The correlation between relatives with assortative mating

The equilibrium correlation between various close relatives is calculated for phenotypic assortative mating for a character determined by additive loci without dominance and an uncorrelated environment. It is supposed that the phenotypes of spouses have a bivariate normal distribution and environment and heredity are normally distributed. Heredity is Gaussian if either there are many alleles with approximately normally distributed effects at each of an arbitrary number of loci or the trait is controlled by many loci, each of which makes only a small contribution. It is also assumed that the regression of the phenotype or genotype of an individual on the phenotype or genotype of any one of his relatives is linear. The results show that with the above assumptions Fisher's formulae for the correlation between relatives hold with no restrictions on the linkage map.