Estimating Population Size with Noninvasive Capture-Mark-Recapture Data

Abstract:  Estimating population size of elusive and rare species is challenging. The difficulties in catching such species has triggered the use of samples collected noninvasively, such as feces or hair, from which genetic analysis yields data similar to capture-mark-recapture (CMR) data. There are, however, two differences between classical CMR and noninvasive CMR. First, capture and recapture data are gathered over multiple sampling sessions in classical CMR, whereas in noninvasive CMR they can be obtained from a single sampling session. Second, because of genotyping errors and unlike classical CMR, there is no simple relationship between (genetic) marks and individuals in noninvasive CMR. We evaluated, through simulations, the reliability of population size estimates based on noninvasive CMR. For equal sampling efforts, we compared estimates of population size N obtained from accumulation curves, a maximum likelihood, and a Bayesian estimator. For a closed population and without sampling heterogeneity, estimates obtained from noninvasive CMR were as reliable as estimates from classical CMR. The sampling structure (single or multiple session) did not alter the results, the Bayesian estimator in the case of a single sampling session presented the best compromise between low mean squared error and a 95% confidence interval encompassing the parametric value of N in most simulations. Finally, when suitable field and lab protocols were used, genotyping errors did not substantially bias population size estimates (bias < 3.5% in all simulations). The ability to reliably estimate population size from noninvasive samples taken during a single session offers a new and useful technique for the management and conservation of elusive and rare species.     

Continuous-time capture-recapture population estimation when capture probabilities vary over time

Closed capture-recapture (CR) estimators have been used extensively to estimate population size. Most closed CR approaches have been developed and evaluated for discrete-time models, but there has been little effort to evaluate their continuous-time counterparts. Continuous-time estimators — developed using maximum likelihood theory by Craig (1953) and Darroch (1958), and martingale theory by Becker (1984) — that allow capture probabilities to vary over time were evaluated using Monte Carlo simulation. Overall, the ML estimators had a smaller MSE. The estimators performed well when model assumptions were upheld, and were somewhat robust to heterogeneity in capture probabilities. However, the estimators were not robust to behavioural effects in the capture probabilities. Time lag effects (periods when animals might be unavailable for immediate recapture) on continuous-time estimates were also investigated and results indicated a positive bias which was greater for smaller populations. There was no gain in performance when using a continuous-time estimator versus a discrete-time estimator on the same simulated data. Usefulness of the continuous-time approach may be limited to study designs where animals are easier to sample using continuous-time methodology.     

Estimating Population Size of Elusive Animals with DNA from Hunter-Collected Feces: Four Methods for Brown Bears

Abstract:  Noninvasive genetic methods can be used to estimate animal abundances and offer several advantages over conventional methods. Few attempts have been made, however, to evaluate the accuracy and precision of the estimates. We compared four methods of estimating population size based on fecal sampling. Two methods used rarefaction indices and two were based on capture-mark-recapture (CMR) estimators, one combining genetic and field data. Volunteer hunters and others collected 1904 fecal samples over 2 consecutive years in a large area containing a well-studied population of brown bears ( Ursus arctos ). On our 49,000-km² study area in south-central Sweden, population size estimates ranged from 378 to 572 bears in 2001 and 273 to 433 bears in 2002, depending on the method of estimation used. The estimates from the best model in the program MARK appeared to be the most accurate, based on the minimum population size estimate from radio-marked bears in a subsection of our sampling area. In addition, MARK models included heterogeneity and temporal variation in detection probabilities, which appeared to be present in our samples. All methods, though, incorrectly suggested a biased sex ratio, probably because of sex differences in detection probabilities and low overall detection probabilities. The population size of elusive animals can be estimated reliably over large areas with noninvasive genetic methods, but we stress the importance of an adequate and well-distributed sampling effort. In cases of biased sampling, calibration with independent estimates may be necessary. We recommend that this noninvasive genetic approach, using the MARK models, be used in the future in areas where sufficient numbers of volunteers can be mobilized.     

Optimization of capture–recapture monitoring of elusive species illustrated with a threatened grasshopper

Information on population sizes and trends of threatened species is essential for their conservation, but obtaining reliable estimates can be challenging. We devised a method to improve the precision of estimates of population size obtained from capture–recapture studies for species with low capture and recapture probabilities and short seasonal activity, illustrated with population data of an elusive grasshopper (Prionotropis rhodanica). We used data from 5 capture–recapture studies to identify methodological and environmental factors affecting capture and recapture probabilities and estimates of population size. In a simulation, we used the population size and capture and recapture probability estimates obtained from the field studies to identify the minimum number of sampling occasions needed to obtain unbiased and robust estimates of population size. Based on these results we optimized the capture–recapture design, implemented it in 2 additional studies, and compared their precision with those of the nonoptimized studies. Additionally, we simulated scenarios based on thresholds of population size in criteria C and D of the International Union for Conservation of Nature (IUCN) Red List to investigate whether estimates of population size for elusive species can reliably inform red-list assessments. Identifying parameters that affect capture and recapture probabilities (for the grasshopper time since emergence of first adults) and optimizing field protocols based on this information reduced study effort (−6% to −27% sampling occasions) and provided more precise estimates of population size (reduced coefficient of variation) compared with nonoptimized studies. Estimates of population size from the scenarios based on the IUCN thresholds were mostly unbiased and robust (only the combination of very small populations and little study effort produced unreliable estimates), suggesting capture–recapture can be considered reliable for informing red-list assessments. Although capture–recapture remains difficult and costly for elusive species, our optimization procedure can help determine efficient protocols to increase data quality and minimize monitoring effort.     

Estimating the abundance of mouse populations of known size: promises and pitfalls of new methods.

Knowledge of animal abundance is fundamental to many ecological studies. Frequently, researchers cannot determine true abundance, and so must estimate it using a method such as mark-recapture or distance sampling. Recent advances in abundance estimation allow one to model heterogeneity with individual covariates or mixture distributions and to derive multimodel abundance estimators that explicitly address uncertainty about which model parameterization best represents truth. Further, it is possible to borrow information on detection probability across several populations when data are sparse. While promising, these methods have not been evaluated using mark-recapture data from populations of known abundance, and thus far have largely been overlooked by ecologists. In this paper, we explored the utility of newly developed mark-recapture methods for estimating the abundance of 12 captive populations of wild house mice (Mus musculus). We found that mark-recapture methods employing individual covariates yielded satisfactory abundance estimates for most populations. In contrast, model sets with heterogeneity formulations consisting solely of mixture distributions did not perform well for several of the populations. We show through simulation that a higher number of trapping occasions would have been necessary to achieve good estimator performance in this case. Finally, we show that simultaneous analysis of data from low abundance populations can yield viable abundance estimates.     

A generalized estimating equations approach for capture–recapture closed population models

The estimation of population density animal population parameters, such as capture probability, population size, or population density, is an important issue in many ecological applications. Capture–recapture data may be considered as repeated observations that are often correlated over time. If these correlations are not taken into account then parameter estimates may be biased, possibly producing misleading results. We propose a generalized estimating equations (GEE) approach to account for correlation over time instead of assuming independence as in the traditional closed population capture–recapture studies. We also account for heterogeneity among observed individuals and over-dispersion, modelling capture probabilities as a function of covariates. The GEE versions of all closed population capture–recapture models and their corresponding estimating equations are proposed. We evaluate the effect of accounting for correlation structures on capture–recapture model selection based on the quasi-likelihood information criterion (QIC). An example is used for an illustrative application and for comparison to currently used methodology. A Horvitz–Thompson-like estimator is used to obtain estimates of population size based on conditional arguments. A simulation study is conducted to evaluate the performance of the GEE approach in capture-recapture studies. The GEE approach performs well for estimating population parameters, particularly when capture probabilities are high. The simulation results also reveal that estimated population size varies on the nature of the existing correlation among capture occasions.     

Determining Optimal Population Monitoring for Rare Butterflies

Abstract: Determining population viability of rare insects depends on precise, unbiased estimates of population size and other demographic parameters. We used data on the endangered St. Francis' satyr butterfly (Neonympha mitchellii francisci) to evaluate 2 approaches (mark–recapture and transect counts) for population analysis of rare butterflies. Mark–recapture analysis provided by far the greatest amount of demographic information, including estimates (and standard errors) of population size, detection, survival, and recruitment probabilities. Mark–recapture analysis can also be used to estimate dispersal and temporal variation in rates, although we did not do this here. Models of seasonal flight phenologies derived from transect counts (Insect Count Analyzer) provided an index of population size and estimates of survival and statistical uncertainty. Pollard–Yates population indices derived from transect counts did not provide estimates of demographic parameters. This index may be highly biased if detection and survival probabilities vary spatially and temporally. In terms of statistical performance, mark–recapture and Pollard–Yates indices were least variable. Mark–recapture estimates were less likely to fail than Insect Count Analyzer, but mark–recapture estimates became less precise as sampling intensity decreased. In general, count‐based approaches are less costly and less likely to cause harm to rare insects than mark–recapture. The optimal monitoring approach must reconcile these trade‐offs. Thus, mark–recapture should be favored when demographic estimates are needed, when financial resources enable frequent sampling, and when marking does not harm the insect populations. The optimal sampling strategy may use 2 sampling methods together in 1 overall sampling plan: limited mark–recapture sampling to estimate survival and detection probabilities and frequent but less expensive transect counts.     

Modeling misidentification errors that result from use of genetic tags in capture–recapture studies

Misidentification of animals is potentially important when naturally existing features (natural tags) such as DNA fingerprints (genetic tags) are used to identify individual animals. For example, when misidentification leads to multiple identities being assigned to an animal, traditional estimators tend to overestimate population size. Accounting for misidentification in capture–recapture models requires detailed understanding of the mechanism. Using genetic tags as an example, we outline a framework for modeling the effect of misidentification in closed population studies when individual identification is based on natural tags that are consistent over time (non-evolving natural tags). We first assume a single sample is obtained per animal for each capture event, and then generalize to the case where multiple samples (such as hair or scat samples) are collected per animal per capture occasion. We introduce methods for estimating population size and, using a simulation study, we show that our new estimators perform well for cases with moderately high capture probabilities or high misidentification rates. In contrast, conventional estimators can seriously overestimate population size when errors due to misidentification are ignored.     

Importance of Accounting for Detection Heterogeneity When Estimating Abundance: the Case of French Wolves

Abstract: Assessing conservation strategies requires reliable estimates of abundance. Because detecting all individuals is most often impossible in free‐ranging populations, estimation procedures have to account for a <1 detection probability. Capture–recapture methods allow biologists to cope with this issue of detectability. Nevertheless, capture–recapture models for open populations are built on the assumption that all individuals share the same detection probability, although detection heterogeneity among individuals has led to underestimating abundance of closed populations. We developed multievent capture–recapture models for an open population and proposed an associated estimator of population size that both account for individual detection heterogeneity (IDH). We considered a two‐class mixture model with weakly and highly detectable individuals to account for IDH. In a noninvasive capture–recapture study of wolves we based on genotypes identified in feces and hairs, we found a large underestimation of population size (27% on average) occurred when IDH was ignored.     

Estimating abundance: a non parametric mark recapture approach for open and closed systems

We present a novel, non-parametric, frequentist approach for capture-recapture data based on a ratio estimator, which offers several advantages. First, as a non-parametric model, it does not require a known underlying distribution for parameters nor the associated assumptions, eliminating the need for post-hoc corrections or additional modeling to account for heterogeneity and other violated assumptions. Second, the model explicitly deals with dependence of trials by considering trials to be dependent; therefore, cluster sampling is handled naturally and additional adjustments are not necessary. Third, it accounts for ordering, utilizing the fact that a system with a small population will have a greater frequency of recaptures “early” in the survey work compared to an identical system with a larger population. We provide mathematical proof that our estimator attains asymptotic minimum variance under open systems. We apply the model to a data set of bottlenose dolphins (Tursiops truncatus) and compare results to those from classic closed models. We show that the model has an impressive rate of convergence and demonstrate that there’s an inverse relationship between population size and the proportion of the population that need to be sampled, while achieving the same degree of accuracy for abundance estimates. The model is flexible and can apply to ecological situations as well as other situations that lend themselves to capture recapture sampling.     

Closed population estimation models and their extensions in Program MARK

Program MARK provides > 65 data types in a common configuration for the estimation of population parameters from mark-encounter data. Encounter information from live captures, live resightings, and dead recoveries can be incorporated to estimate demographic parameters. Available estimates include survival (S or ϕ), rate of population change (λ), transition rates between strata (Ψ), emigration and immigration rates, and population size (N). Although N is the parameter most often desired by biologists, N is one of the most difficult parameters to estimate precisely without bias for a geographically and demographically closed population. The set of closed population estimation models available in Program MARK incorporate time (t) and behavioral (b) variation, and individual heterogeneity (h) in the estimation of capture and recapture probabilities in a likelihood framework. The full range of models from M ₀ (null model with all capture and recapture probabilities equal) to M _tbh are possible, including the ability to include temporal, group, and individual covariates to model capture and recapture probabilities. Both the full likelihood formulation of Otis et al. (1978) and the conditional model formulation of Huggins (1989, 1991) and Alho (1990) are provided in Program MARK, and all of these models are incorporated into the robust design (Kendall et al. 1995, 1997; Kendall and Nichols 1995) and robust-design multistrata (Hestbeck et al. 1991, Brownie et al. 1993) data types. Model selection is performed with AICc (Burnham and Anderson 2002) and model averaging (Burnham and Anderson 2002) is available in Program MARK to provide estimates of N with standard error that reflect model selection uncertainty.     

Demographic Connectivity for Ursid Populations at Wildlife Crossing Structures in Banff National Park

Wildlife crossing structures are one solution to mitigating the fragmentation of wildlife populations caused by roads, but their effectiveness in providing connectivity has only been superficially evaluated. Hundreds of grizzly (Ursus arctos) and black bear (Ursus americanus) passages through under and overpasses have been recorded in Banff National Park, Alberta, Canada. However, the ability of crossing structures to allow individual and population‐level movements across road networks remains unknown. In April 2006, we initiated a 3‐year investigation into whether crossing structures provide demographic connectivity for grizzly and black bears in Banff National Park. We collected hair with multiple noninvasive methods to obtain genetic samples from grizzly and black bears around the Bow Valley. Our objectives were to determine the number of male and female grizzly and black bears that use crossing structures; examine spatial and temporal patterns of crossings; and estimate the proportions of grizzly and black bear populations in the Bow Valley that use crossing structures. Fifteen grizzly (7 female, 8 male) and 17 black bears (8 female, 9 male) used wildlife crossing structures. The number of individuals detected at wildlife crossing structures was highly correlated with the number of passages in space and time. Grizzly bears used open crossing structures (e.g., overpasses) more often than constricted crossings (e.g., culverts). Peak use of crossing structures for both bear species occurred in July, when high rates of foraging activity coincide with mating season. We compared the number of bears that used crossings with estimates of population abundance from a related study and determined that substantial percentages of grizzly (15.0% in 2006, 19.8% in 2008) and black bear (17.6% in 2006, 11.0% in 2008) populations used crossing structures. On the basis of our results, we concluded wildlife crossing structures provide demographic connectivity for bear populations in Banff National Park. Conectividad Demográfica para Poblaciones de Úrsidos en Estructuras para Cruce de Vida Silvestre en el Parque Nacional Banff     

Robust, comparable population metrics through collaborative photo-monitoring of whale sharks Rhincodon typus.

The formulation of conservation policy for species that are rare and migratory requires broad cooperation to ensure that adequate levels of standardized data collection are achieved and that the results of local analyses are comparable. Estimates of apparent survival rate, relative change in abundance, and proportions of newly marked and returning individuals can inform local management decisions while highlighting corresponding changes at other linked research stations. We have applied computer-assisted photo-identification and mark-recapture population modeling to whale sharks Rhincodon typus at Ningaloo Marine Park (NMP), Western Australia, to create a baseline trend for comparison with other regional aggregations of the species. We estimate several ecological parameters of interest, including an average apparent survival rate of 0.55 yr(-1) for sharks newly marked (new) and 0.83 yr(-1) for sharks captured in multiple seasons (philopatric). The average proportion of philopatric sharks is found to be 0.65 of the total population, and we derive an average population growth rate of 1.12 yr(-1) for them. Our analysis uncovered significant heterogeneity in capture and survival probabilities in this study population; our chosen model structures and data analysis account for these influences and demonstrate a good overall fit to the time-series data. The results show good correspondence between capture probability and an available measure of recapture effort, suggesting that unmodeled systematic effects contribute insignificantly to the model fits. We find no evidence of a decline in the whale shark population at NMP, and our results provide metrics of value to their future management. Overall, our study suggests an effective approach to analyzing and modeling mark-recapture data for a rare species using computer-assisted photo-identification and opportunistic data collection from ecotourism to ensure the quality and volume of data required for population analysis.     

Estimating demographic parameters for capture–recapture data in the presence of multiple mark types

In mark-recapture studies, various techniques can be used to uniquely identify individual animals, such as ringing, tagging or photo-identification using natural markings. In some long-term studies more than one type of marking procedure may be implemented during the study period. In these circumstances, ignoring the different mark types can produce biased survival estimates since the assumption that the different mark types are equally catchable (homogeneous capture probability across mark types) may be incorrect. We implement an integrated approach where we simultaneously analyse data obtained using three different marking techniques, assuming that animals can be cross-classified across the different mark types. We discriminate between competing models using the AIC statistic. This technique also allows us to estimate both relative mark-loss probabilities and relative recapture efficiency rates for the different marking methods. We initially perform a simulation study to explore the different biases that can be introduced if we assume a homogeneous recapture probability over mark type, before applying the method to a real dataset. We make use of data obtained from an intensive long-term observational study of UK female grey seals (Halichoerus grypus) at a single breeding colony, where three different methods are used to identify individuals within a single study: branding, tagging and photo-identification based on seal coat pattern or pelage.     

Use of Spatial Capture‐Recapture Modeling and DNA Data to Estimate Densities of Elusive Animals

Abstract: Assessment of abundance, survival, recruitment rates, and density (i.e., population assessment) is especially challenging for elusive species most in need of protection (e.g., rare carnivores). Individual identification methods, such as DNA sampling, provide ways of studying such species efficiently and noninvasively. Additionally, statistical methods that correct for undetected animals and account for locations where animals are captured are available to efficiently estimate density and other demographic parameters. We collected hair samples of European wildcat (Felis silvestris) from cheek‐rub lure sticks, extracted DNA from the samples, and identified each animals’ genotype. To estimate the density of wildcats, we used Bayesian inference in a spatial capture‐recapture model. We used WinBUGS to fit a model that accounted for differences in detection probability among individuals and seasons and between two lure arrays. We detected 21 individual wildcats (including possible hybrids) 47 times. Wildcat density was estimated at 0.29/km² (SE 0.06), and 95% of the activity of wildcats was estimated to occur within 1.83 km from their home‐range center. Lures located systematically were associated with a greater number of detections than lures placed in a cell on the basis of expert opinion. Detection probability of individual cats was greatest in late March. Our model is a generalized linear mixed model; hence, it can be easily extended, for instance, to incorporate trap‐ and individual‐level covariates. We believe that the combined use of noninvasive sampling techniques and spatial capture‐recapture models will improve population assessments, especially for rare and elusive animals.     

On the Estimation of Dispersal Kernels from Individual Mark-Recapture Data

We present a new method for estimating a distribution of dispersal displacements (a dispersal kernel) from mark-recapture data. One conventional method of calculating the dispersal kernel assumes that the distribution of displacements are Gaussian (e.g. resulting from a diffusion process) and that individuals remain within sampled areas. The first assumption prohibits an analysis of dispersal data that do not exhibit the Gaussian distribution (a common situation); the second assumption leads to underestimation of dispersal distance because individuals that disperse outside of sampling areas are never recaptured. Our method eliminates these two assumptions. In addition, the method can also accommodate mortality during a sampling period. This new method uses integrodifference equations to express the probability of spatial mark-recapture data; associated dispersal, survival, and recapture parameters are then estimated using a maximum likelihood method. We examined the accuracy of the estimators by applying the method to simulated data sets. Our method suggests designs for future mark-recapture experiments. Received: January 2004 / Revised: July 2005     

Estimating Sonoran pronghorn abundance and survival with fecal DNA and capture–recapture methods

Population abundance estimates are important for management but can be challenging to determine in low‐density, wide‐ranging, and endangered species, such as Sonoran pronghorn (Antilocapra americana sonoriensis). The Sonoran pronghorn population has been increasing; however, population estimates are currently derived from a biennial aerial count that does not provide survival or recruitment estimates. We identified individuals through noninvasively collected fecal DNA and used robust‐design capture–recapture to estimate abundance and survival for Sonoran pronghorn in the United States from 2013 to 2014. In 2014 we generated separate population estimates for pronghorn gathered near 13 different artificial water holes and for pronghorn not near water holes. The population using artificial water holes had 116 (95% CI 102–131) and 121 individuals (95% CI 112–132) in 2013 and 2014, respectively. For all locations, we estimated there were 144 individuals (95% CI 132–157). Adults had higher annual survival probabilities (0.83, 95% CI 0.69–0.92) than fawns (0.41, 95% CI 0.21–0.65). Our use of targeted noninvasive genetic sampling and capture–recapture with Sonoran pronghorn fecal DNA was an effective method for monitoring a large proportion of the population. Our results provided the first survival estimates for this population in over 2 decades and precise estimates of the population using artificial water holes. Our method could be used for targeted sampling of broadly distributed species in other systems, such as in African savanna ecosystems, where many species congregate at watering sites.     

Toward accurate and precise estimates of lion density

Reliable estimates of animal density are fundamental to understanding ecological processes and population dynamics. Furthermore, their accuracy is vital to conservation because wildlife authorities rely on estimates to make decisions. However, it is notoriously difficult to accurately estimate density for wide‐ranging carnivores that occur at low densities. In recent years, significant progress has been made in density estimation of Asian carnivores, but the methods have not been widely adapted to African carnivores, such as lions (Panthera leo). Although abundance indices for lions may produce poor inferences, they continue to be used to estimate density and inform management and policy. We used sighting data from a 3‐month survey and adapted a Bayesian spatially explicit capture‐recapture (SECR) model to estimate spatial lion density in the Maasai Mara National Reserve and surrounding conservancies in Kenya. Our unstructured spatial capture‐recapture sampling design incorporated search effort to explicitly estimate detection probability and density on a fine spatial scale, making our approach robust in the context of varying detection probabilities. Overall posterior mean lion density was estimated to be 17.08 (posterior SD 1.310) lions >1 year old/100 km², and the sex ratio was estimated at 2.2 females to 1 male. Our modeling framework and narrow posterior SD demonstrate that SECR methods can produce statistically rigorous and precise estimates of population parameters, and we argue that they should be favored over less reliable abundance indices. Furthermore, our approach is flexible enough to incorporate different data types, which enables robust population estimates over relatively short survey periods in a variety of systems. Trend analyses are essential to guide conservation decisions but are frequently based on surveys of differing reliability. We therefore call for a unified framework to assess lion numbers in key populations to improve management and policy decisions.     

Age-dependent survival analyzed with Bayesian models of mark-recapture data

We describe a Bayesian random effects model of mark-recapture data that accounts for age-dependence in survival and individual heterogeneity in capture probabilities and survival. The model is applied to data on the Glanville fritillary butterfly (Melitaea cinxia) collected from a population enclosed in a large cage in the field. The cage population consisted of a mixture of butterflies originating from newly established and old populations in a large metapopulation in the Aland Islands in Finland. The explanatory variables in the model included the effects of temperature, sex, and population type (new vs. old) on capture probabilities, and the effects of age, sex, population type, and day vs. night on survival. We found that mortality rate increased with age, that mortality rate was much higher during the day than during the night, and that the life span of females originating from newly established populations was shorter than the life span of females from old populations. Capture probability decreased with increasing temperature and decreased with increasing mobility of individuals.     

Design based estimation for ranked set sampling in finite populations

In this paper, we consider design-based estimation using ranked set sampling (RSS) in finite populations. We first derive the first and second-order inclusion probabilities for an RSS design and present two Horvitz–Thompson type estimators using these inclusion probabilities. We also develop an alternate Hansen–Hurwitz type estimator and investigate its properties. In particular, we show that this alternate estimator always outperforms the usual Hansen–Hurwitz type estimator in the simple random sampling with replacement design with comparable sample size. We also develop formulae for ratio estimator for all three developed estimators. The theoretical results are augmented by numerical and simulation studies as well as a case study using a well known data set. These show that RSS design can yield a substantial improvement in efficiency over the usual simple random sampling design in finite populations.