A regional meta-model for stock-recruitment analysis using an empirical Bayesian approach

A regional stock-recruitment meta-model is developed using a hierarchical Bayesian framework to combine information from multiple fish populations. The use of the meta-model is illustrated through analysis of the regional stock-recruitment parameters of the coho salmon (Oncorhynchus kisutch) within two large fisheries management units in southern and northern British Columbia. We construct our regional prior distribution from an analysis of all stock-recruitment data rather than by the more usual approach of assuming a prior distribution. That preliminary analysis indicated that the regional prior distribution for the two parameters of the Ricker model was bivariate normal-lognormal (NLN) with a high degree of correlation between the two Ricker parameters. Because this distribution had not been fully developed, we formulated the density function for the NLN distribution and proved some of its important properties. An empirical Bayesian approach was then used to estimate the regional distributions of the Ricker parameters and derived management parameters. Characterization of the distributional properties of productivity within management regions is a necessary step for resource managers seeking to prosecute mixed-stock fisheries while conserving population diversity.