© 2003 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
Setting biological reference points for Atlantic salmon stocks: transfer of information from data-rich to sparse-data situations by Bayesian hierarchical modelling
a INRA, UMR EQHC 65 rue de St Brieuc, 35042 Rennes cedex, France
b GRESE laboratory ENGREF, 19 avenue du Maine, 75732 Paris cedex 15, France
c Agricultural and Environmental Sciences Division DARDNI, Newforge Lane, Belfast BT9 5PX, Northern Ireland, UK
d Environment Agency, National Salmon and Trout Fisheries Centre Rivers House, St Mellons Business Park, Cardiff CF3 OLT, Wales, UK
e INRA, UMR ECOBIOP BP 3, 64310 St Pée s/Nivelle, France
f Institute of Freshwater Fisheries, Vagnhöfda Reykjavik 112, Iceland
g Norwegian Institute for Nature Research Tungasletta 2, 7485 Trondheim, Norway
h Salmon Research Agency of Ireland Furnace, Newport, Co. Mayo, Ireland
i Freshwater Fisheries Laboratory, Field Station 16 River Street, Montrose, Angus DD10 8DL, Scotland, UK
j Department of Environment, County Governor of Møre and Romsdal 6404 Molde, Norway
*Correspondence to E. Prévost; tel: +33 2 23 48 52 48; fax: +33 2 23 48 54 40. e-mail: prevost{at}roazhon.inra.fr.
We present an application of Bayesian hierarchical modelling of stock–recruitment (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.
Keywords: Atlantic salmon, Bayesian, biological reference points, hierarchical model, stock and recruitment
Received 24 March 2003; accepted 27 August 2003.
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