Bayesian Estimation of Age and Length at 50% Maturity

Abstract

Fish age and length at 50% maturity are used extensively in the management of exploited fish populations. These parameters are historically estimated using logistic regression models (e.g., frequentist inference) for individual year-classes and often fail to converge or result in insignificant results when a small sample size is used. The sample-size problem motivated us to evaluate whether a hierarchical logistic regression model fit using frequentist inference or Bayesian inference, could improve our ability to fit these models. Our objective was to compare Bayesian and frequentist inference for estimating age and length at 50% maturity to determine whether the models produced similar values. To make this evaluation, we used a long-term data set of Yellow Perch Perca flavescens from southern Lake Michigan. Frequentist inference of the year-class-specific models resulted in significant results when sample size was sufficiently large, a result that occurred in 76% of the models. The hierarchical model produces estimates of age (or length) at 50% maturity for all year-classes using both frequentist and Bayesian inference. However, Bayesian inference of the hierarchical model resulted in more precise parameter estimates and provided the complete posterior distribution in one seamless and easy approach, and the computation time was 78% to 83% faster. We suggest that a hierarchical model fit using Bayesian inference of age (or length) at 50% maturity is an improvement over frequentist interference methods by providing more information about the population of interest, particularly when sample sizes are limited.

Received December 11, 2012; accepted March 28, 2013

ACKNOWLEDGMENTS

This study was funded by the Division of Federal Aid of the U.S. Fish and Wildlife Service and administered through the Indiana Department of Natural Resources (IDNR) as well as Ball State University. We thank IDNR for allowing us the use of their facilities during the collection of the Yellow Perch data. We also thank the many staff and students at Ball State University who contributed to this project over the years. Lastly, we thank the anonymous reviewers for their insightful comments.