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 mutationâ€selectionâ€drift balance was examined by computer simulation using parameter values inferred for human height, a wellâ€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
