Hierarchical Bayesian analysis of capture–mark–recapture data

Abstract

We present a hierarchical Bayesian model (HBM) for capture–mark–recapture (CMR) data analysis. It aims at estimating the probability of capture (θi) and the total population size (Ni) in a series of I years i = 1,...,I. The HBM assumes that the θis and Nis are sampled from a common probability distribution with unknown parameters. It is compared with the model assuming independence between years in the θis and Nis (ABM). We show how a transfer of information between years is organized by the HBM. We compare the merits of HBM vs. ABM to estimate the spawning run and smolt run of an Atlantic salmon (Salmo salar) population of the River Oir (France) over a period of 17 years. In the spawners case, yearly data are poorly informative. Consequently, the HBM greatly improves posterior inferences compared with the ABM in terms of dispersion and robustness to the choice of prior. In the smolts case, the HBM does not significantly improve inferences compared with the ABM because data are more informative. We discuss why hierarchical modeling should be recommended in any ecological study where the data are collected on several sampling units that share some common features.