The effect of long-range linkage disequilibrium on allele-frequency dynamics under stabilizing selection

Abstract

Stabilizing selection on a polygenic trait reduces the traits genetic variance by (i) generating correlations (linkage disequilibria) between opposite-effect alleles throughout the genome, and (ii) selecting against rare alleles at loci that affect the trait, eroding heterozygosity at these loci. Here, we show that the linkage disequilibria, which stabilizing selection generates on a rapid timescale, slow down the subsequent allele-frequency dynamics at individual loci, which proceed on a much longer timescale. Exploiting this separation of timescales, we obtain expressions for the expected per-generation change in minor-allele frequency at individual loci, as functions of the effect sizes at these loci, the strength of selection on the trait, its variance and heritability, and the linkage relations among loci. Using whole-genome simulations, we show that our expressions predict allele-frequency dynamics under stabilizing selection more accurately than the formulae that have previously been used for this purpose. Our results have implications for understanding the genetic architecture of complex traits.