Comparing Bayesian and Frequentist Approaches for GGE Bi-plot Analysis in Multi-Environment Trials in Sorghum

The GGE stands for genotype main effect (G) added to genotype by environment (GE) interaction. GGE-biplot a graphical tool was applied to study adaptation of 18 sorghum genotypes to the six environments using data from a multi-environment trials (MET) conducted in randomized complete block designs at two locations during 2009-2012 in Sudan. Analysis of variance was used to test the significance of GE interactions, estimates of variance components and predicted means were obtained using restricted maximum likelihood REML method. A number of priors for the variance components of the model were considered for Bayesian analysis using R2WinBUGS software. The best set of priors was selected using the deviance information criterion (DIC). Thus, the predicted estimates of GE means using REML method for frequentist approach and posterior estimates for the Bayesian approach were used for the graphical presentation of the genotypes and the environments. In frequentist approach, the first two principal components accounted for 64% of variation in total GGE interactions where the individual two principal components accounted for PC1=43% and PC2=23% respectively. The Bayesian approach accounted for 89% variation in the total GGE interaction with PC1=58% and PC2=31% respectively. The Bayesian GGE biplot analysis explained much larger proportion of variation in GGE interaction in comparison with frequentist approach, and thus resulted in a more powerful inference on the adaptation of genotypes to the environments considered.