Rates of change in quantitative traits from fixation of new mutations.

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Abstract
Expressions are derived for the response to directional selection for a quantitative trait that comes from fixation of new mutations in a finite population. For additive genes with a distribution of mutant gene effects symmetric about zero, the response from fixing mutations occurring in a single generation is 2 Ni sigma 2M/sigma, in which N is the effective population size, i is the selection intensity, sigma is the phenotypic standard deviation, and sigma 2M is the increment in variance in the generation immediately after occurrence of the mutations. This response is 2N times that immediately after occurrence of the mutations. With continuous mutation each generation, the asymptotic rate of response is also 2Ni sigma 2M/sigma and the asymptotic variance is independent of i. For completely dominant mutations with symmetric effects, the rates are Ni sigma 2M/sigma; and for recessive mutations the rates are proportional to (Ni)1/2. If the distribution of mutant gene effects, a, is not symmetric about zero, responses depend on the mean square of effects of mutations with positive effect, rather than on the variance of their effects. Rates of change in fitness and of traits correlated with fitness are also analyzed. It is argued that new mutations have contributed substantially to long-term responses in many laboratory selection experiments.