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.     

Estimation of the size of an open population from capture-recapture data using weighted martingale methods

A weighted martingale method, akin to a moving average, is proposed to allow the use of modified closed-population methods in the estimation of the size of a smoothly changing open population when there are frequent capture occasions. We concentrate here on modifications to martingale estimating functions for model Mt, but a wide range of closed-population estimators may be modified in this fashion. The method is motivated by and applied to weekly capture-recapture data from the Mai Po bird sanctuary in Hong Kong. Simulations show that the weighted martingale estimator compared well with the Jolly-Seber estimator when the conditions for the latter to be valid are met, and it performed far better when individuals were allowed to leave and reenter the population. Expressions are derived for the asymptotic bias and variance of the estimator in an appendix.     

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 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.     

The Petersen–Lincoln Estimator and its Extension to Estimate the Size of a Shared Population

The Petersen–Lincoln estimator has been used to estimate the size of a population in a single mark release experiment. However, the estimator is not valid when the capture sample and recapture sample are not independent. We provide an intuitive interpretation for “independence” between samples based on 2 × 2 categorical data formed by capture/non‐capture in each of the two samples. From the interpretation, we review a general measure of “dependence” and quantify the correlation bias of the Petersen–Lincoln estimator when two types of dependences (local list dependence and heterogeneity of capture probability) exist. An important implication in the census undercount problem is that instead of using a post enumeration sample to assess the undercount of a census, one should conduct a prior enumeration sample to avoid correlation bias. We extend the Petersen–Lincoln method to the case of two populations. This new estimator of the size of the shared population is proposed and its variance is derived. We discuss a special case where the correlation bias of the proposed estimator due to dependence between samples vanishes. The proposed method is applied to a study of the relapse rate of illicit drug use in Taiwan. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Estimating Black Bear Density Using DNA Data From Hair Snares

ABSTRACT DNA-based mark-recapture has become a methodological cornerstone of research focused on bear species. The objective of such studies is often to estimate population size; however, doing so is frequently complicated by movement of individual bears. Movement affects the probability of detection and the assumption of closure of the population required in most models. To mitigate the bias caused by movement of individuals, population size and density estimates are often adjusted using ad hoc methods, including buffering the minimum polygon of the trapping array. We used a hierarchical, spatial capture-recapture model that contains explicit components for the spatial-point process that governs the distribution of individuals and their exposure to (via movement), and detection by, traps. We modeled detection probability as a function of each individual's distance to the trap and an indicator variable for previous capture to account for possible behavioral responses. We applied our model to a 2006 hair-snare study of a black bear (Ursus americanus) population in northern New York, USA. Based on the microsatellite marker analysis of collected hair samples, 47 individuals were identified. We estimated mean density at 0.20 bears/km². A positive estimate of the indicator variable suggests that bears are attracted to baited sites; therefore, including a trap-dependence covariate is important when using bait to attract individuals. Bayesian analysis of the model was implemented in WinBUGS, and we provide the model specification. The model can be applied to any spatially organized trapping array (hair snares, camera traps, mist nests, etc.) to estimate density and can also account for heterogeneity and covariate information at the trap or individual level.     

Heterogeneous capture rates in low density populations and consequences for capture-recapture analysis of camera-trap data

Closed population capture-recapture analysis of camera-trap data has become the conventional method for estimating the abundance of individually recognisable cryptic species living at low densities, such as large felids. Often these estimates are the only information available to guide wildlife managers and conservation policy. Capture probability of the target species using camera traps is commonly heterogeneous and low. Published studies often report overall capture probabilities as low as 0.03 and fail to report on the level of heterogeneity in capture probability. We used simulations to study the effects of low and heterogeneous capture probability on the reliability of abundance estimates using the M_h jack-knife estimator within a closed-population capture-recapture framework. High heterogeneity in capture probability was associated with under- and over-estimates of true abundance. The use of biased abundance estimates could have serious conservation management consequences. We recommend that studies present capture frequencies of all sampled individuals so that policy makers can assess the reliability of the abundance estimates.     

Comparison of enumeration and Jolly-Seber estimation of population size in the common voleMicrotus arvalis

Capture-recapture data on common volesMicrotus arvalis (Pallas, 1779) in central Europe have been almost exclusively analysed by means of the enumeration technique (minimum number alive or calendar of catches). Here we compare enumeration and Jolly-Seber (JS) estimation of population size in the common vole using live-trapping data from an alfalfa field-population in southern Moravia, Czech Republic. Over the entire study the enumeration estimate of the population size was smaller by an average of 28% than the JS estimate. The negative bias increased with density, decreased with both capture probability and the survival rate, and was more pronounced in males at high density. We conclude that the method of direct enumeration is not reliable for estimating population size in the common vole.     

cameratrapR: An R package for estimating animal density using camera trapping data

• 1.Camera trapping plays an important role in wildlife surveys, and provides valuable information for estimation of population density. While mark-recapture techniques can estimate population density for species that can be individually recognized or marked, there are no robust methods to estimate density of species that cannot be individually identified.
• 2.We developed a new approach to estimate population density based on the simulation of individual movement within the camera grid. Simulated animals followed a correlated random walk with the movement parameters of segment length, angular deflection, movement distance and home-range size derived from empirical movement paths. Movement was simulated under a series of population densities. We used the Random Forest algorithm to determine the population density with the highest likelihood of matching the camera trap data. We developed an R package, cameratrapR, to conduct simulations and estimate population density.
• 3.Compared with line transect surveys and the random encounter model, cameratrapR provides more reliable estimates of wildlife density with narrower confidence intervals. Functions are provided to visualize movement paths, derive movement parameters, and plot camera trapping results.
• 4.The package allows researchers to estimate population sizes/densities of animals that cannot be individually identified and cameras are deployed in a grid pattern.

     

Understanding implications of detection heterogeneity in wildlife abundance estimation

Negative bias in mark-recapture abundance estimators due to heterogeneity in detection (capture) probability is a well-known problem, but we believe most biologists do not understand why heterogeneity causes bias and how bias can be reduced. We demonstrate how heterogeneity creates dependence and bias in mark-recapture approaches to abundance estimation. In comparison, heterogeneity, and hence estimator bias, is not as problematic for distance sampling and mark-resight methods because both techniques estimate detection probabilities based on a known quantity. We show how the introduction of a known number of individuals planted into a study population prior to a mark-recapture survey can reduce bias from heterogeneity in detection probability. We provide examples with simulation and an analysis of motion-sensitive camera data from a study population of introduced eastern wild turkeys (Meleagris gallopavo silvestris) of known size with a subset of telemetered birds. In choosing a method for abundance estimation, careful consideration should be given to assumptions and how heterogeneity in detection probability can be accommodated for each application.     

The effect of attractant lures in camera trapping: a case study of population estimates for the Iberian lynx (Lynx pardinus)

Capture–recapture analysis of camera trap data is a conventional method to estimate the abundance of free-ranging wild felids. Due to notorious low detection rates of felids, it is important to increase the detection probability during sampling. In this study, we report the effectiveness of attractants as a tool for improving the efficiency of camera trap sampling in abundance estimation of Iberian lynx. We developed a grid system of camera stations in which stations with and without attractant lures were spatially alternated across known Iberian lynx habitat. Of the ten individuals identified, five were detected at stations with no attractant (blind sets), and nine, at the lured stations. Thirty-eight percent of blind set station’s independent captures and 10?% of lured station’s independent captures resulted in photographs unsuitable for correct individual identification. The total capture probability at lured stations was higher than that obtained at blind set stations. The estimates obtained with blind set cameras underestimated the number of lynxes compared to lured cameras. In our study, it appears that the use of lures increased the efficiency of trail camera captures and, therefore, the accuracy of capture–recapture analysis. The observed failure to detect known individuals at blind set camera stations may violate capture–recapture assumptions and bias abundance estimates.     

Use of Occupancy Models to Estimate the Influence of Previous Live Captures on DNA-Based Detection Probabilities of Grizzly Bears

Abstract: Large carnivores potentially change their behavior following physical capture, becoming less responsive to the attractants that resulted in their capture, which can bias population estimates where the change in behavior is not appropriately modeled. We applied occupancy models to efficiently estimate and compare detection probabilities of previously collared grizzly bears (Ursus arctos) with bears captured at DNA hair-snag sites that were not previously collared. We found that previously captured bears had lower detection probabilities, although their detection probabilities were still >0, implying that they were still visible to be sampled via the DNA hair-snag grid, which was able to detect finer differences in capture probabilities of previously collared bears compared with Huggins closed-captures population models. To obtain relatively unbiased population estimates for DNA surveys, heterogeneity caused by previous live capture should be accounted for in the population estimator. (JOURNAL OF WILDLIFE MANAGEMENT 72(3):589–595; 2008)     

Estimation of population size based on additive hazards models for continuous-time recapture experiments

We use the semiparametric additive hazards model to formulate the effects of individual covariates on the capture rates in the continuous-time capture-recapture experiment, and then construct a Horvitz-Thompson-type estimator for the unknown population size. The resulting estimator is consistent and asymptotically normal with an easily estimated variance. Simulation studies show that the asymptotic approximations are adequate for practical use when the average capture probabilities exceed .5. Ignoring covariates would underestimate the population size and the coverage probability is poor. A wildlife example is provided.     

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.     

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.     

How Does Spatial Study Design Influence Density Estimates from Spatial Capture-Recapture Models?

When estimating population density from data collected on non-invasive detector arrays, recently developed spatial capture-recapture (SCR) models present an advance over non-spatial models by accounting for individual movement. While these models should be more robust to changes in trapping designs, they have not been well tested. Here we investigate how the spatial arrangement and size of the trapping array influence parameter estimates for SCR models. We analysed black bear data collected with 123 hair snares with an SCR model accounting for differences in detection and movement between sexes and across the trapping occasions. To see how the size of the trap array and trap dispersion influence parameter estimates, we repeated analysis for data from subsets of traps: 50% chosen at random, 50% in the centre of the array and 20% in the South of the array. Additionally, we simulated and analysed data under a suite of trap designs and home range sizes. In the black bear study, we found that results were similar across trap arrays, except when only 20% of the array was used. Black bear density was approximately 10 individuals per 100 km(2). Our simulation study showed that SCR models performed well as long as the extent of the trap array was similar to or larger than the extent of individual movement during the study period, and movement was at least half the distance between traps. SCR models performed well across a range of spatial trap setups and animal movements. Contrary to non-spatial capture-recapture models, they do not require the trapping grid to cover an area several times the average home range of the studied species. This renders SCR models more appropriate for the study of wide-ranging mammals and more flexible to design studies targeting multiple species.     

Movement behaviour of woodland rodents: looking from beyond small trapping grids

Live-trapping of rodents was conducted over a 12-ha plot on unevenly spaced trap lines, with inner lines forming a 3.5-ha grid of closely spaced traps. This design was used to estimate the probability that bank volesClethrionomys glareolus (Schreber, 1780) and yellow-necked miceApodemus flavicollis (Melchior, 1834) trapped in small grids are true residents rather than visitors from the surrounding area. On average, 12% of the voles and 19% of the mice were trapped within and beyond the grid in the same trapping sessions. As these were mainly wide-ranging males moving over the plot, home ranges of males may be underestimated on small grids. In total, 36% of voles and 39% of mice that were marked in spring-summer were trapped at least once in their life beyond the grid. Typically, these were individuals shifting home ranges and migrating to or from the grid. The size of lifetime ranges of rodents was significantly larger than temporary home ranges and may therefore be underestimated on small grids. “Single--capture” individuals were mainly true transients rather than visitors. Only 12% of voles and 15% of mice resided on the plot for longer time than in the grid.     

Are nest-detection probability methods relevant for estimating turtle dove breeding populations? a case study in Moroccan agroecosystems

Knowing the population size of game is a basic prerequisite to determining adequate hunting management and conservation strategies and setting up appropriate hunting quotas. This study compared three methods complete count, capture–recapture and N-mixture modelling to estimate a turtle dove Streptopelia turtur breeding population using nest counts. We randomly sampled 143 fruit farms (60 orange orchards and 83 olive orchards) situated in an irrigated area in Morocco at the peak of breeding activity. We calculated the probability of detecting active turtle dove nests using information from two observers who independently searched the same sample plots. We found that (a) the capture–recapture method provided more precise results of nest abundance than N-mixture modelling, and that (b) the probability of nest detection was noticeably different between the two study orchards—higher in the orange orchards than in the olive orchards. Although these two methods are easy to implement and cost-effective for estimating population abundance on a large spatial scale, our results demonstrate that the resulting estimates are prone to bias depending on the tree height of the plantations. Of the three methods for estimating turtle dove abundance, complete counts were preferable for assessing population size. Using the complete counts, the density of turtle dove nests was found to be 2.96 nests/ha in the orange orchards and 0.93 nests/ha in the olive orchards. A density extrapolation to the entire surface area of the Tadla Region indicated a minimum breeding population size of 58,969 pairs (95 % confidence interval: 48,550–69,353).     

Surveying an endangered saproxylic beetle, Osmoderma eremita, in Mediterranean woodlands: a comparison between different capture methods

Measuring population size is riddled with difficulties for wildlife biologists and managers, and in the case of rare species, it is sometimes practically impossible to estimate abundance, whereas estimation of occupancy is possible. Furthermore, obtaining reliable population size estimates is not straightforward, as different sampling techniques can give misleading results. A mark-recapture study of the endangered saproxylic beetle Osmoderma eremita was performed in central Italy by applying four independent capture methods within a study area where 116 hollow trees were randomly selected to set traps. Detection probability and population size estimates were drawn from each of these four capture methods. There were strong differences in detection probability among methods. Despite using pheromone and beetle manipulation, capture histories were not affected by trap-happiness or trap-shyness. Population size estimates varied considerably in both abundance and precision by capture method. A number of 0.5 and 0.2 adult beetles per tree was estimated using the whole data set by closed and open population models, respectively. Pitfall trap appeared the optimal method to detect the occurrence of this species. Since in the southern part of its distribution range, a single population of O. eremita is widespread in the landscape, and includes beetles from more than one hollow tree, conservation efforts should focus not only on preserving few and isolated monumental hollow trees, but should be extended to large stands.     

Estimation of population density of European pine marten in central Italy using camera trapping

Evaluating presence and abundance of small carnivores is essential for their conservation. In Italy, there is scarce information on European pine marten distribution, and no data are published on its abundance. Camera traps have been widely used to estimate population density applying capture–recapture models for species in which individual recognition is possible. Here we estimate the abundance of European pine martens in central Italy using camera trapping and a model that allows the estimation of population density without the need for individual recognition Rowcliffe et al. (Anim Conserv 11:185–186, 2008). Camera trapping was also used to evaluate habitat use patterns by martens. Fifteen camera traps were deployed in 90 placements for 15 days each, for a total of 1,334 camera days. Pine martens were captured in 24% of camera trap placements with a mean trap success rate of 0.33 photographs per camera placement. Estimated pine marten population density in the study area was 0.34 individuals km⁻². Marten trap rate was not strongly associated with any habitat type, although there were trends towards lower probability of records at locations with high coverage of cultivated fields and higher probability of records at locations with high coverage of human-made woodland. The results suggest that pine martens in this area are not confined to wooded habitat. To our knowledge, this study is the first application of the Rowcliffe et al. (Anim Conserv 11:185–186, 2008) method to a wild carnivore population and, furthermore, the first estimation of population density of pine martens in Italy.