Abstract
Genotype-environment interactions may be a potent force maintaining genetic variation in quantitative traits in natural populations. This is shown by a simple model of additive polygenic inheritance in which the additive contributions of alleles vary with the environment. Under simplifying symmetry assumptions, the model implies that the variance of the phenotypes produced across environments by a multilocus genotype decreases as the number of heterozygous loci increases. In the region of an optimal phenotype, the mapping from the quantitative trait into fitness is concave, and the mean fitness of a genotype will increase with the number of heterozygous loci. This leads to balancing selection, polymorphism, and potentially high levels of additive genetic variance, even though all allelic effects remain additive within each specific environment. An important implication of the model is that the variation maintained by genotype-environment interactions is difficult to study with the restricted range of environments represented in typical experiments. In particular, if fluctuations in allelic effects are pervasive, as suggested by the extensive literature on genotype-environment interactions, efforts to estimate genetic parameters in a single environment may be of limited value.