A semiparametric Bayesian approach to estimating maximum reproductive rates at low population sizes

The maximum annual reproductive rate (i.e., the slope at the origin in a stock-recruitment relationship) is one of the most important biological reference points in fisheries; it sets the upper limit to sustainable fishing mortality. Estimating the maximum reproductive rate by fitting parametric models to stock-recruitment data may not be a robust approach because two statistically indistinguishable models can generate radically different estimates. To mitigate this issue, we developed a flexible, semiparametric Bayesian approach based on a conditional Gaussian process prior specifically designed to estimate the maximum annual reproductive rate, and applied it to analyze simulated stock-recruitment data sets. Compared with results based on other Gaussian process priors, we found that the conditional Gaussian process prior provided superior results: the accuracy and precision of estimates were enhanced without increasing model complexity. Moreover, compared with parametric alternatives, performance of the conditional Gaussian process prior was comparable to that of the data-generating model and always better than the wrong model.