhibit behavior that is more complex than simple first‐order Markov movement between sites, when it is necessary to devise and fit appropriate models to data. We consider the Arnason–Schwarz model for multisite capture–recapture data, which incorporates just first‐order Markov movement, and also two alternative models that allow for memory, the Brownie model and the Pradel model. We use simulation to compare two alternative tests which may be undertaken to determine whether models for multisite capture–recapture data need to incorporate memory. Increasing the complexity of models runs the risk of introducing parameters that cannot be estimated, irrespective of how much data are collected, a feature which is known as parameter redundancy. Rouan et al. (JABES, 2009, pp 338–355) suggest a constraint that may be applied to overcome parameter redundancy when it is present in multisite memory models. For this case, we apply symbolic methods to derive a simpler constraint, which allows more parameters to be estimated, and give general results not limited to a particular configuration. We also consider the effect sparse data can have on parameter redundancy and recommend minimum sample sizes. Memory models for multisite capture–recapture data can be highly complex and difficult to fit to data. We emphasize the importance of a structured approach to modeling such data, by considering a priori which parameters can be estimated, which constraints are needed in order for estimation to take place, and how much data need to be collected. We also give guidance on the amount of data needed to use two alternative families of tests for whether models for multisite capture–recapture data need to incorporate memory.     

Bayesian latent class models for capture–recapture in the presence of missing data

We propose a method for estimating the size of a population in a multiple record system in the presence of missing data. The method is based on a latent class model where the parameters and the latent structure are estimated using a Gibbs sampler. The proposed approach is illustrated through the analysis of a data set already known in the literature, which consists of five registrations of neural tube defects.     

Estimating individual fitness in the wild using capture–recapture data

The concept of Darwinian fitness is central in evolutionary ecology, and its estimation has motivated the development of several approaches. However, measuring individual fitness remains challenging in empirical case studies in the wild. Measuring fitness requires a continuous monitoring of individuals from birth to death, which is very difficult to get in part because individuals may or may not be controlled at each reproductive event and recovered at death. Imperfect detection hampers keeping track of mortality and reproductive events over the whole lifetime of individuals. We propose a new statistical approach to estimate individual fitness while accounting for imperfect detection. Based on hidden process modelling of longitudinal data on marked animals, we show that standard metrics to quantify fitness, namely lifetime reproductive success, individual growth rate and lifetime individual contribution to population growth, can be extended to cope with imperfect detection inherent to most monitoring programs in the wild. We illustrate our approach using data collected on individual roe deer in an intensively monitored population.     

Monitoring tiger populations using intensive search in a capture–recapture framework

Tigers (Panthera tigris) today face multiple threats to their survival in the form of habitat loss, poaching, depletion of wild prey through illegal hunting and loss of connectivity between populations. Monitoring of tigers is crucial to evaluate their status and react adaptively to management problems. Though camera traps are becoming increasingly popular with researchers enumerating cryptic and elusive animals, they have not been embedded in the regular management activities of tiger reserves. Tiger monitoring, though an important part of the management, is usually implemented using the unreliable pugmark approach. Camera trap-based studies are few, usually of short duration, and are generally conducted by individual scientists and organizations. In this study, we integrate photographic mark–recapture with the routine activity of searching and locating tigers for tourist viewing by the park management in meadows of Kanha Tiger Reserve which form a part of the tourism zone. We validate the density estimates from “tiger search approach” against those obtained from camera trapping and radio-telemetry conducted in conjunction in the same area. Tiger density (\( \hat{D} \) (SE [\( \hat{D} \)]) per 100 km² for camera traps and tiger search, respectively, was estimated at 12.0 (1.95) and 12.0 (1.76) when effective trapping area was estimated using the half mean maximum distance moved (½ MMDM), 7.6 (1.94) and 7.5 (1.97) using the home range radius, 7.3 (1.49) and 7.5 (1.97) with the full MMDM, and 8.0 (3.0) and 6.88 (2.39) with the spatial likelihood method in Program DENSITY 4.1. Camera trapping, however, was five times more expensive than the tiger search method. Our study suggests that “tiger search approach” can be used as a regular monitoring tool in the tourism zones of tiger reserves, where often most of the source populations are located.     

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.     

Methods to mark termites with protein for mark–release–recapture and mark–capture type studies

Studies were conducted to investigate the feasibility of marking the southwestern desert subterranean termite, Heterotermes aureus (Snyder), with rabbit immunoglobulin G (IgG) protein for mark–release–recapture (MRR) and mark–capture type studies. Qualitative laboratory studies were conducted to determine how long reagent-grade rabbit IgG is retained on or in H. aureus that were marked either externally with a topical spray, internally by feeding them a rabbit IgG-marked food source, or both internally and externally (double marked). Marked termites were detected by an anti-rabbit IgG enzyme-linked immunosorbent assay. Data indicated that the termites retained the mark for at least 35 days, regardless of the marking procedure. A second series of laboratory studies were conducted to determine how fast H. aureus acquire the mark after feeding on cardboard bait that was either sprayed or soaked in different formulations of rabbit IgG. The IgGs tested were a highly purified and costly reagent grade IgG at 5.0 mg/ml and a less pure and less costly technical grade rabbit IgG at 1.0 mg/ml. The results showed that termites acquired both marks equally well after exposure to the soaked cardboard treatment. The advantages and limitations of protein marking termites with rabbit IgG for MRR or mark–capture termite studies are discussed.     

An improved procedure to estimate wolf abundance using non-invasive genetic sampling and capture–recapture mixture models

Non-invasive genetic sampling (NGS) is increasingly used to estimate the abundance of rare or elusive species such as the wolf (Canis lupus), which cannot be directly counted in forested mountain habitats. Wolf individual and familial home ranges are wide, potentially connected by long-range dispersers, and their populations are intrinsically open. Appropriate demographic estimators are needed, because the assumptions of homogeneous detection probability and demographic closeness are violated. We compiled the capture–recapture record of 418 individual wolf genotypes identified from ca. 4,900 non-invasive samples, collected in the northern Italian Apennines from January 2002 to June 2009. We analysed this dataset using novel capture–recapture multievent models for open populations that explicitly account for individual detection heterogeneity (IDH). Overall, the detection probability of the weakly detectable individuals, probably pups, juveniles and migrants (P = 0.08), was ca. six times lower than that of the highly detectable wolves (P = 0.44), probably adults and dominants. The apparent annual survival rate of weakly detectable individuals was lower (Φ = 0.66) than those of highly detectable wolves (Φ = 0.75). The population mean annual finite rate of increase was λ = 1.05 ± 0.11, and the mean annual size ranged from N = 117 wolves in 2003 to N = 233 wolves in 2007. This procedure, combining large-scale NGS and multievent IDH demographic models, provides the first estimates of abundance, multi-annual trend and survival rates for an open large wolf population in the Apennines. These results contribute to deepen our understanding of wolf population ecology and dynamics, and provide new information to implement sound long-term conservation plans.     

Erratum to: Using multistate capture–mark–recapture models to quantify effects of predation on age-specific survival and population growth in black-tailed deer

Effective species management and conservation relies on accurate estimates of vital rates and an understanding of their link to environmental variables. We used multistate capture–mark–recapture models to directly quantify effects of predation on age-specific survival of black-tailed deer Odocoileus hemionus columbianus in California, USA. Survival probabilities were derived from individual encounter histories of 136 fawns and 57 adults monitored over 4 years. Based on results from our survival analysis we parameterized a Lefkovitch matrix and used elasticity analyses to investigate contributions of mortality due to predation to changes in population growth. We found strong evidence for age-specific survival including senescence. Survival of females >1 year old was consistently low (0.56 ± 0.18 for yearlings, 0.77 ± 0.13 for prime-aged females, and 0.55 ± 0.08 for senescent individuals), primarily due to high puma Puma concolor predation during summer. Predation from black bears Ursus americanus and coyotes Canis latrans was the primary cause for low annual survival of fawns (0.24 ± 0.16). Resulting estimates of population growth rates were indicative of a strongly declining population (λ = 0.82 ± 0.13). Despite high sensitivity to changes in adult survival, results from a lower-level elasticity analysis suggested that predation on fawns was the most significant individual mortality component affecting population decline. Our results provide a rare, direct link between predation, age-specific survival and the predicted population decline of a common ungulate species. The magnitude of predation was unexpected and suggests that ungulates in multi-predator systems struggle to cope with simultaneous reductions in survival probabilities from predators targeting different age classes.     

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.     

Evaluation of childhood acute leukemia incidence and underreporting in Brazil by capture–recapture methodology

Background: Population-based cancer registries (PBCR) are important in cancer epidemiology as they provide the basis for monitoring cancer incidence. Childhood acute lymphoblastic leukemia (ALL) is said to have lower incidence in developing countries, which has implications for its pathogenesis, but there are few studies concerning the completeness of cancer registries in developing countries. This study analyzes the number of cases and incidence of childhood acute lymphoblastic leukemia in three different cities in Brazil and estimates underreporting cases and possible PBCR failures. Methods: We evaluated the completeness of PBCR and the incidence rates of childhood ALL from three different Brazilian cities using the two-source capture–recapture method. The sources used were a population-based registry and databases from a diagnosis reference laboratory in 2001 and the Chapman's formula was used to calculate the estimates. Results: The estimated incidence was 5.76, 6.32 and 5.48 per 100,000 inhabitants for Salvador, Recife and Belo Horizonte, respectively. The estimated completeness of childhood ALL in PBCRs was 15.5%, 35.4% and 29.2%, respectively, for Salvador, Recife and Belo Horizonte. Conclusions: There was a high estimated underreporting of childhood leukemia cases in some Brazilian cities. The relationship between information systems and the capture–recapture method application improved epidemiological estimates. Childhood acute lymphoblastic leukemia incidence rates are similar to those of developed countries.     

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.     

How well do reduced models capture the dynamics in models of interacting neurons?

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations. Rigorous results on existence and uniqueness of nonequilibrium steady states are proved. These network models are then compared to very simple reduced models driven by the same mean excitatory and inhibitory currents. Discrepancies in firing rates between network and reduced models are investigated and explained by correlations in spiking, or partial synchronization, working in concert with “nonlinearities” in the time evolution of membrane potentials. The use of simple random walks and their first passage times to simulate fluctuations in neuronal membrane potentials and interspike times is also considered.