The model for the additive, dominant and epistatic effects of the locus pair may be extended to include their effects on the response to an environmental covariate (G × E interaction). Following the approach of, e.g. Bucio Alanis and Hill (1966) and developed by Jinks and his coworkers (see Mather and Jinks 1982) genotypes differ in their regression on the environmental covariate. Just as differences in the main effects of the gene pair may be represented by the parameters da, db, ha, hb, iab, jab, jba and lab, so an analogous parameterization may be used to account for genotypic differences in the (e.g. linear) regression of phenotype on measured environment. For example, the regression of the AAbb genotype on environment is βm + βda − βdb where βm is the regression of the mid-homozygote on the environment, βda the homozygous effect of locus A/a on regression and βdb the homozygous effect of the B/b locus on response to the environment.
