Sex and population dynamics

Abstract

Chaos has been found in many mathematical models of population dynamics. This suggests that it should be a common feature of natural populations, quite in contrast to the scarcity of systems where it has been demonstrated. We suggest in this paper that the reason for this contrast may lie in the reproductive system. Whereas ecological modelling traditionally deals with asexual organisms, we introduce sexual reproduction (and thus explicit population genetics) into the population dynamic models. As specific examples, we describe the effect of sexual reproduction on two models (a host-parasite model and a predator-prey model) which exhibit chaotic behaviour for many sets of parameters. The results show that sexual reproduction generally reduces the complexity of the system, leading to a stable equilibrium or other forms of simple dynamics, or at least reducing the fluctuations of the system. Thus the chaotic behaviour predicted by many population dynamic models may be restricted to systems with asexual reproduction.