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.