In this paper an extension of the biometric model of Mather and Jinks for the analysis of variation with digenic epistasis is presented. Epistatic effects can contribute favorably to the determination of the genotypic values of selected individuals or families and of superior hybrids. Selection will be inefficient, however, if there is a large number of interacting genes because the epistatic components of the between-family and within-family genotypic variances are very high compared to the portion attributable to the average effects of genes. Selection tends to be efficient when the number of interacting genes is reduced, but this depends on the magnitude of due to dominance and environmental variances. The dominance component (H) and the epistatic component due to interactions between homozygous and heterozygous genic combinations (J) can only be estimated when one or more quadratic statistics from the S3 generation, obtained by randomly mating F2 individuals, are used.
