ADDITIVE-MULTIPLICATIVE APPROXIMATION OF GENOTYPE-ENVIRONMENT INTERACTION

A model of genotype-environment interaction in quantitative traits is considered. The model represents an expansion of the traditional addit ive (first degree polynomial) approximation of genotypic and environme ntal effects to a second degree polynomial incorporating a multiplicat ive term besides the additive terms. An experimental evaluation of the model is suggested and applied to a trait in Drosophila melanogaster. The environmental variance of a genotype in the model is shown to be a function of the genotypic value: it is a convex parabola. The broad sense heritability in a population depends not only on the genotypic a nd environmental variances, but also on the position of the genotypic mean in the population relative to the minimum of the parabola. It is demonstrated, using the model, that GxE interaction may cause a substa ntial non-linearity in offspring-parent regression and a reversed resp onse to directional selection. It is also shown that directional selec tion may be accompanied by an increase in the heritability.