Identification and quantification of heteroscedasticity in stock–recruitment relationships

Abstract

Nonconstant variance (heteroscedasticity) in the stock–recruitment (S-R) relationship is proposed as an important factor in sustainable fisheries management, but its reliable estimation from noisy populations is problematic. We developed methods for both frequentist and Bayesian approaches to test whether we can accurately estimate the degree of heteroscedasticity in 90 published S-R populations. We estimated the confidence interval for the heteroscedastic regression model via a parametric bootstrap approach and the credible interval for the Bayesian method via a Markov chain Monte Carlo sampling algorithm. We found strong evidence of negative heteroscedasticity in several stocks, regardless of the statistical paradigm, the details of density dependence, and the methods used to generate the original populations. This statistical framework, together with its associated freely available software, provides an efficient and reliable setting for assessing heteroscedasticity of the S-R relationship in fisheries.