Comparisons of meta-analytic methods for deriving a probability distribution for the steepness of the stock–recruitment relationship

Abstract

The steepness parameter of the stock–recruitment relationship (the proportion of unfished recruitment when spawning biomass is reduced to 20% of its unfished level) is a key parameter in stock assessment models, and hence in the provision of scientific management advice for many fisheries. Prior probability distributions for steepness have been used when conducting assessments of US west coast groundfish in the absence of data to estimate steepness reliably. These priors have been developed by applying meta-analytic methods to the results from stock assessments, but the performances of these methods have not been evaluated. Three potential methods for applying meta-analysis to construct steepness priors are available: non-linear mixed models, Bayesian hierarchical methods, and a novel method which approximates marginal likelihoods using likelihood profiles. These methods are evaluated using simulation. The profile method is found to perform best. Estimates of the parameters which define the steepness prior are uncertain owing primarily to uncertainty associated with the results of the stock assessments which provide the input for the meta-analysis methods, and because of the small number of stocks available for inclusion in the meta-analysis.