Interactions of selection, linkage and drift in the dynamics of polygenic characters

We study the dynamics under directional truncation selection of the genetic variability of a quantitative character controlled by a finite number of possibly linked loci with additive effects. After the first generation of selection, the build-up of linkage disequilibria (Bulmer effect) is analytically demonstrated from a genetical point of view in an infinite population. In the following generations, the dynamics of the system in a finite population are predicted using analytic recurrences under a multi-normal approximation, and computer simulations. The effects of recombination on the dynamics of linkage disequilibria induced by selection and drift, and the consequences for the additive genetic variance are then analysed and discussed from the simulation results. Compared to the rapid exploitation of genetic variability promoted by high recombination rates, low recombination rates promote an early storage of genetic variability in repulsion associations of alleles and a possible late release of genetic variance in the population, so that the variability of the character may be maintained over a longer period of time. In some cases, favourable recombination events in tightly linked systems induce an increase of the additive variance of the character, which may explain some results observed in long-term selection experiments. Our results emphasize that the joint effects of selection, linkage and drift must not be neglected in theoretical quantitative genetics, and require further investigation.