Molecular clock rates at loci under stabilizing selection.

Under stabilizing selection in a finite population, lambda, the rate of allelic substitutions at a locus is approximately lambda approximately mu(1 + S)-1/2, where mu is the mutation rate. S, the stringency of selection upon new mutants, is defined by S = NVm/Vs, where N is the population size and Vm/Vs is a measure of the average fitness decrease experienced by new mutants. The approximation holds both for a "lonely" locus, which is the sole provider of genetic variation for the character under selection, and for an "embedded" locus, which is not. In both cases I use the Crow and Kimura model of a continuum of alleles with Gaussian selection and mutation. Monte Carlo simulations corroborate the substitution rate formula. Some molecular evolution data suggest the potential utility and limitations of the formula for estimating population size, mutation, and selection parameters. This work agrees with the rest of nearly neutral theory in emphasizing the important role of population size for substitution rates.