Modeling Annual Growth Variation using a Hierarchical Bayesian Approach and the von Bertalanffy Growth Function, with Application to Lake Trout in Southern Lake Huron

Abstract

We compared two models for time-varying growth using a hierarchical Bayesian approach to inference. Both models were derived from the same time-invariant von Bertalanffy growth function (VBGF), and our model comparisons were based on the deviance information criterion. We fit models to length and age data for 15,675 individual lake trout Salvelinus namaycush collected during annual spring gill-net surveys in southern Lake Huron from 1976 to 2004. We found that a model structured with both year and cohort effects outperformed a model that only used the same year-specific VBGF parameters for all age-groups. For the better model, the full version that allowed all VBGF parameters to vary over time also outperformed alternatives for which some parameters were constant. Length at age changed greatly over the 1976–2004 period, and in some years different ages changed in different directions. These complex patterns, which were due to the combination of cohort-specific growth and year-specific changes in growth environment, were well captured by our model. When we modeled growth as varying over time, inferences about VBGF parameters differed between the two models, and correlations among VBGF parameters also differed from the usually reported relations based on time-invariant models.