Equivalence of the mixed and regressive models for genetic analysis. I. Continuous traits

The mixed model of segregation analysis specifies major gene effects and partitions the residual variance into polygenic and environmental components. The model explains familial correlations essentially in terms of genetic causation. The regressive model, on the other hand, is constructed by successively conditioning on ancestral phenotypes and major genes. Familial patterns of dependence are described in terms of correlations without necessarily introducing a particular scheme of causal relationship. These two approaches are compared both theoretically and numerically through computer simulations for the case of continuous traits on nuclear families. The class D regressive model, which is characterized by equal sib-sib correlations, is mathematically and numerically equivalent to the mixed model. The simpler class A regressive model, which is also characterized by equal sib-sib correlations determined in this case by the common parentage, provides good estimates of the mixed model parameters: major gene parameters and residual polygenic heritability, derived from the parent-offspring correlation. However, in the absence of a major gene, the restriction imposed by the class A model on the sibling correlation can affect the conclusions of segregation analysis: False inference of a major gene was observed in two out of ten replicates. Our simulations also indicate that the mixed model allowing for different heritabilities in adults and children leads to correct estimates of the major gene parameters and residual familial correlations (parent-offspring and sib-sib) as specified by the class A model. For all the models studied, major gene effects, when present, are correctly detected and estimated.