Use of supplementary genotypes in AMMI analysis

Improving stability of crop yield in a target production environment is an important breeding objective. It is well known that selection for better stability generally results in lower mean yields and, conversely, that selection for higher mean yields may lead to poorer stability. This paper explores the equivalence between the singular value decomposition used in AMMI analysis and the spectral decomposition used in principal components analysis. This equivalence enables scores of a "supplementary genotype" made up of the highest yield value within each environment to be obtained, and these may serve as the ideal check treatment for selection purposes. These scores are used to (1) display this check in a biplot graph, thereby providing a qualitative comparison with the real genotypes related to their interaction with environments; (2) obtain estimates of the squared distances from the projection of each real genotype to the projection of the "supplementary treatment", thereby allowing conclusions to be made on the yield stability of each real genotype. This procedure was effective in identifying the most stable soybean cultivars in an example shown for illustration.