Generalized models–A new tool for the investigation of ecological systems

Abstract

Ecological systems are commonly studied either by explicit conventional models or by abstract random matrix models. Here we review and extend the method of generalized structural kinetic modeling, that offers an intermediate approach between these extremes. Generalized models describe the dynamic capabilities of a system with a given structure, but do not restrict the processes in the model to specific functional forms. The approach is based on the direct construction of the Jacobian in every point of parameter space in such a way that each term appearing in the Jacobian is directly accessible to measurement and has a well defined ecological interpretation. We show that generalized models can be used to study the local asymptotic stability of steady states and reveal certain features of the global dynamics. Among other examples we illustrate the method on a spatial predator-prey system and a complex food web.