Bayesian nonparametric analysis of stock–recruitment relationships

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Abstract
The relationship between current abundance and future recruitment to the stock is fundamental to managing fish populations. However, many different recruitment models are plausible and the data are 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 use it to estimate several fishery reference points. We applied this method to artificial data sets generated from a variety of parametric models and compare the results with the fit of Ricker and Beverton–Holt models. We found that the Bayesian nonparametric method fit the data nearly as well 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 (Ophiodon elongatus) 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.

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