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REVIEW & INTERPRETATION

Statistical Analysis of Yield Trials by AMMI and GGE

Crop and Soil Sciences, 519 Bradfield Hall, Cornell University, Ithaca, NY 14853

^* Corresponding author (hgg1{at}cornell.edu)

The Additive Main effects and Multiplicative Interaction (AMMI) model, Genotype main effects and Genotype x Environment interaction (GGE) model, and Principal Components Analysis (PCA) are singular value decomposition (SVD) based statistical analyses often applied to yield-trial data. This paper presents a systematic comparison, using both statistical theory and empirical investigations, while considering both current practices and best practices. Agricultural researchers using these analyses face two inevitable choices. First is the choice of a model for visualizing data. AMMI is decidedly superior, not for statistical reasons, but rather for agricultural reasons. AMMI partitions the overall variation into genotype main effects, environment main effects, and genotype x environment interactions. These three sources of variation present agricultural researchers with different challenges and opportunities, so it is best to handle them separately, while still considering all three in an integrated manner. Second is the choice of a member of a given model family for gaining predictive accuracy. AMMI, GGE, and other SVD-based model families are essentially equivalent, but best practices require model diagnosis for each individual dataset to determine which member is most predictively accurate. Making these two choices well allows researchers to extract more usable information from their data, thereby increasing efficiency and accelerating progress.

Abbreviations: AEC, average environment coordinate • AIC, Akaike information criterion • AMMI, Additive Main effects and Multiplicative Interaction • AOV, analysis of variance • ATC, average tester (genotype) coordinate • BIC, Bayesian information criterion • df, degrees of freedom • GE, genotype x environment • GE', prime, signal-rich part of the interaction • GE*, spurious, noise-rich part of the interaction • GGE, Genotype main effects and Genotype x Environment interaction • PC, principal component • PCA, principal components analysis • SS, sum of squares • SVD, singular value decomposition

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