Abstract
Ecosystems are dynamic systems in which organisms survive subject to a complex web of interactions. Are ecosystems intrinsically stable or do they naturally develop into a chaotic state where mass extinction is an unavoidable consequence of the dynamics? To study this problem we developed a computer model in which the organisms and their interactions 'evolve' by a 'natural selection' process. The organisms exist on a multi-dimensional lattice defined both by a diverse physical landscape that does not change and by the presence of other species that are evolving. This multidimensional lattice defines a dynamic vector of 'niches.' The possible niches include the fixed physical landscape and all of the species themselves. Species may evolve that specialize or that are adapted to many niches. The particular niches that individual species are adapted to occupy are not built into the model. These interactions develop as a consequence of the selection process. As species in the model evolve, a complex food web develops. We found evidence for a 'critical' level of biodiversity at which ecosystems are highly susceptible to extinction. Our model suggests the critical biodiversity point is not a point of attraction in the evolutionary process. Our system naturally reaches an ordered state where global perturbations are required to cause mass extinction. Reaching the ordered state beyond the critical point, however, is kinetically limited because the susceptibility to extinction is so high near the critical biodiversity. We quantify this behavior as analagous to a physical phase transition and suggest model independent measures for the susceptibility to extinction, order parameter, and effective temperature. These measures may also be applied to natural (real) ecosystems to study evolution and extinction on Earth as well as the influence of human activity on ecosystem stability.