Covariances of relatives stemming from a population undergoing mixed self and random mating

We consider covariances of all parent and first-generation relatives from outcrossing or self-fertilization in a parent population that is in equilibrium with respect to these processes. The results, which are for any number of alleles and loci with additive and dominance effects, are phrased in terms of six quadratic genetic components whose coefficients are given by descent measures for equilibrium populations. Because of the variation in the inbreeding coefficients for this system of mating, the expressions include joint contributions of loci to the variances and covariances of relatives. By inclusion of the full complement of relatives, all quadratic components can be estimated. The findings of Ghai (1982, Biometrics 38, 87-92) for compound functions of the covariances with two alleles at a single locus are analyzed in terms of the more general model.