Simulation of quantitative characters from qualitatively acting genes : I. Nonallelic gene interactions involving two or three loci.

The phenotypic values associated with the 3 (n) genotypes obtained from all combinations of genes at n segregating loci, each with two alleles, can be completely described in terms of 3 (n) parameters, 3 (n) - 1 of which are attributed to the genetic effects of alleles at the n loci. The descriptions provide a system of linear equations, which can be solved for parameters specifying n additive, n dominance and 3 (n) - 2n - 1 epistatic components of genetic effect. The solutions of the equations were obtained for two- and three-locus cases. The simple linear combination model was convenient for interpreting classical gene interactions in terms of biometrically definable parameters.By the use of the unique solutions of the linear equations, the genetic parameters were directly estimated from the phenotypic values reported by three groups of workers for simplified genetic systems consisting of two or three loci. In most cases nonallelic gene interactions accounted for a major part of the total genetic effect. Conventional biometrical methods of partitioning genotypic sums of squares into various components were found to be inadequate for evaluating the role of epistasis in these simplified genetic systems.