Estimating von Bertalanffy parameters with individual and environmental variations in growth.

Variation among individuals is an ubiquitous feature of natural populations. However, the relative roles of intrinsic individual differences and stochastic processes in generating variation remain poorly understood. For somatic growth, identifying the contribution of individual and stochastic processes to observed variation in size has important implications both for basic and applied biology. Here we propose and develop methods for estimating individual variation in growth using size-at-age data. We modify the von Bertalanffy growth model to explicitly incorporate individual, environmental, and stochastic variation and provide analytic expressions for the mean and variance of length-at-age in populations. We use a Bayesian statistical model to estimate individual variation from length-at-age data and apply the model to simulated data to test its efficacy. Although a first step towards understanding individual variation, we demonstrate that estimating individual variation from observational samples is possible and provide a platform for future analytical and statistical developments.