MAINTENANCE OF POLYGENIC VARIATION IN SPATIALLY STRUCTURED POPULATIONS: ROLES FOR LOCAL MATING AND GENETIC REDUNDANCY.

Although heritable genetic variation is critical to the evolutionary process, we know little about how it is maintained. Obviously, mutation-selection balance must play a role, but there is considerable doubt over whether it can account for heritabilities as high as 0.5, which are commonly found in natural populations. Most models of mutation-selection balance assume panmictic populations. In this paper we use Monte Carlo simulations to examine the effect of isolation by distance on the variation maintained by mutation in a polygenic trait subject to optimizing selection. We show that isolation by distance can substantially increase the total variation maintained in continuous populations over a wide range of dispersal patterns, but only if more than one genotype produces the optimal phenotype (genetic redundancy). Isolation by distance alone has only a slight effect on the variation maintained in the total population for neutral alleles. The combined effect of isolation by distance and genetic redundancy, however, allows the maintenance of substantial variation despite strong stabilizing selection. The mechanism is straightforward. Isolation by distance allows mutation and drift to operate independently in different parts of the population. Because of their independent evolutionary histories, different parts of the population independently draw from the available set of redundant genotypes. Because the genotypes are redundant, selection does not discriminate among them, and they will persist until eliminated by drift. The population as a whole maintains many distinct genotypes. We show that this process allows mutation to maintain high levels of variation, even under strong stabilizing selection, and that over a moderate range of dispersal patterns the amount of variation maintained in the entire population is independent of both the strength of selection and the variance of the dispersal distance. Furthermore, we show that individual heterozygosity is increased in locally mating populations when selection is strong. Finally, our simulations provide a rough picture of how selection and the dispersal pattern influence the spatial distribution of genetic and phenotypic variation.