The impact of background selection in mutation-selection-drift balance models of complex trait evolution

Abstract

Background selection (BGS)--the reduction of linked neutral diversity via the purging of deleterious mutations--is a pervasive force in genomic evolution. However, its impact on complex phenotypes remains poorly understood because classical theory treats fitness effects as fixed rather than emerging from a phenotype-to-fitness map. Here, we investigate the impact of BGS across three phenotypic selection frameworks: exponential directional, a liability threshold model, and stabilizing selection. First, we develop an effectively non-recombining block approximation for the site frequency spectrum (SFS) and show that this framework accurately describes the skew in the site frequency spectrum in the weak mutation regime typical of humans. Second, we show that phenotypic impacts of BGS depend on how selection is coupled across loci. In the liability threshold model, strong synergistic epistasis generates a global compensation mechanism--driven by tiny shifts in the mean phenotype-- that propagates BGS effects to strongly selected variants otherwise immune to linked selection. This coupling reduces genetic variance across almost the entire effect-size distribution by an amount determined by a non-linear average of local effective population size reductions across the genome. Conversely, under stabilizing selection, BGS can counter-intuitively increase genetic variance. This occurs because BGS shifts strongly selected sites into the weakly selected underdominant regime where they persist at intermediate frequencies longer than in the equivalent directional selection model. Our results inform both longstanding evolutionary conversations regarding synergistic epistasis and efforts to model the impact of background selection on individual variants in recombining genomes. SignificanceNatural selection against deleterious mutations reshapes genetic variation through background selection, a process typically modeled as a local reduction in effective population size. We show that the consequences of this reduction for genetic architecture are mediated by the relationship between phenotype and fitness. Extending background selection theory to complex traits, we show that in models with strong synergistic epistasis, a global compensation mechanism propagates the effects of selection to strongly selected variants. Furthermore, we find that background selection can counter-intuitively increase genetic variation under stabilizing selection. Our work shows that the total impact of background selection on functional variation thus depends on the answers to longstanding questions about the ultimate sources of variance in fitness.