QUANTITATIVE GENETICS AND POPULATION-DYNAMICS

This study examines the dynamics of a competition and a host-parasite model in which the interactions are determined by quantitative charact ers. Both models are extensions of one-dimensional difference equation s that can exhibit complicated dynamics. Compared to these basic model s, the phenotypic variability given by the quantitative characters red uces the size of the density fluctuations in asexual populations. With sexual reproduction, which is described by modeling the genetics of t he quantitative character explicitly with many haploid loci that deter mine the character additively, this reduction in fitness variance is m agnified. Moreover, quantitative genetics can induce simple dynamics. For example, the sexual population can have a two-cycle when the asexu al system is chaotic. This paper discusses the consequences for the ev olution of sex. The higher mean growth rate implied by the lower fitne ss variance in sexual populations is an advantage that can overcome a twofold intrinsic growth rate of asexuals. The advantage is bigger whe n the asexual population contains only a subset of the phenotypes pres ent in the sexual population, which conforms with the tangled bank the ory for the evolution of sex and shows that tangled bank effects also occur in host-parasite systems. The results suggest that explicitly de scribing the genetics of a quantitative character leads to more flexib le models than the usual assumption of normal character distributions, and therefore to a better understanding of the character's impact on population dynamics.