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Statistical Analysis of Yield Trials by AMMI and GGE: Further Considerations

^a Crop and Soil Sciences, Cornell Univ., Ithaca, NY 14853
^b Bioinformatics Unit, Institut für Pflanzenbau und Grünland, Universität Hohenheim, 70599 Stuttgart, Germany
^c CRA-Istituto Sperimentale per le Colture Foraggere, Viale Piacenza 29, 26900 Lodi, Italy

View larger version (13K): [in this window] [in a new window]   Figure 1. AMMI1 biplot for an Ontario wheat trial. The genotype and environment means are shown on the abscissa, with a vertical line at the grand mean of 4.186 Mg ha–1. The principal component (PC) 1 scores are shown on the ordinate, with a horizontal line at 0. This graph captures 93.4% of the yield variability.

View larger version (11K): [in this window] [in a new window]   Figure 2. AMMI1 mega-environment display for an Ontario wheat trial. Environment means are shown on the abscissa and principal component (PC) 1 scores on the ordinate. There are two mega-environments, with genotype G18 winning in environments E5 and E7 and genotype G8 winning elsewhere.

View larger version (21K): [in this window] [in a new window]   Figure 3. Adaptive responses for Ontario wheat genotypes according to the AMMI1 model. Principal component (PC) 1 scores for the nine environments are shown on the abscissa and nominal yields for the 18 genotypes on the ordinate. The two genotypes, G8 and G18, that win over some range of PC1 scores are identified individually, whereas the responses of the losers are indicated by thin lines. Note that G18 wins in E5 and E7, whereas G8 wins in the other seven environments.

View larger version (14K): [in this window] [in a new window]   Figure 4. An AMMI2 mega-environment display for an Ontario wheat trial. To avoid clutter, genotype winners are identified only for the three mega-environments that include one or more environments. In addition, G10 would have won for an environment located in the small triangular region at the top, G17 for the bottom left region, G5 for the bottom middle region, and G4 for a region too small to be shown. This graph was constructed with even singular value partitioning (SVP) and no axis rescaling (although other SVP and rescaling choices would leave mega-environment assignments invariant). Products of genotype and environment scores, summed for both principal components, approximate interactions and are in units of yield, namely Mg ha–1. This AMMI2 display incorporates 86.7% of the genotype + genotype x environment information, whereas its genotype main effects and genotype x environment interaction 2 (GGE2) counterpart incorporates only 78.0%. (PC, principal component.)

View larger version (12K): [in this window] [in a new window]   Figure 5. A scatterplot of mean yield and instability for the 18 genotypes in an Ontario wheat trial. Mean yield is a genotype's average over the environments, including only those seven environments comprising a single mega-environment. Instability is measured as a genotype's contribution to the sum of squares for genotype-by-environment interaction. The vertical line shows the grand mean of 3.96 Mg ha–1, and the horizontal line shows the average instability of 0.523.

View larger version (10K): [in this window] [in a new window]   Figure 6. A scatterplot of discriminating power and representativeness for those seven environments comprising a single mega-environment from an Ontario wheat trial. For each environment, discriminating power is measured as the standard deviation of the 18 genotypes in that environment and representativeness is measured as the correlation between genotype values in the environment and genotype means across all environments. The vertical line shows the average discriminating power of 0.723, and the horizontal line shows the average representativeness of 0.812.