Multifactorial inheritance with cultural transmission and assortative mating. I. Description and basic properties of the unitary models

A general linear of familial resemblance is described which allows for cultural transmission from parent to offspring, polygenic inheritance, phenotypic assortative mating, common environment, maternal and paternal effects, and threshold effects. Three special cases are described in detail which are particularly useful when data are only available about a few classes of relatives reared in intact families. The cultural model, the polygenic model, and the pseudopolygenic model share the common feature that all factors which are transmitted from parent to offspring may be represented by one parameter without any loss of information. We introduce a new model, termed the unitary model, which includes these models and is appropriate when combined genetic and cultural transmission is present and when data are available only for individuals reared in intact nuclear families. The basic properties of these models are explored using path analysis and computer simulation, including description of the relationship between parameters under random and assortative mating, rate of approach to equilibrium, and constraints on the magnitude of the parameters.General formulae for familial resemblance in extended pedigrees are given for any ancestor or descendant of either vertical or collateral relatives. Estimation procedures are described and a FORTRAN program TAU, available upon request, is used to provide maximum likelihood estimates of the parameters from reported correlations. A powerful test for detecting the presence of cultural transmission is suggested and applied to simulated data and to data sets reported by others for human stature, for which cultural transmission is suggested. In addition, it is shown that there is no need to postulate dominance to account for available data about height.