Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Abstract

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution. EPISTATIC variance in quantitative traits arises from the interaction effects or epistasis between segregating genes at two or more loci that affect these complex traits. Such gene interaction is a common phenomenon because many factors have, for example, a regulatory role in a hierarchical system (Phillips 2008). The statistical theory of quantitative genetics following Fisher (1918) is based on a partition between average effects across loci, which contribute to the additive genetic variance, and to interactions within loci and between loci, which contribute to the dominance and epistatic variance, respectively (Cockerham 1954;Kempthorne 1954). The magnitudes of these components of the genotypic variance each depend on the frequencies, the effects, and the interactions among the contributing genes (see also Falconer and Mackay 1996;Lynch and Walsh 1998). The actual causal genetic factors are usually not known, but many quantitative genetic analyses, including selection on metric traits, have been applied successfully without such knowledge.Among quantitative geneticists, interest in epistasis continues, both to understand the genetic architecture and as a potential way to improve the genomic predictions of disease and quantitative traits, utilizing some of the unexplained parts of the genetic variation (e.g., Carlborg and Haley 2004;Nelson et al. 2013;Mackay 2014). Despite the obviou...

The effect of gene interactions on the long-term response to selection

“…(To see this, compare the variance of the trait in a diploid population at Hardy−Weinberg proportions, q 2 : 2pq : p 2 , with that after complete inbreeding, q : 0 : p). However, it is unlikely that higher-order components will be large enough for this effect to be substantial (6). With two alleles per locus, the kth order variance is proportional to ∼ ðpqÞ k , the product of allele frequencies across the interacting loci.…”

“…There has been a long-standing debate about the effect of genetic interactions on adaptation (1)(2)(3)(4)(5)(6)(7). Although some claim that they are unimportant because they contribute very little to the total genetic variance of a population, and consequently to its short-term response, others claim that their long-term effects can be substantial.…”

How does epistasis influence the response to selection?

“…However, it is still unlikely that higher-order variance components can be substantial, for two reasons. First, for biallelic loci with allele frequencies p, q, V A(k) is proportional to (2pq) k , and as the product of allele frequencies pq is less than one-fourth, we expect 2 k − 1 V A(k) to decrease with k, especially when the contributing alleles are rare (Maki-Tanila and Hill, 2014). Second, for the additive variance to be much smaller than epistatic variance, the marginal effects of alleles must be small-as, for example, for variation in fitness components that is maintained by balancing selection.…”

Modeling additive and non-additive effects in a hybrid population using genome-wide genotyping: prediction accuracy implications

“…Epistatic effects-although a potential source of bias in estimating additive and dominance effects-are often overlooked in experimental quantitative genetic studies (Lynch and Walsh, 1998). Research is now underway to determine its importance with regard to complex traits (Mäki-Tanila and Hill, 2014). Different strategies have been implemented through quantitative genetics models, quantitative trait loci (QTL) or mutation-QTL experiments (Mackay, 2014), but there is still no consensus on its importance.…”