Interaction of Genotype and Environment in Continuous Variation: I. Description

Abstract

Phenotypes given by a number of genotypes in each of several environments can be described in terms of the genetic parameters, d and h, the environmental parameter e, and interaction parameters, gd and gh, which specify the variation of d and h with environment. The relations listed by Haldane among the 4 phenotypes arising from 2 genotypes and 2 environments are definable by inequalities between these parameters. When genotype-environment interactions are present in the sense that the g''s are not negligible, the variances of segregating families include, besides the usual D, H and E components, terms in Vgd, Vgh, the variances over environment of gd, gh respectively. If more than one gene is involved, and there is no linkage, the additional terms involve GD =[SIGMA]Vegd, GH = [SIGMA]Vgh. In the expressions for the total variances of F2 and later generations, Gd and GH appear with the same coefficients as D and H respectively, but do not usually partition in the same way between the variances of different rank. The E component itself also shows changes from generation to generation which depend on the magnitude of the g''s.