AMS2004-1: Bayesian Non-parametric Analysis of Stock-Recruitment Relationships

Stephan B. Munch, Athanasios Kottas and Marc Mangel
12/31/2004 09:00 AM
Applied Mathematics & Statistics
The relationship between current abundance and future recruitment to the stock is fundamental to managing fish populations. There is general agreement about the basic attributes such a relationship should possess. However, many different models may be derived from these attributes and the data are often insufficient to distinguish among them. Although nonparametric methods may be used to circumvent this problem, these are devoid of biological underpinnings. Here we present a Bayesian nonparametric approach that allows straightforward incorporation of prior biological information and show how it may be used to estimate several fishery reference points. We applied this method to several artificial data sets generated from a variety of parametric models and compare the results to the fit of Ricker and Beverton-Holt models. We found that the Bayesian nonparametric method fit the data nearly as good as the true parametric model and always performed better than incorrect parametric alternatives. The estimated reference points agree closely with true values calculated for the underlying parametric model. Finally, we apply the method to empirical data for lingcod and several salmonids. Since this method is capable of reproducing the behavior of any of the parametric models and provides flexible, data-driven estimates of stock-recruitment relationships, it should be of great value in fisheries applications where the true functional relationship is always unknown.