ABSTRACT
In this paper we outline a framework for dealing in a reasonably general manner with individual-based population models. As the resulting mathematical structures are necessarily stochastic, we spend some effort delineating the cases which allow clear-cut deterministic approximations. The most important exceptions are those cases where, at some time or other, the number of individuals in a key category is bound to be low, or in which interactions among individuals are extremely local and yet large numbers of individuals are coupled in a chain- or net-like fashion.
As a second topic, we review some general results for the class of physiologically structured population models, to wit the conditional linearity principle (conditional on the time course of the environmental conditions, the population process is linear in the initial state), the calculation of invasion criteria, a potpourri of model simplification principles, and some useful and relatively straightforward numerical and analytical techniques for the spatially homogeneous case.
As a third topic, we consider a general modeling philosophy which explicitly tries to account for the inherent conflict between our wish for comprehension and the large amounts of detail present in any concrete situation. Within this framework we discuss possible strategies for ascertaining that conclusions from simple models have some wider applicability, and the corresponding need for appropriate higher order concepts.
Finally we provide some pointers to important, but also very difficult, open problems.
