Population size estimates based on the frequency of genetically assigned parent–offspring pairs within a subsample

Estimating population density as precise as possible is a key premise for managing wild animal species. This can be a challenging task if the species in question is elusive or, due to high quantities, hard to count. We present a new, mathematically derived estimator for population size, where the estimation is based solely on the frequency of genetically assigned parent–offspring pairs within a subsample of an ungulate population. By use of molecular markers like microsatellites, the number of these parent–offspring pairs can be determined. The study's aim was to clarify whether a classical capture–mark–recapture (CMR) method can be adapted or extended by this genetic element to a genetic‐based capture–mark–recapture (g‐CMR). We numerically validate the presented estimator (and corresponding variance estimates) and provide the R‐code for the computation of estimates of population size including confidence intervals. The presented method provides a new framework to precisely estimate population size based on the genetic analysis of a one‐time subsample. This is especially of value where traditional CMR methods or other DNA‐based (fecal or hair) capture–recapture methods fail or are too difficult to apply. The DNA source used is basically irrelevant, but in the present case the sampling of an annual hunting bag is to serve as data basis. In addition to the high quality of muscle tissue samples, hunting bags provide additional and essential information for wildlife management practices, such as age, weight, or sex. In cases where a g‐CMR method is ecologically and hunting‐wise appropriate, it enables a wide applicability, also through its species‐independent use.     

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.     

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.     

Estimating abundance and population trends when detection is low and highly variable: A comparison of three methods for the Hermann's tortoise

Assessing population trends is a basic prerequisite to carrying out adequate conservation strategies. Selecting an appropriate method to monitor animal populations can be challenging, particularly for low-detection species such as reptiles. This study compares 3 detection-corrected abundance methods (capture–recapture, distance sampling, and N-mixture) used to assess population size of the threatened Hermann's tortoise. We used a single dataset of 432 adult tortoise observations collected at 118 sampling sites in the Plaine des Maures, southeastern France. We also used a dataset of 520 tortoise observations based on radiotelemetry data collected from 10 adult females to estimate and model the availability (g0) needed for distance sampling. We evaluated bias for N-mixture and capture–recapture, by using simulations based on different values of detection probabilities. Finally, we conducted a power analysis to estimate the ability of the 3 methods to detect changes in Hermann's tortoise abundances. The abundance estimations we obtained using distance sampling and N-mixture models were respectively 1.75 and 2.19 times less than those obtained using the capture–recapture method. Our results indicated that g0 was influenced by temperature variations and can differ for the same temperature on different days. Simulations showed that the N-mixture models provide unstable estimations for species with detection probabilities <0.5, whereas capture–recapture estimations were unbiased. Power analysis showed that none of the 3 methods were precise enough to detect slow population changes. We recommend that great care should be taken when implementing monitoring designs for species with large variation in activity rates and low detection probabilities. Although N-mixture models are easy to implement, we would not recommend using them in situations where the detection probability is very low at the risk of providing biased estimates. Among the 3 methods allowing estimation of tortoise abundances, capture–recapture should be preferred to assess population trends. © 2013 The Wildlife Society.     

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)     

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.     

Mark—Recapture Accurately Estimates Census for Tuatara,a Burrowing Reptile

Abstract: Estimates of population size are necessary for effective management of threatened and endangered species, but accurate estimation is often difficult when species are cryptic. We evaluated effectiveness of mark–recapture techniques using the Lincoln–Peterson estimator for predicting true census size of a population of tuatara (Sphenodon punctatus), a burrowing reptile that is a conservation priority in New Zealand. We found that Lincoln–Peterson estimates (NŇ = 85) were accurate for predicting the census size (N = 87) after only a 3-day mark–recapture survey. We recommend this method as a cost-effective way to accurately estimate population size for isolated, inaccessible tuatara populations, because it requires limited personnel, expertise, and time, and has low environmental impact on fragile sites.     

Estimating repertoire size in a songbird: a comparison of three techniques

Many animals produce multiple types of breeding vocalizations that, together, constitute a vocal repertoire. In some species, the size of an individual’s repertoire is important because it correlates with brain size, territory size or social behaviour. Quantifying repertoire size is challenging because the long recordings needed to sample a repertoire comprehensively are difficult to obtain and analyse. The most basic quantification technique is simple enumeration, where one counts unique vocalization types until no new types are detected. Alternative techniques estimate repertoire size from subsamples, but these techniques are useful only if they are accurate. Using 12 years of acoustic data from a population of rufous-and-white wrens in Costa Rica, we used simple enumeration to measure the repertoire size for 40 males. We then compared these to the estimates generated by three estimation techniques: curve fitting, capture–recapture and a new technique based on the coupon collector’s problem. To understand how sampling effort affects the accuracy and precision of estimates, we applied each technique to six different-sized subsets of data per male. When averaged across subset sizes, the capture–recapture and coupon collector techniques showed the highest accuracy, whereas the curve fitting technique underestimated repertoire size. Precision (the average absolute difference between the estimated and true repertoire size) was significantly better for the capture–recapture technique than the coupon collector and curve fitting techniques. Both accuracy and precision improved as subset size increased. We conclude that capture–recapture is the best technique for estimating the sizes of small repertoires.     

One‐inflation and unobserved heterogeneity in population size estimation

We present the one‐inflated zero‐truncated negative binomial (OIZTNB) model, and propose its use as the truncated count distribution in Horvitz–Thompson estimation of an unknown population size. In the presence of unobserved heterogeneity, the zero‐truncated negative binomial (ZTNB) model is a natural choice over the positive Poisson (PP) model; however, when one‐inflation is present the ZTNB model either suffers from a boundary problem, or provides extremely biased population size estimates. Monte Carlo evidence suggests that in the presence of one‐inflation, the Horvitz–Thompson estimator under the ZTNB model can converge in probability to infinity. The OIZTNB model gives markedly different population size estimates compared to some existing truncated count distributions, when applied to several capture–recapture data that exhibit both one‐inflation and unobserved heterogeneity.     

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

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

Demographic consequences of changing body size in a terrestrial salamander

Changes in climate can alter individual body size, and the resulting shifts in reproduction and survival are expected to impact population dynamics and viability. However, appropriate methods to account for size‐dependent demographic changes are needed, especially in understudied yet threatened groups such as amphibians. We investigated individual‐ and population‐level demographic effects of changes in body size for a terrestrial salamander using capture–mark–recapture data. For our analysis, we implemented an integral projection model parameterized with capture–recapture likelihood estimates from a Bayesian framework. Our study combines survival and growth data from a single dataset to quantify the influence of size on survival while including different sources of uncertainty around these parameters, demonstrating how selective forces can be studied in populations with limited data and incomplete recaptures. We found a strong dependency of the population growth rate on changes in individual size, mediated by potential changes in selection on mean body size and on maximum body size. Our approach of simultaneous parameter estimation can be extended across taxa to identify eco‐evolutionary mechanisms acting on size‐specific vital rates, and thus shaping population dynamics and viability.     

A new method for estimating the size of small populations from genetic mark-recapture data

The use of non-invasive genetic sampling to estimate population size in elusive or rare species is increasing. The data generated from this sampling differ from traditional mark-recapture data in that individuals may be captured multiple times within a session or there may only be a single sampling event. To accommodate this type of data, we develop a method, named capwire, based on a simple urn model containing individuals of two capture probabilities. The method is evaluated using simulations of an urn and of a more biologically realistic system where individuals occupy space, and display heterogeneous movement and DNA deposition patterns. We also analyse a small number of real data sets. The results indicate that when the data contain capture heterogeneity the method provides estimates with small bias and good coverage, along with high accuracy and precision. Performance is not as consistent when capture rates are homogeneous and when dealing with populations substantially larger than 100. For the few real data sets where N is approximately known, capwire's estimates are very good. We compare capwire's performance to commonly used rarefaction methods and to two heterogeneity estimators in program capture: Mh-Chao and Mh-jackknife. No method works best in all situations. While less precise, the Chao estimator is very robust. We also examine how large samples should be to achieve a given level of accuracy using capwire. We conclude that capwire provides an improved way to estimate N for some DNA-based data sets.     

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.     

Estimating the abundance of rare and elusive carnivores from photographic-sampling data when the population size is very small

Conservation and management agencies require accurate and precise estimates of abundance when considering the status of a species and the need for directed actions. Due to the proliferation of remote sampling cameras, there has been an increase in capture–recapture studies that estimate the abundance of rare and/or elusive species using closed capture–recapture estimators (C–R). However, data from these studies often do not meet necessary statistical assumptions. Common attributes of these data are (1) infrequent detections, (2) a small number of individuals detected, (3) long survey durations, and (4) variability in detection among individuals. We believe there is a need for guidance when analyzing this type of sparse data. We highlight statistical limitations of closed C–R estimators when data are sparse and suggest an alternative approach over the conventional use of the Jackknife estimator. Our approach aims to maximize the probability individuals are detected at least once over the entire sampling period, thus making the modeling of variability in the detection process irrelevant, estimating abundance accurately and precisely. We use simulations to demonstrate when using the unconditional-likelihood M ₀ (constant detection probability) closed C–R estimator with profile-likelihood confidence intervals provides reliable results even when detection varies by individual. If each individual in the population is detected on average of at least 2.5 times, abundance estimates are accurate and precise. When studies sample the same species at multiple areas or at the same area over time, we suggest sharing detection information across datasets to increase precision when estimating abundance. The approach suggested here should be useful for monitoring small populations of species that are difficult to detect.     

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.     

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.     

Validation of mark‐recapture population estimates for invasive common carp,Cyprinus carpio,in Lake Crescent,Tasmania

A mark‐recapture study based on the Petersen method was implemented in 1998 to estimate the abundance of the invasive common carp, Cyprinus carpio L., in Lake Crescent, Tasmania. Multiple gear types were employed to minimise capture bias, with multiple capture and recapture events providing an opportunity to compute and compare Petersen and Schnabel estimates. A single Petersen estimate on recapture data and two Schnabel estimates – one each on mark (forward‐Schnabel estimate) and recapture (reverse‐Schnabel estimate) data – were conducted. An independent long‐term double tag study facilitated estimation of the annual natural mortality. Subsequent fish‐down of the population suggests that, in all likelihood, the carp have been eradicated from the lake, providing an unprecedented opportunity to verify the forward population estimates carried out in 1998. Results suggest that all three estimates were close to the true population size, with the reverse‐Schnabel estimate being the most accurate and within 1% of the true population in this relatively large lake (～2365 ha). Greater accuracy of the reverse‐Schnabel approach can be attributed to either minimised fish behavioural (i.e. gear susceptibility or avoidance) or computational bias associated with the forward‐Schnabel and Petersen approaches, respectively. While the original estimates served as a guide in eradication of carp from the lake, the ultimate validation provides a reliable framework for abundance estimation of this invasive fish in relatively large water bodies elsewhere.     

Assessing the abundance of Bristol Bay belugas with genetic mark‐recapture methods

The Bristol Bay stock of beluga whales (Delphinapterus leucas) is genetically distinct and resides in Bristol Bay year‐round. We estimated the abundance of this population using genetic mark‐recapture, whereby genetic markers from skin biopsies, collected between 2002 and 2011, were used to identify individuals. We identified 516 individual belugas in two inner bays, 468 from Kvichak Bay and 48 from Nushagak Bay, and recaptured 75 belugas in separate years. Using a POPAN Jolly‐Seber model, abundance was estimated at 1,928 belugas (95% CI = 1,611–2,337), not including calves, which were not sampled. Most belugas were sampled in Kvichak Bay at a time when belugas are also known to occur in Nushagak Bay. The pattern of genetic recaptures and data from belugas with satellite transmitters suggested that belugas in the two bays regularly mix. Hence, the estimate of abundance likely applies to all belugas within Bristol Bay. Simulations suggested that POPAN estimates of abundance are robust to most forms of emigration, but that emigration causes negative bias in both capture and survival probabilities. Because it is likely that some belugas do not enter the sampling area during sampling, our estimate of abundance is best considered a minimum 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.