Analysis of genetic and environmental sources of variation in serum cholesterol in Tecumseh, Michigan. V. Variance components estimated from pedigrees.

The human geneticist who wishes to estimate the genetic and environmental components of a quantitative trait has the choice of several sampling designs. Sets of monozygous and dizygous twins, parents and their offspring, and full siblings are often the most convenient samples but invariably yield estimators of genetic variance which are biased by shared environmental factors. More recently, fixed combinations of related and unrelated individuals have been proposed as sampling strategies to improve the separation of genetic and shared environmental correlations between relatives. These fixed designs take the form of family sets (Schull et al. 1970; Chakraborty et al. 1977) or sets of monozygous twins, their spouses and offspring (Nance & Corey, 1976). Unfortunately, human data cannot easily be collected according to a fixed design. A convenient sample usually consists of families which vary in the genetic relatedness of their members. Most human studies have utilized regression coefficients and interclass correlations estimated from pairs of individuals or intraclass correlations from subsets of individuals selected from a random sample of families. These statistics are generally contrasted to estimate the fractions of phenotypic variance due to genetic and environmental factors. The strategies available for combining these estimators do not adequately account for the double counting of individuals and alleles which may occur. For example, the full sib correlations and the parent-offspring correlations are usually estimated from individuals drawn from the same array of nuclear families. Elston (1975) has shown that the correlations between these correlation estimates may not be trivial. Despite the obvious implication, the precise effect of using correlated estimates on inferences about heritability estimates is not clear at this time. In order to minimize the inflation of type I1 error it is not uncommon to discard a large portion of the data. For example, in the Tecumseh Community Health Study, from the 6366 individuals typed for 12 blood markers, less than 100 genetically independent family sets, consisting of an index, a sib and a cousin could be constructed (Orr, personal communication). If the assumption of independence of family sets was rigorously met, only 5 yo of the available data could be utilized and the effect of the nonindependent index-sib and index-cousin correlations would still be unresolved. More importantly, samples of pairs or sets of relatives are usually not randomly sampled and therefore may not represent the same phenotypic variability of a quantitative trait that is determined by t,he frequency distribution of genotypes and environments among and within pedigrees which define the population. Alternatively, we may use the procedure of maximum likelihood estimation (MLE) to combine all of the information available in a sample of randomly selected pedigrees to obtain