Summary
The conditions are discussed under which the regression (bD/S) over a range of environments of the difference between two genotypes, X and Y, on their sum will be linear. It is shown that if the slope of this regression falls outside the range – 1 to 1, the two genotypes must be responding in opposite directions to the changes in the environment. The relations of bD/S to bY/X and bX/Y, the regressions of X and Y on one another, are derived and the effects of error variation are considered. The three regressions are derivable from one another in principle, and the most useful values will be obtained by estimating from the data the one which is least subject to distortion by error variation and deriving the others from it. The best starting point will commonly, but not always, be bD/S.
The treatment is extended to the analysis of multi-line experiments, due to Perkins and Jinks, in which each line is regressed on the mean of them all. It is shown how estimates of such regressions, not open to the statistical objections of regressing a variate onto another of which it itself is a part, can be obtained by starting with the regression of each line on the mean of the rest. The value of bD/S for any pair of the constituent lines can be derived directly from the multi-line analysis, and indeed once the analysis is available any group of lines can be readily compared with any other such group.
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Mather, K., Caligari, P. Genotype × environment interactions. Heredity 33, 43–59 (1974). https://doi.org/10.1038/hdy.1974.63
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DOI: https://doi.org/10.1038/hdy.1974.63
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