Persistence of Transients in Spatially Structured Ecological Models

Simple discrete-time ecological models for a species with alternating reproduction and dispersal are shown to have complex transient dynamics. If the density dependence (nonlinearity) is strong enough, then the time required to reach the final dynamics is usually very long, approaching thousands of generations, and there are typically very sudden changes in the form of the dynamics. Apparent chaos can change to cycles or vice versa. These results are consistent with observed sudden changes in the form of the dynamics of a single species and imply that transient dynamics of ecological models may be more relevant than long-term behavior.