The Croonian Lecture, 1985 - When two and two do not make four: nonlinear phenomena in ecology

Abstract

The simplest mathematical models describing the dynamics of natural populations of plants and animals are nonlinear. These models can exhibit an astonishing array of dynamical behaviour, ranging from stable points to period-doubling bifurcations that produce a cascade of stable cycles, to apparently random fluctuations; that is, simple deterministic systems can produce chaotic dynamics. This review shows how these ideas illuminate some of the observed properties of real populations in the field and laboratory, and explores some of the practical implications. When unpredictable environmental fluctuations are superimposed on such deterministic models, there are further complications both in the analysis and interpretation of data (what factors regulate the population?) and in the management of resources (how should fish quotas be set in an uncertain environment?).