Summary
Examples of genotype × environment interactions in Nicotiana rustica that appear to be simply linearly related to the additive environmental value (ej) 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 ej 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.
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Jinks, J., Pooni, H. Non-linear genotype × environment interactions arising from response thresholds. Heredity 43, 57–70 (1979). https://doi.org/10.1038/hdy.1979.59
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DOI: https://doi.org/10.1038/hdy.1979.59
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