The significance for breeding of linear regression analysis of genotype-environment interactions

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Abstract
Methods of regression analysis of genotype-environment interaction are considered in relation to existing theory dealing with the relative efficiencies of selection for general or specific adaptation to the environment, and the choice of environments for assessment. The two alternative models involving regression on to environmental effects (model 2) or genotypic effects (model 3) are equivalent when regression lines are concurrent, but are shown to be mutually exclusive when concurrence is absent. Formulae relating the rates of advance under selection for general and specific adaptation are given, and can be used as a guide to the choice of an effective breeding strategy. When model (3) regression is important, then selection for general adaptation will be an efficient strategy but may be further enhanced by the use of environments with high regression coefficients () for assessment. The advance following assessment in a single environment (kth) is expected to be better than that under n randomly chosen environments if k>n-1. If model (2) regression is also important (i.e. regression is concurrent), then the best selector environments can be chosen on the basis of their means. If, on the other hand, model (3) regression does not hold, then selection for general adaptation will be inefficient and it is preferable to group the environments to achieve more homogeneity. When model (2) regression holds, then this grouping can be carried out on the basis of the mean expression of the environments.