Chaos and the dynamics of biological populations

Abstract

As first emphasized in the early 1970s, the nonlinearities that are inherent in simple models for the regulation of plant and animal populations can lead to chaotic dynamics. This review deals with a variety of instances where chaotic phenomena can arise, particularly in interactions between prey and predators (including hosts and pathogens, hosts and parasitic insects, and harvested populations). Some of the complications in disentangling deterministic chaos from environmental noise will be discussed. The combination of population biology with population genetics leads to an even richer assortment of nonlinear phenomena and to the suggestion that many genetic polymorphisms may vary cyclically or chaotically (rather than being steady, as usually is assumed implicitly). I argue that complex dynamics - including chaos - is likely to be pervasive in population biology and population genetics, even in seemingly simple situations. But superimposed environmental noise, in heterogeneous natural settings, will usually complicate the dynamics, making it unlikely that population data will exhibit elegant properties (such as universalities in period doubling) associated with the underlying maps. The existence of chaotic régimes of dynamical behaviour can, however, invalidate standard techniques for analysing population data to reveal density-dependent mechanisms; this, I believe, may currently be the most significant implication of dynamical chaos for population biology.