The correlation between relatives in a random mating population

Abstract The variance of a characteristic in a random mating diploid population is partitioned into two components, the genotypic variance and the environmental variance. The genotypic variance is then separated into components which can be attributed to the additively genetic effects, the dominance deviations and the epistatic effects. The total epistatic variance is subdivided into components arising from interactions among sets of 2, 3, ..., n loci and the interaction variance from a particular number of loci is shown to be composed of portions attributable in a certain sense to the interaction of additive and/or dominance effects of genes. For example, the epistatic variance arising from two loci consists of three distinct parts: additive-by-additive, additive-by-dominance and dominance-by-dominance variance. It is then shown that the covariances, and hence the correlations, between relatives which are not inbred, can be expressed in terms of the components of genotypic variance. The basic result is that if σ2x is a component of the genotypic variance, where X contains r additive and s dominance effects, the covariance between two relatives with respect to σ2x is equal to (1/2) (ϕ + ϕ1)r ϕϕ1g, where ϕ and ϕ1 are easily calculated from the pedigree of the relatives.