Setting biological reference points for Atlantic salmon stocks: transfer of information from data-rich to sparse-data situations by Bayesian hierarchical modelling

We present an application of Bayesian hierarchical modelling of stockerecruitment (SR) relationships aiming at estimating Biological Reference Points (BRP) for European Atlantic salmon (Salmo salar) stocks. The structure of the hierarchical SR model developed distinguishes two nested levels of randomness, within-river and between rivers. It is an extension of the classical Ricker model, where the parameters of the Ricker function are assumed to be different between rivers, but drawn from a common probability distribution conditionally on two covariates: river size and latitude. The output of ultimate interest is the posterior predictive distribution of the SR parameters and their associated BRP for a new river with no SR data. The flexible framework of the Bayesian hierarchical SR analysis is a step towards making the most comprehensive use of detailed stock monitoring programs for improving management advice. Posterior predictive inferences may be imprecise due to the relative paucity of information introduced in the analysis compared to the variability of the stochastic process modeled. Even in such cases, direct extrapolation of results from local data-rich stocks should be dismissed as it can lead to a major underestimation of our uncertainty about management parameters in sparse-data situations. The aggregation of several stocks under a regional complex improves the precision of the posterior predictive inferences. When several stocks are managed jointly, even imprecise knowledge about each component of the aggregate can be valuable. The introduction of covariates to explain between stock variations provides a significant gain in the precision of the posterior predictive inferences. Because we must be able to measure the covariates for all the stocks of interest, i.e. mostly sparse-data cases, the number of covariates which can be used in practice is limited. The definition of the assemblage of stocks which we model as exchangeable units, conditionally on the covariates, remains the most influential choice to be made when attempting to transfer information from data-rich to sparse-data situations.