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.     

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.     

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.     

Ecological and methodological factors affecting detectability and population estimation in elusive species

Although mark-recapture methods are among the most powerful tools for monitoring wildlife populations, the secretive nature of some species requires a comprehensive understanding of the factors that affect capture probability to maximize accuracy and precision of population parameter estimates (e.g., population size and survivorship). Here, we used aquatic snakes as a case study in applying rigorous mark-recapture methods to estimate population parameters for secretive species. Specifically, we used intensive field sampling and robust design mark-recapture analyses in Program MARK to test specific hypotheses about ecological and methodological factors influencing detectability of two species of secretive aquatic snakes, the banded watersnake (Nerodia fasciata), and the black swamp snake (Seminatrix pygaea). We constructed a candidate set of a priori mark-recapture models incorporating various combinations of time- and sex-varying capture and recapture probabilities, behavioral responses to traps (i.e., trap-happiness or trap-shyness), and temporary emigration, and we ranked models for each species using Akaike's Information Criterion. For both banded watersnakes and black swamp snakes we found strong support for time-varying capture and recapture probabilities and strong trap-happy responses, factors that can bias population estimation if not accommodated in the models. We also found evidence of sex-dependent temporary emigration in black swamp snakes. Our study is among the first comprehensive assessments of factors affecting detectability in snakes and provides a framework for studies aimed at monitoring populations of other secretive species. © 2010 The Wildlife Society.     

Assessing species richness trends: Declines of bees and bumblebees in the Netherlands since 1945

Estimating and predicting temporal trends in species richness is of general importance, but notably difficult because detection probabilities of species are imperfect and many datasets were collected in an opportunistic manner. We need to improve our capabilities to assess richness trends using datasets collected in unstandardized procedures with potential collection bias. Two methods are proposed and applied to estimate richness change, which both incorporate models for sampling effects and detection probability: (a) nonlinear species accumulation curves with an error variance model and (b) Pradel capture–recapture models. The methods are used to assess nationwide temporal trends (1945–2018) in the species richness of wild bees in the Netherlands. Previously, a decelerating decline in wild bee species richness was inferred for part of this dataset. Among the species accumulation curves, those with nonconstant changes in species richness are preferred. However, when analyzing data subsets, constant changes became selected for non‐Bombus bees (for samples in collections) and bumblebees (for spatial grid cells sampled in three periods). Smaller richness declines are predicted for non‐Bombus bees than bumblebees. However, when relative losses are calculated from confidence intervals limits, they overlap and touch zero loss. Capture–recapture analysis applied to species encounter histories infers a constant colonization rate per year and constant local species survival for bumblebees and other bees. This approach predicts a 6% reduction in non‐Bombus species richness from 1945 to 2018 and a significant 19% reduction for bumblebees. Statistical modeling to detect species richness time trends should be systematically complemented with model checking and simulations to interpret the results. Data inspection, assessing model selection bias, and comparisons of trends in data subsets were essential model checking strategies in this analysis. Opportunistic data will not satisfy the assumptions of most models and this should be kept in mind throughout.     

Balancing Precision and Risk: Should Multiple Detection Methods Be Analyzed Separately in N-Mixture Models?

Using multiple detection methods can increase the number, kind, and distribution of individuals sampled, which may increase accuracy and precision and reduce cost of population abundance estimates. However, when variables influencing abundance are of interest, if individuals detected via different methods are influenced by the landscape differently, separate analysis of multiple detection methods may be more appropriate. We evaluated the effects of combining two detection methods on the identification of variables important to local abundance using detections of grizzly bears with hair traps (systematic) and bear rubs (opportunistic). We used hierarchical abundance models (N-mixture models) with separate model components for each detection method. If both methods sample the same population, the use of either data set alone should (1) lead to the selection of the same variables as important and (2) provide similar estimates of relative local abundance. We hypothesized that the inclusion of 2 detection methods versus either method alone should (3) yield more support for variables identified in single method analyses (i.e. fewer variables and models with greater weight), and (4) improve precision of covariate estimates for variables selected in both separate and combined analyses because sample size is larger. As expected, joint analysis of both methods increased precision as well as certainty in variable and model selection. However, the single-method analyses identified different variables and the resulting predicted abundances had different spatial distributions. We recommend comparing single-method and jointly modeled results to identify the presence of individual heterogeneity between detection methods in N-mixture models, along with consideration of detection probabilities, correlations among variables, and tolerance to risk of failing to identify variables important to a subset of the population. The benefits of increased precision should be weighed against those risks. The analysis framework presented here will be useful for other species exhibiting heterogeneity by detection method.     

Rejection of Schmidt et al.'s estimators for bear population size

Aerial distance sampling of bears to estimate population size has been used throughout many parts of Alaska. The distance sampling models are complex since they need to account for undetected bears and differences in detection probabilities. This will require covariates and mark‐recapture data. The models proposed by Schmidt et al. do not use covariates or mark‐recapture data and are inappropriate for these surveys.     

Integrating sign surveys and telemetry data for estimating brown bear (Ursus arctos) density in the Romanian Carpathians

Accurate population size estimates are important information for sustainable wildlife management. The Romanian Carpathians harbor the largest brown bear (Ursus arctos) population in Europe, yet current management relies on estimates of density that lack statistical oversight and ignore uncertainty deriving from track surveys. In this study, we investigate an alternative approach to estimate brown bear density using sign surveys along transects within a novel integration of occupancy models and home range methods. We performed repeated surveys along 2‐km segments of forest roads during three distinct seasons: spring 2011, fall‐winter 2011, and spring 2012, within three game management units and a Natura 2000 site. We estimated bears abundances along transects using the number of unique tracks observed per survey occasion via N‐mixture hierarchical models, which account for imperfect detection. To obtain brown bear densities, we combined these abundances with the effective sampling area of the transects, that is, estimated as a function of the median (± bootstrapped SE) of the core home range (5.58 ± 1.08 km²) based on telemetry data from 17 bears tracked for 1‐month periods overlapping our surveys windows. Our analyses yielded average brown bear densities (and 95% confidence intervals) for the three seasons of: 11.5 (7.8–15.3), 11.3 (7.4–15.2), and 12.4 (8.6–16.3) individuals/100 km². Across game management units, mean densities ranged between 7.5 and 14.8 individuals/100 km². Our method incorporates multiple sources of uncertainty (e.g., effective sampling area, imperfect detection) to estimate brown bear density, but the inference fundamentally relies on unmarked individuals only. While useful as a temporary approach to monitor brown bears, we urge implementing DNA capture–recapture methods regionally to inform brown bear management and recommend increasing resources for GPS collars to improve estimates of effective sampling area.     

Making use of multiple surveys: Estimating breeding probability using a multievent‐robust design capture–recapture model

Increased environmental stochasticity due to climate change will intensify temporal variance in the life‐history traits, and especially breeding probabilities, of long‐lived iteroparous species. These changes may decrease individual fitness and population viability and is therefore important to monitor. In wild animal populations with imperfect individual detection, breeding probabilities are best estimated using capture–recapture methods. However, in many vertebrate species (e.g., amphibians, turtles, seabirds), nonbreeders are unobservable because they are not tied to a territory or breeding location. Although unobservable states can be used to model temporary emigration of nonbreeders, there are disadvantages to having unobservable states in capture–recapture models. The best solution to deal with unobservable life‐history states is therefore to eliminate them altogether. Here, we achieve this objective by fitting novel multievent‐robust design models which utilize information obtained from multiple surveys conducted throughout the year. We use this approach to estimate annual breeding probabilities of capital breeding female elephant seals (Mirounga leonina). Conceptually, our approach parallels a multistate version of the Barker/robust design in that it combines robust design capture data collected during discrete breeding seasons with observations made at other times of the year. A substantial advantage of our approach is that the nonbreeder state became “observable” when multiple data sources were analyzed together. This allowed us to test for the existence of state‐dependent survival (with some support found for lower survival in breeders compared to nonbreeders), and to estimate annual breeding transitions to and from the nonbreeder state with greater precision (where current breeders tended to have higher future breeding probabilities than nonbreeders). We used program E‐SURGE (2.1.2) to fit the multievent‐robust design models, with uncertainty in breeding state assignment (breeder, nonbreeder) being incorporated via a hidden Markov process. This flexible modeling approach can easily be adapted to suit sampling designs from numerous species which may be encountered during and outside of discrete breeding seasons.     

Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels

Coloniality has mainly been studied from an evolutionary perspective, but relatively few studies have developed methods for modelling colony dynamics. Changes in number of colonies over time provide a useful tool for predicting and evaluating the responses of colonial species to management and to environmental disturbance. Probabilistic Markov process models have been recently used to estimate colony site dynamics using presence–absence data when all colonies are detected in sampling efforts. Here, we define and develop two general approaches for the modelling and analysis of colony dynamics for sampling situations in which all colonies are, and are not, detected. For both approaches, we develop a general probabilistic model for the data and then constrain model parameters based on various hypotheses about colony dynamics. We use Akaike's Information Criterion (AIC) to assess the adequacy of the constrained models. The models are parameterised with conditional probabilities of local colony site extinction and colonization. Presence–absence data arising from Pollock's robust capture–recapture design provide the basis for obtaining unbiased estimates of extinction, colonization, and detection probabilities when not all colonies are detected. This second approach should be particularly useful in situations where detection probabilities are heterogeneous among colony sites. The general methodology is illustrated using presence–absence data on two species of herons. Estimates of the extinction and colonization rates showed interspecific differences and strong temporal and spatial variations. We were also able to test specific predictions about colony dynamics based on ideas about habitat change and metapopulation dynamics. We recommend estimators based on probabilistic modelling for future work on colony dynamics. We also believe that this methodological framework has wide application to problems in animal ecology concerning metapopulation and community dynamics.     

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.     

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.     

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.     

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).     

Augmenting superpopulation capture-recapture models with population assignment data

Summary Ecologists applying capture–recapture models to animal populations sometimes have access to additional information about individuals' populations of origin (e.g., information about genetics, stable isotopes, etc.). Tests that assign an individual's genotype to its most likely source population are increasingly used. Here we show how to augment a superpopulation capture–recapture model with such information. We consider a single superpopulation model without age structure, and split each entry probability into separate components due to births in situ and immigration. We show that it is possible to estimate these two probabilities separately. We first consider the case of perfect information about population of origin, where we can distinguish individuals born in situ from immigrants with certainty. Then we consider the more realistic case of imperfect information, where we use genetic or other information to assign probabilities to each individual's origin as in situ or outside the population. We use a resampling approach to impute the true population of origin from imperfect assignment information. The integration of data on population of origin with capture–recapture data allows us to determine the contributions of immigration and in situ reproduction to the growth of the population, an issue of importance to ecologists. We illustrate our new models with capture–recapture and genetic assignment data from a population of banner‐tailed kangaroo rats Dipodomys spectabilis in Arizona.     

Using soundscape recordings to estimate bird species abundance, richness, and composition

ABSTRACT Point counts are the most frequently used technique for sampling bird populations and communities, but have well‐known limitations such as inter‐ and intraobserver errors and limited availability of expert field observers. The use of acoustic recordings to survey birds offers solutions to these limitations. We designed a Soundscape Recording System (SRS) that combines a four‐channel, discrete microphone system with a quadraphonic playback system for surveying bird communities. We compared the effectiveness of SRS and point counts for estimating species abundance, richness, and composition of riparian breeding birds in California by comparing data collected simultaneously using both methods. We used the temporal‐removal method to estimate individual bird detection probabilities and species abundances using the program MARK. Akaike's Information Criterion provided strong evidence that detection probabilities differed between the two survey methods and among the 10 most common species. The probability of detecting birds was higher when listening to SRS recordings in the laboratory than during the field survey. Additionally, SRS data demonstrated a better fit to the temporal‐removal model assumptions and yielded more reliable estimates of detection probability and abundance than point‐count data. Our results demonstrate how the perceptual constraints of observers can affect temporal detection patterns during point counts and thus influence abundance estimates derived from time‐of‐detection approaches. We used a closed‐population capture–recapture approach to calculate jackknife estimates of species richness and average species detection probabilities for SRS and point counts using the program CAPTURE. SRS and point counts had similar species richness and detection probabilities. However, the methods differed in the composition of species detected based on Jaccard's similarity index. Most individuals (83%) detected during point counts vocalized at least once during the survey period and were available for detection using a purely acoustic technique, such as SRS. SRS provides an effective method for surveying bird communities, particularly when most species are detected by sound. SRS can eliminate or minimize observer biases, produce permanent records of surveys, and resolve problems associated with the limited availability of expert field observers.     

Double-Observer Line Transect Methods: Levels of Independence

Summary .  Double-observer line transect methods are becoming increasingly widespread, especially for the estimation of marine mammal abundance from aerial and shipboard surveys when detection of animals on the line is uncertain. The resulting data supplement conventional distance sampling data with two-sample mark–recapture data. Like conventional mark–recapture data, these have inherent problems for estimating abundance in the presence of heterogeneity. Unlike conventional mark–recapture methods, line transect methods use knowledge of the distribution of a covariate, which affects detection probability (namely, distance from the transect line) in inference. This knowledge can be used to diagnose unmodeled heterogeneity in the mark–recapture component of the data. By modeling the covariance in detection probabilities with distance, we show how the estimation problem can be formulated in terms of different levels of independence. At one extreme, full independence is assumed, as in the Petersen estimator (which does not use distance data); at the other extreme, independence only occurs in the limit as detection probability tends to one. Between the two extremes, there is a range of models, including those currently in common use, which have intermediate levels of independence. We show how this framework can be used to provide more reliable analysis of double-observer line transect data. We test the methods by simulation, and by analysis of a dataset for which true abundance is known. We illustrate the approach through analysis of minke whale sightings data from the North Sea and adjacent waters.     

Known Knowns,Known Unknowns,and Unknown Unknowns: Coverage in MS Experiments

A mathematical model from ecology, namely, the capture–recapture model with a closed population and time‐varying and heterogeneous individual probabilities of capture, is implemented to model the number of protein identifications across the various cycles of a mass spectroscopy experiment. Rcapture, a package available in the R computing environment, can easily provide estimates of the cardinality of the proteome from such experiments. Alternatively, model fitting can be undertaken in other software platforms, such as Matlab, that can accommodate general linear models. It has not escaped our notice that capture–recapture models can be more broadly applied to other settings, so as to estimate the number of missing observations in an experiment.     

Hidden population size estimation and diagnostics using two respondent-driven samples with applications in Armenia

Estimating the size of hidden populations is essential to understand the magnitude of social and healthcare needs, risk behaviors, and disease burden. However, due to the hidden nature of these populations, they are difficult to survey, and there are no gold standard size estimation methods. Many different methods and variations exist, and diagnostic tools are needed to help researchers assess method-specific assumptions as well as compare between methods. Further, because many necessary mathematical assumptions are unrealistic for real survey implementation, assessment of how robust methods are to deviations from the stated assumptions is essential. We describe diagnostics and assess the performance of a new population size estimation method, capture–recapture with successive sampling population size estimation (CR-SS-PSE), which we apply to data from 3 years of studies from three cities and three hidden populations in Armenia. CR-SS-PSE relies on data from two sequential respondent-driven sampling surveys and extends the successive sampling population size estimation (SS-PSE) framework by using the number of individuals in the overlap between the two surveys and a model for the successive sampling process to estimate population size. We demonstrate that CR-SS-PSE is more robust to violations of successive sampling assumptions than SS-PSE. Further, we compare the CR-SS-PSE estimates to population size estimations using other common methods, including unique object and service multipliers, wisdom of the crowd, and two-source capture–recapture to illustrate volatility across estimation methods.     

Combining capture–recapture data and pedigree information to assess heritability of demographic parameters in the wild

Quantitative genetic analyses have been increasingly used to estimate the genetic basis of life‐history traits in natural populations. Imperfect detection of individuals is inherent to studies that monitor populations in the wild, yet it is seldom accounted for by quantitative genetic studies, perhaps leading to flawed inference. To facilitate the inclusion of imperfect detection of individuals in such studies, we develop a method to estimate additive genetic variance and assess heritability for binary traits such as survival, using capture–recapture (CR) data. Our approach combines mixed‐effects CR models with a threshold model to incorporate discrete data in a standard ‘animal model’ approach. We employ Markov chain Monte Carlo sampling in a Bayesian framework to estimate model parameters. We illustrate our approach using data from a wild population of blue tits (Cyanistes caeruleus) and present the first estimate of heritability of adult survival in the wild. In agreement with the prediction that selection should deplete additive genetic variance in fitness, we found that survival had low heritability. Because the detection process is incorporated, capture–recapture animal models (CRAM) provide unbiased quantitative genetics analyses of longitudinal data collected in the wild.