Non-linear genotype × environment interactions arising from response thresholds

Abstract

SUMMARYExamples of genotype x environment interactions in Xicotiene rustica that appear to be simply linearly related to the additive environmental value (ej) and others in which this does not appear to be tbe case have been analysed hy testing the goodness-of-fit of linear, quadratic and two intersecting-straightline models of this relationship. In varieties 1 and 5 and their F5 cross there is no significant improvement in goodness-of-fit over the linear model from either the quadratic or the two straight-line models. En 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, Dl0, 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.

Genetical variation for enzyme activity in a population of Drosophila melanogaster

“…The application of the analysis of Jinks and Pooni (1979) to variation in the molecular phenotype has been remarkably successful. For most lines the remainder variation was not statistically significant indicating that one of the three models, linear, quadratic and two intersecting-straight-lines adequately describe the relationship between genotype and environment.…”

“…and corresponds to the reduction in the remainder sum of squares of the quadratic regression attributable to fitting two intersecting straight lines rather than a quadratic regression. The only difference from the presentation given by Jinks and Pooni (1979) relates to the item linear regression. As mentioned earlier under conditions of no genotype-environment interaction the regression of line mean onto additive environmental value e1, will yield a slope of unity.…”

“…In all other respects the analysis is as presented by Jinks and Pooni (1979). The test of significance for an improvement in fit for a model of genotypeenvironment interaction based upon two intersecting-straight-lines was determined conservatively by adjusting the probability values obtained from the corresponding test of significance for the a posterior!…”

“…There are then two possible pairs of intersecting straight lines. The procedure here, as in the analysis of Jinks and Pooni (1979) is to apply a correction to the probability corresponding to the improvement in fit, whenever it is less than the critical level of 5 per cent, in this case by a multiplication of two. If the probability corresponding to the variance ratio test of significance is still <5 per cent, then a model based upon two intersecting-straight-lines has been accepted.…”

“…The present study examines the response in ADH activity of a set of 18 highly inbred lines derived from the population "Texas" in relation to normal variations in the laboratory environment. The novel feature of this study is the application of a recently published method for the detailed study of genotype-environment interaction, due to Jinks and Pooni (1979), to the character enzyme activity. The method is particularly useful since it allows an assessment of the relative sensitivities of lines to environmental variation of an unspecified or ill-defined nature as may be expected in the ecology of natural or even laboratory populations.…”