Expected influence of linkage disequilibrium on genetic variance caused by dominance and epistasis on quantitative traits.

Linkage disequilibrium (LD) influences the genetic variation in a quantitative trait contributed by two or more loci, with positive LD increasing the variance. The magnitude of LD also affects the relative magnitude of dominance and epistatic variation. We quantify the extent of the non-additive variance expected within populations, deriving analytical expressions for simple models and using numerical simulation in finite population more generally. As LD generates non-independence among loci, a simple partition into additive, dominance and epistatic components is not possible, so we merely distinguish between additive and non-additive components based on comparing covariances among close relatives, such as full sibs, half sibs and offspring-parent. As tight linkage is needed to yield substantial LD in outbred populations, we ignore recombination in the generation used to estimate components and it is analogous to a multi-allelic model. The expected magnitude of the non-additive variance is generally increased but not greatly so by the LD in outbred populations. Thus, as found in previous studies for unlinked loci, independent of the type and strength of gene interaction, the epistatic variance contributes little to the total.