Genotype × Environment Interacion in multi-environment Trials using shrinkage factors for ammi models

Abstract

Shrinkage factors applied to the additive main effects and multiplicative interaction (AMMI) models improve prediction of cultivar responses in multi-environment trials (MET). Estimates of shrinkage factors based on the eigenvalue partition (EVP) method may get a further improvement in the predictions of cell means. Objectives of this work were: (1) to compare the EVP-based shrinkage method with unshrunken AMMI, best linear unbiased predictor (BLUP) and other shrunken method (herein named CCC), when they were applied to five maize MET and simulation data; (2) to assess by cross validation the equation which estimates the standard error of predicted means (SEPM) based on the EVP theory; (3) to estimate the genotype × environment interaction (GEI) variance components after applying the EVP shrinkage method to the five maize MET. Empirical data of five maize MET and simulation data were used for cross validation of the methods using the root mean square predictive difference (RMSPD) criterion. The RMSPD of the shrunken EVP predicted cell means was generally smaller than those of the other methods, suggesting that the EVP method was generally better predictor than the other methods. The truncated AMMI was the worst among the four methods studied. The EVP-based equation, which predicts the SEPM, was a good predictor as determined by the RMSPD cross validation criterion, with the advantage that it does not need one replication for validation. Estimates of mean squares, and GEI and error variances associated with the GEI effects were smaller for the shrunken EVP predicted effects than for the original data.