Restrictions on Components of Variance for Epistatic Models

If a disease is caused by several loci, then the additive variance at each locus may represent only small portions of the total genetic variance, while epistatic variance components may explain a significant amount of the total genetic variance. In this paper we first give simple general formulations to derive all the components of total genetic variance in a random sample for any multilocus model. We then derive these components for a series of fifteen models that have been proposed as being the two-allele two-locus models most likely for disease. We discuss the restrictions and limitations on the penetrance and the gene frequencies, implied by the disease prevalence, for each model. We investigate the relative magnitudes of the components of variance for the various models and show that in six of the models one or other of the epistatic variance components can be larger than each of the other components. It is suggested that investigations be undertaken to develop appropriate sampling and analytical techniques to detect these variance components by linkage analysis.