Estimation of the size of an open population using local estimating equations II: a partially parametric approach

Kernel smoothing methods are applied to extend a modification of the closed population approach of Lloyd and Yip (1991, in Estimating Equations, 65-88) to open populations with frequent capture occasions. The method complements previous nonparametric methods and, when the parametric assumptions are met, simulations show the new method has a smaller integrated mean squared error than the previous fully nonparametric method. The method is applied to capture-recapture data on short-tailed shearwaters collected annually for 48 years.     

Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities

Heterogeneity in detection probabilities has long been recognized as problematic in mark-recapture studies, and numerous models developed to accommodate its effects. Individual heterogeneity is especially problematic, in that reasonable alternative models may predict essentially identical observations from populations of substantially different sizes. Thus even with very large samples, the analyst will not be able to distinguish among reasonable models of heterogeneity, even though these yield quite distinct inferences about population size. The problem is illustrated with models for closed and open populations.     

Semiparametric estimation of animal abundance using capture-recapture data from open populations

A semiparametric partially linear model for the size of an open population is proposed and inference is conducted using weighted martingale estimating equations. This extends a previous nonparametric approach to modeling capture-recapture data for open populations with frequent capture occasions. Analytic expressions for the large sample variances are derived and these are confirmed in a simulation study. The method is illustrated on monthly penguin banding data collected over 6 years.     

Estimation of age-specific breeding probabilities from capture-recapture data

We provide a new method for estimating the age-specific breeding probabilities from recaptures or resightings of animals marked as young. Our method is more direct than previous methods and allows the modeler to fit and compare models where the age-specific breeding proportions are equal over different cohorts or are a function of external covariates.     

Modeling association among demographic parameters in analysis of open population capture-recapture data

We present a hierarchical extension of the Cormack-Jolly-Seber (CJS) model for open population capture-recapture data. In addition to recaptures of marked animals, we model first captures of animals and losses on capture. The parameter set includes capture probabilities, survival rates, and birth rates. The survival rates and birth rates are treated as a random sample from a bivariate distribution, thus the model explicitly incorporates correlation in these demographic rates. A key feature of the model is that the likelihood function, which includes a CJS model factor, is expressed entirely in terms of identifiable parameters; losses on capture can be factored out of the model. Since the computational complexity of classical likelihood methods is prohibitive, we use Markov chain Monte Carlo in a Bayesian analysis. We describe an efficient candidate-generation scheme for Metropolis-Hastings sampling of CJS models and extensions. The procedure is illustrated using mark-recapture data for the moth Gonodontis bidentata.     

Robust design and the use of auxiliary variables in estimating population size for an open population

We consider the problem of estimating the population size for an open population where the data are collected over secondary periods within primary periods according to a robust design suggested by Pollock (1982, Journal of Wildlife Management 46, 757-760). A conditional likelihood is used to estimate the parameters associated with a generalized linear model in which the capture probability is assumed to have a logistic form depending on individual covariates. A Horvitz-Thompson-type estimator is used to estimate the population size for each primary period and the survival probabilities between primary periods. The asymptotic properties of the proposed estimators are investigated through simulation and are found to perform well. A data set for such a robust design of a small-mammal capture-recapture study conducted at Dummy Bottom within Browns Park National Wildlife Refuge is analyzed.     

Petersen and removal population size estimates: combining methods to adjust and interpret results when assumptions are violated

Synopsis We present ways to test the assumptions of the Petersen and removal methods of population size estimation and ways to adjust the estimates if violations of the assumptions are found. We were motivated by the facts that (1) results of using both methods are commonly reported without any reference to the testing of assumptions, (2) violations of the assumptions are more likely to occur than not to occur in natural populations, and (3) the estimates can be grossly in error if assumptions are violated. We recognize that in many cases two days in the field is the most time fish biologists can spend in obtaining a population estimate, so the use of alternative models of population estimation that require fewer assumptions is precluded. Hence, for biologists operating with these constraints and only these biologists, we describe and recommend a two-day technique that combines aspects of both capture-recapture and removal methods. We indicate how to test: most of the assumptions of both methods and how to adjust the population estimates obtained if violations of the assumptions occur. We also illustrate the use of this combined method with data from a field study. The results of this application further emphasize the importance of testing the assumptions of whatever method is used and making appropriate adjustments to the population size estimates for any violations identified.     

Detection of reduction in population size using data from microsatellite loci

We demonstrate that the mean ratio of the number of alleles to the range in allele size, which we term M, calculated from a population sample of microsatellite loci, can be used to detect reductions in population size. Using simulations, we show that, for a general class of mutation models, the value of M decreases when a population is reduced in size. The magnitude of the decrease is positively correlated with the severity and duration of the reduction in size. We also find that the rate of recovery of M following a reduction in size is positively correlated with post-reduction population size, but that recovery occurs in both small and large populations. This indicates that M can distinguish between populations that have been recently reduced in size and those which have been small for a long time. We employ M to develop a statistical test for recent reductions in population size that can detect such changes for more than 100 generations with the post-reduction demographic scenarios we examine. We also compute M for a variety of populations and species using microsatellite data collected from the literature. We find that the value of M consistently predicts the reported demographic history for these populations. This method, and others like it, promises to be an important tool for the conservation and management of populations that are in need of intervention or recovery.     

Bayesian estimation of movement and survival probabilities from capture-recapture data

The Arnason–Schwarz model is usually used for estimatingsurvival and movement probabilities of animal populations fromcapture-recapture data. The missing data structure of this capture-recapturemodel is exhibited and summarised via a directed graph representation.Taking advantage of this structure we implement a Gibbs samplingalgorithm from which Bayesian estimates and credible intervalsfor survival and movement probabilities are derived. Convergenceof the algorithm is proved using a duality principle. We illustrateour approach through a real example.     

Estimation of breeding population size using DNA‐based pedigree reconstruction in brown bears

Robust estimates of demographic parameters are critical for effective wildlife conservation and management but are difficult to obtain for elusive species. We estimated the breeding and adult population sizes, as well as the minimum population size, in a high‐density brown bear population on the Shiretoko Peninsula, in Hokkaido, Japan, using DNA‐based pedigree reconstruction. A total of 1288 individuals, collected in and around the Shiretoko Peninsula between 1998 and 2020, were genotyped at 21 microsatellite loci. Among them, 499 individuals were identified by intensive genetic sampling conducted in two consecutive years (2019 and 2020) mainly by noninvasive methods (e.g., hair and fecal DNA). Among them, both parents were assigned for 330 bears, and either maternity or paternity was assigned to 47 and 76 individuals, respectively. The subsequent pedigree reconstruction indicated a range of breeding and adult (≥4 years old) population sizes: 128–173 for female breeders and 66–91 male breeders, and 155–200 for female adults and 84–109 male adults. The minimum population size was estimated to be 449 (252 females and 197 males) in 2019. Long‐term continuous genetic sampling prior to a short‐term intensive survey would enable parentage to be identified in a population with a high probability, thus enabling reliable estimates of breeding population size for elusive species.     

Estimating the ratio of effective to actual size of an age‐structured population from individual demographic data

The effective population size is a central concept for understanding evolutionary processes in a finite population. We employ Fisher's reproductive value to estimate the ratio of effective to actual population size for an age‐structured population with two sexes using random samples of individual vital rates. The population may be subject to environmental stochasticity affecting the vital rates. When the mean sex ratio at birth is known, improved efficiency is obtained by utilizing the records of total number of offspring rather than considering separately female and male offspring. We also show how to incorporate uncertain paternity.