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.

Keywords: additive variance; epistasis; multilocus models; quantitative genetics; selection.

Figure 1

Multilocus models with gene interaction involving four to 30 loci. The proportion of additive variance (gray), two-locus (red), three-locus (dark red) and four-locus (blue) epistatic variance in the total genotypic variance for models with different numbers of loci with interactions of all orders among them. The loci have equal effects and allele frequencies (p), and either (A) positive (synergistic) or (B) negative (antagonistic) interaction effects, all of the same absolute value as the single locus effect. (A) [aaaaa] = [aaaa] = [aaa] = [aa] = a. (B) [aaaaa] = [aaaa] = [aaa] = [aa] = −a.

Figure 2

Expected components of genetic variance under gene–gene interaction. As Figure 1, but for fewer loci, assumed allele frequency (p) distributions of P = 0.5, uniform and U-shaped (N = 100) distribution (respective expected heterozygosities E(H)) with two- and three-locus interaction effects with (A) constant or (B) declining gene and negative interaction effects with increasing number of loci. (A) [aaa] = [aa] = −a. (B) $a=\sqrt{n},\hspace{0.17em}[aa]=-1/n,\hspace{0.17em}[aaa]=-1/n^{3/2}.\hspace{0.17em}$

Figure 3

Components of genetic variance under dominance. Influence of positive two-locus additive and dominance interaction on (A) the expected values of additive, dominance and epistatic components of genetic variation with allele frequency distributions P = 0.5, uniform and U-shaped distribution, model i: a = d and all interaction terms = 0, j: a = d = [aa] = [ad] = [da] = [dd], and (B) the partition of genetic variation with a varying number of loci with equal allele frequency of 0.5 (V_A gray, V_D dark gray, V_AA red, V_AD+V_DA dark red, V_DD black) and effects like in the model j.