Hierarchical Bayesian modelling with habitat and time covariates for estimating riverine fish population size by successive removal method

We present a hierarchical Bayesian modelling (HBM) framework for estimating riverine fish population size from successive removal data via electrofishing. It is applied to the estimation of the population of Atlantic salmon (Salmo salar) juveniles in the Oir River (France). The data set consists of 10 sampling sites sampled by one or two removals over a period of 20 years (1986-2005). We develop and contrast four models to assess the effect of temporal variations and habitat type on the density of fish and the probability of capture. The Bayes factor and the deviance information criterion are used to com- pare these models. The most credible and parsimonious model is the one that accounts for the effects of the years and the habitat type on the density of fish. It is used to extrapolate the population size in the entire river reach. This paper illustrates that HBM successfully accommodates large but sparse data sets containing poorly informative data for some units. Its condi- tional structure enables it to borrow strength from data-rich to data-poor units, thus improving the estimations. Predictions of the population size of the entire river reach can be derived, while accounting for all sources of uncertainty. Resume : Nous proposons un cadre de modelisation bayesien hierarchique (HBM) pour estimer l'abondance d'une population de juveniles de saumon atlantique (Salmo salar) dans la riviere Oir (France) par la methode des retraits successifs par peche electrique. Le jeu de donnees est compose de 10 sites d'echantillonnage, chacun ayant ete echantillonne par un ou deux passages sur une periode de 20 ans (1986-2005). Quatre modeles sont developpes pour introduire les variations inter- annuelles et les effets du type d'habitat sur la densite et sur la probabilite de capture. Ces modeles sont compares a l'aide du facteur de Bayes et d'un critere d'information base sur la deviance. Le modele retenu est celui qui prend en compte l'effet de l'annee et du type d'habitat sur la densite de juveniles de saumons. Il est utilise pour extrapoler la population de saumon a l'ensemble du cours d'eau. Cet article illustre que les HBM permettent de traiter des jeux de donnees de grande taille dont l'information portee par chaque unite echantillonnee est heterogene. La structure conditionnelle permet d'ameliorer les esti- mations car elle organise un transfert d'information entre les unites. Le modele permet d'obtenir des predictions de l'abondance sur l'ensemble du cours d'eau, tout en prenant en compte les differentes sources d'incertitude.

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