Effect of population structure and stabilizing selection on quantitative genetic variation

We study one of the simplest scenarios of polygenic selection that can be imagined: a subdivided population of diploid individuals expressing an additive trait under spatially homogeneous stabilizing selection. We are interested in the amounts of variation that can be maintained at mutation-selection-migration-drift equilibrium, at individual loci and at the level of the trait, within and among subpopulations. We derive analytical approximations for variance components and summary statistics such as FST and QST under the assumptions of the infinite-island model and compare these with individual-based simulations. We find that: (i) There is a critical migration threshold (which depends on effect sizes of trait loci) below which population structure strongly inflates genic variance in the subdivided population to levels well above those in a panmictic population. Variation within each subpopulation is maximized close to the critical migration rate. (ii) The genetic basis of trait variation across subpopulations is most similar close to this migration threshold and (counter-intuitively) decreases for higher migration rates. This has consequences for the portability of Genome-Wide Association Studies (GWAS) between subpopulations, i.e, the extent to which loci with large contributions to variance in one subpopulation explain variance in other subpopulations. (iii) An analytical mean-field approach based on the single-locus diffusion approximation, together with effective migration and selection parameters (to account for associations between loci), very accurately predicts various quantities.