Chaos reduces species extinction by amplifying local population noise

Abstract

In the mid-1970s, theoretical ecologists were responsible for stimulating interest in nonlinear dynamics and chaos. Ironically, the importance of chaos in ecology itself remains controversial. Proponents of ecological chaos point to its ubiquity in mathematical models and to various empirical findings. Sceptics maintain that the models are unrealistic and that the experimental evidence is equally consistent with stochastic models. More generally, it has been argued that interdemic selection and/or enhanced rates of species extinction will eliminate populations and species that evolve into chaotic regions of parameter space. Fundamental to this opinion is the belief that violent oscillations and low minimum population densities are inevitable correlates of the chaotic state. In fact, rarity is not a necessary consequence of complex dynamical behaviour. But even when chaos is associated with frequent rarity, its consequences to survival are necessarily deleterious only in the case of species composed of a single population. Of course, the majority of real world species (for example, most insects) consist of multiple populations weakly coupled by migration, and in this circumstance chaos can actually reduce the probability of extinction. Here we show that although low densities lead to more frequent extinction at the local level, the decorrelating effect of chaotic oscillations reduces the degree of synchrony among populations and thus the likelihood that all are simultaneously extinguished.