Patterns of genetic polymorphism maintained by fluctuating selection with overlapping generations

We study the form of polymorphisms that can be maintained by the joint effects of generation overlap and randomly fluctuating selection, acting on a quantitative trait affecting offspring viability. The genetic system can be single locus or multilocus, haploid or diploid. Selection is assumed to be stabilizing with a randomly fluctuating optimum, and we assume additive allelic effects without epistasis. For fluctuations above a certain threshold, nonzero genetic variance is maintained in an evolutionarily stable population. Our model allows a continuum of alleles with arbitrary effects at each locus. Nonetheless, the genotype distribution in an evolutionarily stable population is discrete--a polymorphism of a few alleles with distinctly different effects--and often involves only a pair of alleles at each locus. The form of the genotype distribution depends on the number of loci affecting the trait, and on the kurtosis of the distribution of the phenotypic optimum theta. If the trait is affected by several loci, the number of polymorphic loci increases with increased variance of fluctuations in selection. For distributions of theta with negative kurtosis (i.e., lower kurtosis than a Gaussian) the number of polymorphic loci increases gradually (0-->1-->2--> ...M), and the genetic variability is in the form of a few diallelic or triallelic loci with alleles of large effect. For distributions with positive kurtosis, the increase is abrupt (0 -> many) and involves many diallelic loci. These results do not fit the conventional multivariate Gaussian or near-Gaussian models for quantitative traits, but may partially explain recent findings that heritable variation in natural populations is often due to genes of large effect.