MODELS OF MULTIFACTORIAL INHERITANCE .2. COVARIANCE STRUCTURE FOR A SCALAR PHENOTYPE UNDER SELECTIVE ASSORTATIVE MATING AND SEX-DEPENDENT SYMMETRIC PARENTAL-TRANSMISSION

This study concentrates on a scalar trait for a two-sex population entailing symmetric sex-dependent parent-offspring transmission, a nonlinear (selective) assortative mating pattern, and random perturbation factors. A number of qualitative and comparative properties of the equilibrium covariance structure are set forth. In particular, it is shown that the phenotype variance generally increases under attenuated assortative mating tendencies and for an increased level of parent-offspring transmission. Moreover, with more contrasting sex-dependent transmission the sibling covariances diverge from the parent-offspring covariance. Also, shared residual-environmental covariance enhances the sibling covariances. The absolute product moment of the deviation of a child phenotype from the separate parental phenotypes exhibits a minimum for a mixed assortative random mating scheme rather than under extreme assortative mating or pure random mating. We establish that the equilibrium variance of a married individual is reduced compared to the variance of the population at large. Interpretations and implications are discussed. © 1979.