Semiparametric estimation of the maximum reproductive rate

The maximum reproductive rate (i.e., slope at the origin of stock recruitment relationship) is one of the most important biological reference points in fisheries; it can be interpreted as the upper limit to sustainable fishing mortality. However, estimating the maximum reproductive rate by fitting parametric models to stock recruitment data may not be robust; two statistically indistinguishable models can generate radically different results. To circumvent this problem, we developed a semiparametric Bayesian framework for estimating the maximum reproductive rate based on a conditional Gaussian process prior and applied it to simulated stock-recruitment data. Compared to previous results for Gaussian process priors, we found that the conditional prior provided superior results:  the accuracy and precision of estimates was substantially enhanced without increasing model complexity. We apply the new method to analyze data on 600 stocks and compare our estimates of maximum reproductive rates with previous results.