Estimating the Contribution of Among-Individual and Environmental Variation to Variability in Fish Growth: Bayesian Methods for Von Bertalanffy Growth

Among individual variation in growth rate and size-at-age is widespread among fish species. Similarly, temporal variation in the environment is known drive variation in growth rates among year-classes of fish. However, understanding the consequences of growth variation for fisheries, ecology, and evolution requires a mechanistic understanding of the contribution from individual and environmental components to growth variation. In particular, there is a need for methods that can use observational data to partition observed variation in size-at-age into the relative contribution from among-individual and environmental components.

We present a novel, general method for apportioning growth into individual-level and shared environmental components using the von Bertalanffy growth equation.  Specifically, we 1) derive expressions for the expected value and variance in size-at-age when the von Bertalanfy growth parameter, k, is assumed to vary among individuals and environmental conditions are allowed to vary with time and 2) develop Bayesian methods for estimating among individual variation in growth and temporal changes in the environment using a time-series of individuals sampled from a single population. Using simulated data, we demonstrate that our method produces accurate parameter estimates with moderate sample sizes (i.e. sample sizes frequently available from fisheries data). Finally, we estimate among-individual variation in growth for an experimental population of steelhead trout (Oncorhynchus mykiss) exposed to a temporally varying thermal environment.