Assortative mating for a quantitative character

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Abstract
Phenotypic assortative mating is investigated for a character determined by additive loci without dominance and a stochastically independent environment. Conditional-expectation arguments are used to calculate the equilibrium values of the phenotypic variance and the correlation between sundry relatives. For the latter, it suffices to suppose that the regressions of an individual's genotype on his phenotype and of his phenotype on that of his mate are linear. For the former, linearity of the regression of the allelic effects on the phenotype is also posited. The biological implications of these assumptions are discussed.