The object of the development of this paper was to extend the GGE biplot to facilitate rapid screening of genotypes in a multi-environments trial using a pairwise GGE biplot, yielding an adjusted GGE biplot in which the expected vector length of each environment reflects the heritability in that environment (Eq. 12a). In addition, the information presented from the GGE biplot can be converted to mean squared prediction error (MSRP) or mean squared covariance to provide for quick assessment of the accuracy of genotype performance in future environments.
Taking the unscaled GGE biplot multi-environment trial as an example, the unscaled GGE biplot for 100 environments with genotype means has vector lengths (Eq. 5) of (3.549, -0.734, -0.347) for the top line, (5.69, -0.583, -0.445) for the second line, and (7.335, -0.504, -0.515) for the third line. When scaled to (SD, SEM), the environment means have vectors in length (Eq. 8) with (0.0591, 0.0079, 0.0078), (0.0844, 0.0067, 0.0064), and (0.0751, 0.0061, 0.0064). These vectors represent heritability (H values of 0.769, 0.850, and 0.861, respectively). The use of information about SE and H similarly provides for detection of an environment in which a variety of traits vary, and in turn provides for early detection and elimination from the breeding process.
Further, the environment means in the GGE biplot can be converted to values of MSRP and MSCR to reflect accuracy of prediction (Eq. 12b). The MSRP on the top line is 0.0070, and 0.0105 on the second line. Thus, eliminating this environment would not be detrimental to the best mean per environment selected in this case. d2c66b5586