"Holling cycles in simulations of complex food webs"
Challenging the idea of ecosystem stability, C. S. Holling (1986) introduced the concept of the adaptive cycle into ecology. This process, which has been describe in similarly form for economical, technical, social, and physiological complex systems, is briefly sketched like this: Starting with a situation of weak internal organization and low recourse exploitation, the components of the system organize themselves to make exploitation of the system possible (alpha phase). This is followed by a phase of rapid growth and resource exploitation (r phase) that goes along with increasing internal organization and dependencies, until a saturation is reached (K phase). This highly organized state is very fragile. Upon a sufficient perturbation, the system collapses (Omega phase), its internal organization is destroyed and the cycle starts with a new alpha phase. Such a behavior is here reported to be reproducible in dynamical simulations of the food webs (predation networks) of complex ecosystems that are subject to a constant invasion pressure of new species. The simulations allow an investigation of the subtle mix of randomness and determinism involved in Holling cycles, which is inaccessible by the purely heuristic analysis.