Closed-population capture-recapture modeling of samples drawn one at a time

On continuous-time capture-recapture in closed populations

Schofield et al. (2018, Biometrics 74, 626-635) presented simple and efficient algorithms for fitting continuous-time capture-recapture models based on Poisson processes. They also demonstrated by real examples that the standard method of discretizing continuous-time capture-recapture data and then fitting traditional discrete-time models may lead to information loss in population size estimation. In this article, we aim to clarify that key to the approach of Schofield et al. (2018) is the Poisson model assumed for the number of captures of each individual throughout the study, rather than the fact of data being collected in continuous time. We further show that the method of data discretization works equally well as the method of Schofield et al. (2018), provided that a Poisson model is applied instead of the traditional Bernoulli model to the number of captures for each individual on each sampling occasion.

Continuous-time capture-recapture in closed populations

The standard approach to fitting capture-recapture data collected in continuous time involves arbitrarily forcing the data into a series of distinct discrete capture sessions. We show how continuous-time models can be fitted as easily as discrete-time alternatives. The likelihood is factored so that efficient Markov chain Monte Carlo algorithms can be implemented for Bayesian estimation, available online in the R package ctime. We consider goodness-of-fit tests for behavior and heterogeneity effects as well as implementing models that allow for such effects.

A spatially explicit capture-recapture estimator for single-catch traps

Single‐catch traps are frequently used in live‐trapping studies of small mammals. Thus far, a likelihood for single‐catch traps has proven elusive and usually the likelihood for multicatch traps is used for spatially explicit capture–recapture (SECR) analyses of such data. Previous work found the multicatch likelihood to provide a robust estimator of average density. We build on a recently developed continuous‐time model for SECR to derive a likelihood for single‐catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multicatch estimator for various scenarios with nonconstant density surfaces. While the multicatch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height of the detection function. By contrast, the single‐catch estimators of density, distribution, and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constant over the survey region, then the multicatch estimator performs well with single‐catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single‐catch estimator when trap saturation is above about 60%. The estimator's performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single‐catch likelihood with unknown capture times remains intractable for now, researchers using single‐catch traps should aim to incorporate timing devices with their traps.