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When the original GGE biplot is used, the length of the environments in the GGE biplot are scaled by SE j for each genotype, and likewise, the raw phenotypic means in the environments are scaled by SD j for individual genotypes.
where V is the mean square environmental repeatability of the genotypes, e is the mean square error of the environment, and FGM j is phenotypic genotype means in genotype j. The unscaled GGE biplot is a fundamental part of the theory of indirect selection and is used in the updated GGE biplot in this paper (Eq. 8).
In the GGE biplot, the vector length of the environments j = {1,...,J} is proportional to SDj, which is positively associated with the phenotypic variation among genotypes in environment j, and inversely associated with the square of the mean square error of the environments e j. d2c66b5586