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Further, GGE biplots avoid incorrect interpretation of the environmental effects in an environment when those effects are unrelated to the true genotype-by-environmental variance [e.g., Eq. A3 in Probold et al. (2019)] and include genotypes that sample the environmental variance in more than one environment. This effectively increases the power of the biplot to detect differences in genotypic means among environments because the percent of area in the plot occupied by a genotype is a function of both its magnitude and the degree to which that magnitude relates to the true differences in the original data.
The GGE biplot (Eq. 8) also offers the following practical advantages when interpreting it in an analysis of data from a multi-environment trial, such as those used to measure yield components in modern plant breeding. (1) The biplot SE- or SEM- scaled GGE biplot (Eq. 5) captures the overall true, genotypic plus experimental variance, which is determined by the variance and covariance components in that pairwise SE (Eq. 2), while the unscaled GGE biplot (Eq. 4) captures the overall experimental sum of squares that is, in part, driven by differences in the error in the environments. (2) The biplot does not assume that the interacting components are equal in all environments, like a principal components analysis, and therefore may recover information not available in a PCA. (3) The GGE biplot is stationarity-free, as the weighted loadings are computed from an appropriate weighted least squares fit of the genotypic data to the environments.
The regression coefficients of the GGE biplot (Eq. 8) can be used to calculate the mean effective allele substitution effect across environments in the original space. In doing so, the regression coefficients of the GGE biplot can be interpreted as genotypic means, which is the same as interpreting regression coefficients as genotype-by-environment interactions in the original space. d2c66b5586
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