  It has been shown that differences in fecundity variance can influence the
probability of invasion of a genotype in a population, i.e. a genotype with
lower variance in offspring number can be favored in finite populations even if
it has a somewhat lower mean fitness than a competitor. In this paper,
Gillespie's results are extended to population genetic systems with explicit
age structure, where the demographic variance (variance in growth rate)
calculated in the work of Engen and colleagues is used as a generalization of
"variance in offspring number" to predict the interaction between deterministic
and random forces driving change in allele frequency. By calculating the
variance from the life history parameters, it is shown that selection against
variance in the growth rate will favor a genotypes with lower stochasticity in
age specific survival and fertility rates. A diffusion approximation for
selection and drift in a population with two genotypes with different life
history matrices (and therefore, different growth rates and demographic
variances) is derived and shown to be consistent with individual based
simulations. It is also argued that for finite populations, perturbation
analyses of both the growth rate and demographic variances may be necessary to
determine the sensitivity of "fitness" (broadly defined) to changes in the life
history parameters.
