Modeling food-web dynamics: Complexity-stability implications

One of the challenges in the study of complex systems is how to integrate recent network structure discoveries with advances in modeling the dynamics of large non-linear systems. This is important for ecology, where the study of ecological networks - particularly in the form of webs - is a central organizing principle for research into the relationships between ecosystem complexity and diversity, and ecosystem stability, robustness, and persistence. Ecologists and physicists have applied recent advances in statistical mechanics of network topology to food web data. Such studies have uncovered general properties of food web structure, extended previous generalities of 'real-world' network structure, and new insights of complex network structure and robustness. However, although large complex networks of interacting species are observed in nature and their broad-scale structure is well described, few, if any, biologically plausible models have been able to simulate the persistent dynamics of such networks. Advanced theoretical insights into the dynamics of ecological networks are confined to relatively low-dimensional subsystems with less than a half dozen species, or to high-dimensional models that have a priori, biologically implausible stability assumptions. This chapter reviews efforts to characterize food web network structure as well as research into ecological non-linear dynamics. It also discusses approaches that seek to integrate food web structure and dynamics, highlighting factors that appear critical for the persistence and stability of complex species ecosystems.