The covariance of relatives derived from a random mating population.

Attention is drawn to errors common in the derivation of forms for the genotypic covariance of noninbred relatives from a Hardy-Weinberg population of diploids. A synthesis of Fisher's least-squares method of partitioning the genotypic variance and Malécot's probability method of expressing kinship, yields a general form. For one locus, the form is $\text{(P}{}_{\mathrm{ss}}\text{+ P}{}_{\mathrm{sd}}\text{+ P}{}_{\mathrm{ds}}\text{+ P}{}_{\mathrm{dd}}\text{)}\text{1}\text{2}\text{σ}{}_{\mathrm{a}}{}^2\text{+ (P}{}_{\mathrm{ss}}\text{P}{}_{\mathrm{dd}}\text{+ P}{}_{\mathrm{sd}}\text{P}{}_{\mathrm{ds}}\text{) σa}{}_{\mathrm{d}}{}^2$, where σ_a² is the additive genetic variance, α_d² is the variance of dominance deviations, p_ij is the probability that parental gamete i is identical by descent to parental gamete j, i = s, d indexes the parents of one relative, and j = s, d indexes those of the other. The form provides a framework for obtaining the covariance of relatives from an equilibrium population with linkage.