Simulation of quantitative characters from qualitatively acting genes : II. Orthogonal subdivision of hereditary variance in two-locus genetic systems.

The phenotypes associated with the nine genotypes in a quantitative genetic system consisting of two loci, each having two alleles can be described in terms of nine parameters, giving a system of nine linear equations. Populations with desired magnitudes and known nature of intra- and interlocus interactions are obtained by the use of this linear combination model. The total sums of squares for genotypes in these populations are partitioned into orthogonal components denoting additive and dominance effects of the two loci and the four types of nonallelic interactions between them. In most cases, the relative magnitudes of dominance and epistatic variances are found to be considerably smaller than the actual proportions of these genetic effects. Duplicate interaction produces larger epistatic variance than complementary type of gene interaction. At the higher levels of epistasis, dominant epistasis yields much larger epistatic variance than recessive epistasis. No epistatic variance is produced in the absence of epistatic effects. But, appreciable contributions of additive and dominance gene actions to the total genotypic variability are obtained even in the complete absence of these effects, if additive × dominance and dominance × dominance epistatic effects, respectively, are present. It is concluded that in elucidating the nature of gene action in simplified genetic systems, the estimates of first degree parameters obtained from the linear combination model are more useful than the orthogonal components of genotypic sum of squares.