QUASI-PERIODICITY AND CHAOS IN POPULATION-MODELS

Irregular fluctuations,observed in natural population densities were t raditionally attributed to external random influences such as climatic factors. That these may, in contrast, be the result of intrinsic nonl inearities, present even in very simple deterministic models, was firs t mooted by May. Since then, 'chaos' has been shown to occur naturally in many fields of biology, ranging from physiology to the behaviour o f social insects. Ecologists, however, still lack the ultimate proof o f demonstrating conclusively the existence of chaotic population dynam ics outside the world of equations and computer experiments. Further, it has been demonstrated that, in some population models exhibiting ch aos via the period-doubling route, a constant immigration factor inhib its the onset of chaos by a process called period reversal, prompting suggestions that chaos is fragile and easily inhibited. We present thr ee classic host-parasitoid models, whose local stability properties ha ve been extensively studied in the past, but whose chaotic dynamics ha ve not previously been explored. We find that chaos in this class of m odels is reached via quasiperiodicity, a route not normally associated with population models, and is relatively robust against reasonably s mall levels of immigration. This leads us to conclude that chaos could persist in some natural populations, even in the presence of such ext ernal perturbations.