Hierarchic Modeling of Salmon Harvest and Migration

Using fishery recoveries from a tagged cohort of coho salmon, the ocean spatial-temporal abundance of the cohort is predicted using a state-space model. The model parameters, which reflect spatial distribution, mortality, and movement, vary considerably between different cohorts. To evaluate the effect of proposed management plans on a future cohort, uncertainty in the cohort-specific parameters is accounted for by a hierarchic model. As an application, release-recovery and fishing effort data from several cohorts of a hatchery-reared coho salmon stock originating from Washington state are used to calculate maximum likelihood estimates of the hyperparameters. Markov chain Monte Carlo is used to approximate the likelihood for the hyperparameters. The Markov chain simulates the sampling distribution of the state-space model parameters conditional on the data and the estimated hyperparameters and provides empirical Bayes estimates as a by-product. Given the estimated hyperparameters and the hierarchic model, fishery managers can simulate the variation in cohort-specific parameters and variation in the migration and harvest processes to more realistically describe uncertainty in the results of any proposed management plan.