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Analysis of family resemblance. 3. Complex segregation of quantitative traits.

In previous papers of this series, we have introduced problems of family resemblance, which include segregation and path analysis, group differences expressed in families of hybrid ancestry, linkage, mutation screening, parentage exclusion, and recurrence risks [1, 2]. Combination of Wright's path analysis [3] with Fisher's normalizing z transformation [4] was stressed as a means to discriminate among genetic factors, common and random environment, and their second-order effects (gene-environment correlation and assortative mating), both within and among intercrossing racial groups. Path analysis provides optimal discrimination between common environment and genetic factors, while segregation analysis is better for distinguishing major loci. Here we shall consider complex segregation analysis of quantitative traits under a model which includes polygenes, a major locus, and both random and common environment. Most applications of segregation analysis have involved a dichotomy (normal versus affected), which not only has low power to discriminate complex hypotheses but is also out of touch with the needs of genetic counseling [5]. An individual apprehensive of diabetes should submit to a glucose-tolerance test because it has greater predictive power than the occurrence of diabetes among his relatives. Moreover, where familial data are useful, quantitative traits of relatives are often more informative than their affection status. Clearly quantitative as well as qualitative information should be used for both analysis and counseling. When full quantification is not feasible, a trichotomy (normal, intermediate, affected) provides more information than two states. In addition to a major locus, polygenic variation, and environmental effects, our model incorporates a hypothesis about the relation of the quantitative trait to affection. Elston and Stewart [6] discussed mixed models as a generalization of polygenic and major-locus cases and concluded that "extension to the more general genetic models presents no theoretical problems, but may depend on practical advances in computer technology." We have found that the mixed model is within current capabilities. Although not including such complications as multiple alleles and two or more major loci, this model has the advantage of a manageably small