Analysis of size trajectory data using an energetic-based growth model

Individual growth rate of animals is increasingly used as an indicator of ecological stressors. Environmental contaminants often affect physiological processes within individuals, which in turn affect the animal's growth rate. Consequently, there is an increasing need to estimate parameters in physiologically based individual growth models. Here, we present a method for estimating parameters in an energetic-based individual growth model (a dynamic energy budget model). This model is a system of stochastic differential equations in which one of the state variables (the energy reserve) is unobservable. There is no analytical solution to the probability density of size at given age, so we use a numerical nonlinear state-space method to calculate the likelihood. An algorithm to calculate the likelihood is outlined in this paper. This method is general enough to apply to other stochastic differential equation models. We assessed the estimability of parameters in the individual growth model, and analyzed size trajectory data from delta smelt (Hypomesus transpacificus). We expect this method to become an important tool in ecological studies as computers become faster, as the models that we deal with become more complex, and as the data that we collect become more detailed.