A SPATIAL MECHANISM FOR THE EVOLUTION AND MAINTENANCE OF SEXUAL REPRODUCTION

In this paper we discuss a spatial mechanism for the evolution and mai ntenance of sexual reproduction. We consider three related models in w hich sexual reproduction is maintained by parasitism despite the twofo ld reproductive advantage to pathenogenic females. These models take i nto account the fact that the populations are spatially extended and t hat the effective local population size is relatively small. They do n ot rely on the deterministic cycling of genotypes bur on the dynamical ly produced local stochastic genetic variation. The primary model is a probabilistic cellular automaton. In this, for a wide range of parasi te mutation rates, the parasites maintain a spatially genetically hete rogeneous population of sexuals and this allows the sexuals to overcom e the twofold advantage of asexuals because parasites and their adapta tion are much less effective in a stochastic spatial genetic structure . We also consider the case where the sexuality rate S (the proportion of the time the host breeds sexually) is slowly evolving. With such s low mutation, we find that both sexual (S=I) and asexual (S=O) populat ions are evolutionarily stable. We examine two other models which allo w us to consider the mathematical conditions under which the advantage of this spatial genetic structure overcomes the twofold advantage of asexual reproduction.