The stability of ecosystems.

Stability criteria and phase boundaries for complex ecosystems are obtained and contrasted with previously studied scenarios. The stability of such systems is determined by the behaviour of the largest eigenvalue of matrices governing the response of the system to small perturbations. As a result we show that ecosystems with unstructured cooperative interactions between arbitary species can be less stable than had been previously determined. We also examine hierarchical ecologies, and demonstrate their increased stability under certain conditions.