An approach for modelling populations with continuous structured models

The main purpose of this article is to describe the formulation of an appropriate mathematical representation of a population based on physiological attributes relevant to the individual species considered and to the problem under investigation. There are two main parts of the article. The first discusses the relationship between model hypotheses and model conclusions. We will discuss some problems of applicability that arise from employing classical age or size structured models as representations of a population. We describe certain properties of the dynamic behavior of these continuous, structured populations to demonstrate that it is often necessary to include additional physiological variables other than just age and size if one wishes to obtain biologically realistic deterministic population dynamics. We apply the method of characteristics for solving hyperbolic partial differential equations to the population model and discuss problems of interpretation. The second part of the article focuses on the computation of solutions of physiologically structured models. Here we will indicate the motivation and describe the protocol for formulating a dynamic population that was employed in an investigation of effects of toxic chemicals on aquatic populations. Illustrations of the numerical solution of the population model are presented. The protocol is presented because itmore » is generic and the approach seems to be applicable with modification to many environments. 26 refs., 6 figs.« less