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Equation 12a indicates a clear relationship between the vector length of a test environment and genotype performance in that environment (Eq. 8a). When P is small (P 1), the relationship between SD and SE tends to be more Gaussian-like in appearance, and a log transformation of the data (contrary to the maximum likelihood approach) can improve that relationship to approximate a normal distribution and thus remove the logarithmic relationship (Eq. 14c).

As P approaches 1 and H increases, the GGE biplot is guaranteed to be sensitive to most of the biological variation in the experiment (something that a plot of variance vs. mean will never be). However, when H is large (greater than 0.95), the GGE biplot becomes less discriminatory and has less discriminatory power.

A HA-GGE biplot is introduced here as a heritability-adjusted counterpart to the unscaled GGE biplot. While Eqs. 12a and 12b are obtained from Eqs. 8a and 8b, respectively, a mathematical transformation is required to obtain the heritability as the square root of the vector length in the HA-GGE biplot. This transformation is given by Eq. 15.

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