Avenues of Spatially Explicit Population Dynamics Modeling — A par excellence Example for Mathematical Heterogeneity in Ecological Models?

This contribution discusses different approaches to spatially explicit modeling of population dynamics of the intrusion of non-endemic species into patched habitats. Different modeling approaches such as cellular automata, partial differential equations and hybrid Petri nets are summarized. An application of a meta–population model for the Galapagos archipelago is described using a partial differential equation and a Petri net model. A detailed comparison of both models in terms of simulation results and methodology shows how different building blocks of ecological models can be. And the question is raised, how far the integration of models is at all possible and should be aimed at. Results of the investigation give a detailed insight into the problem of scaling ecological models and the core question of what processes should be considered in which scale in terms of space, time or complexity.