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 Malecot's probability method of expressing kinship, yields a general form. For one locus, the form is (P ss + P sd + P ds + P dd ) 1 2 σ a 2 + (P ss P dd + P sd P ds ) σa d 2 , where σa2 is the additive genetic variance, αd2 is the variance of dominance deviations, pij 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.