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Hierarchical Bayesian analysis of capture–mark–recapture data

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We present a hierarchical Bayesian model (HBM) for capture–mark–recapture (CMR) data analysis. It aims at estimating the probability of capture (i) and the total population size (Ni) in a series of I years i = 1,...,I. The HBM assumes that the is and Nis are sampled from a common probability distribution with unknown parameters. It is compared with the model assuming independence between years in the is 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.

Nous proposons un modèle Bayesien hiérarchique (HBM) pour analyser des données de capture–marquage–recapture. Ce modèle permet d'estimer la probabilité de capture (i) et la taille de la population (Ni) pour une série de I années i = 1,...,I. Le HBM suppose que les is et les Nis sont issus a priori d'une même distribution de probabilité dont les paramètres sont inconnus. On le compare à un modèle qui suppose l'indépendance des is et des Nis a priori (ABM). Nous montrons comment le HBM organise le transfert d'information entre les années. Nous comparons les avantages respectifs du HBM et du ABM pour estimer les migrations d'adultes et de smolts de la population de Saumon atlantique (Salmo salar) de la rivière Oir (France). Dans le cas des adultes, les données annuelles sont peu informatives. Le HBM améliore les inférences par rapport au ABM, en terme de dispersion et de robustesse au choix des distributions a priori. Dans le cas des smolts, le HBM n'améliore pas significativement les inférences par rapport au ABM car les données annuelles sont plus informatives. Finalement, nous recommandons d'utiliser un modèle hiérarchique pour analyser des données en écologie dans tous les cas où les données traitées concernent des unités qui partagent une caractéristique commune.

Document Type: Research Article

Publication date: November 1, 2002

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  • Published continuously since 1901 (under various titles), this monthly journal is the primary publishing vehicle for the multidisciplinary field of aquatic sciences. It publishes perspectives (syntheses, critiques, and re-evaluations), discussions (comments and replies), articles, and rapid communications, relating to current research on cells, organisms, populations, ecosystems, or processes that affect aquatic systems. The journal seeks to amplify, modify, question, or redirect accumulated knowledge in the field of fisheries and aquatic science. Occasional supplements are dedicated to single topics or to proceedings of international symposia.
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