Analysis of Genotypic Similarity in Terms of Mean Yield and Stability of Environmental Response in a Set of Maize Hybrids1

An analysis providing full information on hybrid similarity and stability of response to environments is developed and applied to a study of 49 maize (Zea mays L.) hybrids grown at 18 locations. The model provides weighted estimates of hybrid means, coefficients of the regression of each hybrid on an environmental index, and coefficients of the regression of each hybrid on a set of orthogonal residual vectors that are the characteristic vectors of R̂R̂‵ where R̂ is the m ✕ n matrix of estimated deviations from the weighted regressions on the environmental index of n hybrids grown in m environments. Genotypic similarity was defined as euclidian distance between genotypes in the space whose coordinate axes were the 18 locations. In the analysis, the original data were orthogonally transformed into a space whose coordinate axes were the mean vector, environmental index vector, and the characteristic vectors of R̂R̂‵. By means of the transformation, genotypic similarity, mean differences, relative stability, and comparative stability could all be expressed in terms of a model of the regression of genotypic performance on linear comparisons among environments. A cluster analysis arranged the hybrids into groups that were differentiable in terms of means and stability. Differences among means was the greatest source of variation among clusters. Variation in stability was due primarily to response to the environmental index and the first characteristic vector of R̂R̂'.