Simulation-based inference for close-kin mark-recapture: implications for small populations and nonrandom mating

Close-kin mark-recapture (CKMR) uses data on the frequency of kin pair relationships (e.g. parent-offspring, half siblings) in genetic samples from animal populations to estimate parameters such as abundance and adult survival probability. To date, most applications of CKMR have relied on a pseudo-likelihood approximation where pairwise comparisons of relatedness are assumed to be independent. This approximation works well when abundance is high and the sampled fraction of the population is low (as with many marine fisheries), but resultant estimators have inflated nominal confidence interval coverage when applied to small populations. Small populations and nonrandom mating structures also lead to problems with using second-order kin for estimation because one cannot typically differentiate half-siblings from other kin pair types like aunt-niece. In this paper, I assess the utility of approximate Bayesian computation (ABC) as a way of relaxing the pseudo-likelihood independence assumption. Under this approach, one only needs the ability to simulate population and sampling dynamics and to summarize resulting statistics in an informative way (e.g., number of kin pairs of different types). After exploring bias and interval coverage in several simulation studies, I illustrate these procedures on CKMR data from a Canadian caribou population. I show that ABC substantially improves interval coverage, and allows inference for difficult biologies where it would be difficult to calculate the analytical probabilities necessary for a binomial pseudo-likelihood. Simulation-based approaches to inference have great potential for expanding the application of CKMR to small populations and for breeding dynamics that are difficult to model.