Models of multifactorial inheritance: I, multivariate formulations and basic convergence results

A multivariate dynamic model of a vector phenotype trait under the influence of a selective mating pattern, a hierarchy of parental-offspring transmission rules, and random environmental effects is developed. The formulation can incorporate age class effects, geographical variation, asymmetric maternal and paternal contributions, sex-differentiated offspring expression, selective family adoption procedures, and classes of family and pedigree influences. The mating, transmissible, and environmental aspects of family structure parameters can vary systematically or randomly in time. Cultural and biological variables are handled in one framework. Results on the dynamic and equilibrium behavior of these multivariate processes are set forth and interpreted.