GENETIC AND STATISTICAL-ANALYSES OF STRONG SELECTION ON POLYGENIC TRAITS - WHAT, ME NORMAL

We develop a general population genetic framework for analyzing select ion on many loci, and apply it to strong truncation and disruptive sel ection on an additive polygenic trait. We first present statistical me thods for analyzing the infinitesimal model, in which offspring breedi ng values are normally distributed around the mean of the parents, wit h fixed variance. These show that the usual assumption of a Gaussian d istribution of breeding values in the population gives remarkably accu rate predictions for the mean and the variance, even when disruptive s election generates substantial deviations from normality. We then set out a general genetic analysis of selection and recombination. The pop ulation is represented by multilocus cumulants describing the distribu tion of haploid genotypes, and selection is described by the relation between mean fitness and these cumulants. We provide exact recursions in terms of generating functions for the effects of selection on non-c entral moments. The effects of recombination are simply calculated as a weighted sum over all the permutations produced by meiosis. Finally, the new cumulants that describe the next generation are computed from the non-central moments. Although this scheme is applied here in deta il only to selection on an additive trait, it is quite general. For ar bitrary epistasis and linkage, we describe a consistent infinitesimal limit in which the short-term selection response is dominated by infin itesimal allele frequency changes and linkage disequilibria. Numerical multilocus results show that the standard Gaussian approximation give s accurate predictions for the dynamics of the mean and genetic varian ce in this limit. Even with intense truncation selection, linkage dise quilibria of order three and higher never cause much deviation from no rmality. Thus, the empirical deviations frequently found between predi cted and observed responses to artificial selection are not caused by linkage-disequilibrium-induced departures from normality. Disruptive s election can generate substantial four-way disequilibria, and hence ku rtosis; but even then, the Gaussian assumption predicts the variance a ccurately. In contrast to the apparent simplicity of the infinitesimal limit, data suggest that changes in genetic variance after 10 or more generations of selection are likely to be dominated by allele frequen cy dynamics that depend on genetic details.