Dynamics of polygenic variability under stabilizing selection, recombination, and drift.

We study the transient dynamics of the genotypic variance of an additive trait under stabilizing selection, recombination and random drift. We show how interaction of these factors determines the form and the rates of change of different components of the genotypic variance. Let Vg be the genic variance of the trait and CL be the contribution of linkage disequilibrium to the genotypic variance. We demonstrate that the dynamics of the system on the plane (Vg, CL) are typically characterized by a quick approach to a straight line with slow evolution along this line afterwards. We show that the number of loci, n, and the population size, N, affect the expected dynamics of Vg mainly through the ratio N/n. We use our analytical and numerical results in interpreting the published results of artificial stabilizing selection experiments. The analysis suggests that it is drift and not selection that most likely led to the reduction of genetic variability in most of these experiments. Even very strong stabilizing selection only slowly removes polygenic variability from populations.