Role of Overlapping Generations in Maintaining Genetic Variation in a Fluctuating Environment

Population genetics theory suggests that temporally fluctuating selection on pheno- types can act to maintain genetic variance only under very restrictive conditions. However, this conclusion is based on models with discrete nonoverlapping generations. We propose here that temporally fluctuating selection can indeed contribute significantly to the maintenance of genetic variation when the effects of overlapping generations and age-specific or stage-specific selection are considered. We develop a simple model for a population with overlapping generations, experiencing stabilizing selection with a temporally fluctuating optimum, and subject to repeated invasions by mutants with alternative phenotypes. We find that an evolutionarily stable popula- tion must have positive genetic variance maintained by selection so long as the product (variance of fluctuations) times (amount of generation overlap) times (selection intensity) is sufficiently high. This result applies to haploid, diploid, single-locus, or multilocus inheritance, and it does not depend on any form of heterozygote advantage to maintain genetic variance. However, it depends on the map between genotype and phenotype being constrained. If a single genotype can produce an arbitrary distribution of phenotypes, then genetic variance is not maintained by selection.