On the resolution of chaos in population models

Abstract

Some simple equations representing the dynamics of a single population over time are known to be capable of generating extremely complicated behavior. This complicated behavior has been termed chaotic (Li and Yorke, 1975; May, 1974, 1975; May and Oster, 1976; Guckenheimer et al., 1976). The practical consequence of chaotic behavior is a certain inability to describe particular population trajectories with any degree of accuracy. The purpose of this communication is to demonstrate that for certain models, when properly viewed, extremely chaotic populations can behave in very regular and predictable ways, similar to that noted by May (1975). Furthermore, it appears that, in a sense, the more chaotic a population, the more predictable its behavior, at least for a certain class of models.