Generalized Models – a New Tool for the Investigation of Ecological Systems

Ecological systems are commonly studied by very concrete conventional models or very abstract random matrix models. Here we review and extend the approach of generalized structural kinetic modeling, that offers an intermediate way between these extremes. Generalized models describe systems with a specific structure, but do not restrict the processes in the model to specific functional forms. The approach is based on the construction of a locally linear model in every point of parameter space, in such a way that each element of the model is directly accessible to measurement and has a well defined ecological interpretation. Here 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 present results on spatial predator-prey system and a complex food web.