Growth Models for Fisheries: The Effect of Unbalanced Sampling Error On Model Selection, Parameter Estimation, and Biological Predictions

Abstract

Field studies that attempt to estimate the mean growth rates of individuals in a population usually yield unbalanced data and various forms of sampling error. If these data are a poor representation of a population, then the estimates of growth rates may also be unrepresentative of the population. We present an assessment of the performance and uncertainty in 4 growth models—the von Bertalanffy, Gompertz, inverse logistic, and Schnute models—fitted to data with various scenarios of sampling error. The performance of each model was determined by comparing highest likelihoods outcomes to known case outcomes. A Monte Carlo simulation framework was used to generate data consisting of 8 typical scenarios of sampling error common in tag-recapture data. Each growth model was evaluated according to 2 metrics: the error rate (i.e., a metric for model uncertainty) and the prediction error (i.e., the accuracy of biological predictions such as age). Results indicate that an inadequate size range in the data (i.e., a lack of juvenile size classes) would often lead to a high error rate. When negative growth increment data are included, the K parameter of the von Bertalanffy model increased, and the L∞ decreased. The inverse logistic model sometimes produced absurd parameter estimates but nevertheless generated the lowest prediction errors. A high prediction error can potentially have far more serious implications to fishery stock assessments than is currently appreciated. Given widespread use of the von Bertalanffy and Gompertz models, selected solely on the basis of model selection criteria, it is clear that greater care and scrutiny are warranted in the selection of growth models in the presence of sampling error.