An analysis of error structure in modeling the stock–recruitment data of gadoid stocks using generalized linear models

Abstract

When modeling the stock–recruitment (S–R) relationship, the Cushing, Ricker, and other S–R models are fitted to the observed S–R data by estimating parameters with assumptions made concerning the model error structure. Using a generalized linear model approach, we explored and identified the appropriate model error structure in modeling S–R data for gadoid stocks. The S–R parameter estimation was found to be influenced by the choice of error distributions assumed in the analysis. In modeling S–R data for gadoid stocks, the Beverton–Holt model was found to be more sensitive to the assumption of model error distribution than the Cushing and Ricker models. The lognormal and gamma distributions had higher probability of being acceptable model error distributions. Cluster analyses and summary statistics of error distributions in S–R modeling did not show consistent patterns in the identification of an acceptable model error structure among species, geographic distributions, and sample sizes. A better understanding of the factors and mechanisms resulting in differences in the choice of appropriate model error distributions for different populations is needed in future research. We recommend that the generalized linear model be used to identify acceptable model error structures in quantifying S–R relationships.