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

## TL;DR

Stabilizing selection reduces genetic variation by creating correlations between alleles, which slows down how quickly rare alleles disappear from a population.

## Contribution

The paper introduces a mathematical framework that accurately predicts allele-frequency dynamics under stabilizing selection.

## Key findings

- Stabilizing selection generates linkage disequilibria that slow the purging of rare alleles.
- The derived expressions for allele-frequency dynamics outperform previous methods in simulations.
- The results improve the ability to detect and quantify stabilizing selection in genomic data.

## Abstract

Stabilizing selection on a polygenic trait reduces the trait’s 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.

Stabilizing selection—selection for optimal trait values—is likely pervasive across humans and other species. Its phenotypic effect is to reduce trait variance, and it achieves this genetically by favoring compensating combinations of trait-increasing and trait-decreasing variants throughout the genome, generating correlations between them, and by selecting against rare variants at individual loci. We show that the correlations generated by stabilizing selection slow the rate at which it purges rare variants. We characterize this effect mathematically, and show via simulations that the expressions we derive for the frequency dynamics at individual loci are accurate. Our results make possible more precise detection and quantification of stabilizing selection in genomic data.