Non-linear genotype × environment interactions arising from response thresholds

Summary

Examples of genotype × environment interactions in Nicotiana rustica that appear to be simply linearly related to the additive environmental value (e_j) and others in which this does not appear to be the case have been analysed by testing the goodness-of-fit of linear, quadratic and two intersecting-straight-line models of this relationship. In varieties 1 and 5 and their F₁ cross there is no significant improvement in goodness-of-fit over the linear model from either the quadratic or the two straight-line models. In a stratified sample of 10 inbred lines derived from this cross a pair of intersecting-straight-lines was the best model for the only two inbreds to show significant non-linearity. In varieties 2 and 12, their F₁ cross and the four inbred selections derived from it, the best fit is always obtained with the two intersecting-straight-lines. The reasons, however, differ for the different genotypes. In variety 2 it is because the linear rate of response is relatively higher in the better than in the poorer environments, in variety 12 it is because of a change in the reverse direction, while in the F₁ it is because the rate of response more than doubles in the very best environments. Among the four inbreds it is because one of them, D10, reaches a limit to its response in the environments with above average e_j values while of the remaining three inbreds two increase their linear responses in these environments while the third shows a small decrease.

While, therefore, two intersecting-straight-lines appear to be a widely applicable model of the relationship between the interaction of genotype and environment and the additive environmental value, in only one case, D10, which is a low mean performance and low environmental sensitivity selection, is the use of this model necessitated by a genotypic limit to further response to environmental improvement.