Oscillating Populations and Biodiversity Maintenance

Species persistence in the face of competitive or predatory pressure has long been assumed to be a consequence of either dynamic equilibrium or stochastic longevity. More recently, however, the complex intersection of nonlinear dynamics with elementary ecological interactions has provided a distinct platform for conceptualizing the problem of species coexistence. One well-known result from nonlinear dynamics is that oscillating systems will tend to coordinate with one another when coupled, even if the coupling is extremely weak. This elementary result yields remarkable insights in many fields of study. Here I summarize recent results showing that a particular structure emerging from a nonlinear analysis of the classic equations of ecology can be merged with more qualitative ideas to form a possible general framework for analyzing species diversity. As a specific example, I examine the case of two consumer–resource systems that, when coupled, inevitably produce some kind of phase coordination. Understanding the nature of that phase coordination provides a qualitative viewpoint for understanding exclusion and coexistence in this example. Finally, I discuss possible applications to other classical ecological questions.