Abstract
We analyzed a model to determine the factors that facilitate or limit rapid polygenic adaptation. This model includes population genetic terms of mutation and both directional and stabilizing selection on a highly polygenic trait in a diploid population of finite size. First, we derived the equilibrium distribution of the allele frequencies of the multilocus model by diffusion approximation. This formula describing the equilibrium allele frequencies as a mutation-selection-drift balance was examined by computer simulation using parameter values inferred for human height, a well-studied polygenic trait. Second, assuming that a sudden environmental shift of the fitness optimum occurs while the population is in equilibrium, we analyzed the adaptation of the trait to the new optimum. The speed at which the trait mean approaches the new optimum increases with the equilibrium genetic variance. Thus, large population size and/or large mutation rate may facilitate rapid adaptation. Third, the contribution of an individual locus i to polygenic adaptation depends on the compound parameter γipi(0)qi(0) , where γi is the effect size, pi(0) the equilibrium frequency of the trait-increasing allele of this locus, and qi(0) = 1 - pi(0) . Thus, only loci with large values of this parameter contribute coherently to polygenic adaptation. Given that mutation rates are relatively small, this is more likely in large populations, in which the effects of drift are limited.