Bayesian AMMI-based indexes for genotype selection: Integrating novel stability measures for enhanced G × E inference

Abstract

Plant breeders utilize the additive main effects and multiplicative interaction (AMMI) model for analyzing yield data from multi-environment trials (METs) to visualize interaction patterns between genotypes and environments. AMMI-based selection indexes, such as the weighted average of absolute scores (WAAS) and the weighted average of absolute scores combining yield (WAASY), guide breeders in identifying superior varieties within METs. Despite being powerful, the frequentist approach of AMMI model and its derived indices presents challenges for identifying genotypes and environments, causing significant genotype-by-environment (G × E) interactions. This study built upon the Bayesian AMMI framework to allow to perform inferences on AMMI-based selection indexes. The Bayesian versions of WAAS and WAASY (Bayesian weighted average of absolute scores and Bayesian weighted average of absolute scores combining yield) were compared with the frequentist approach. A novel stability measure (SM), using Mahalanobis distance, was also proposed and integrated with yield performance into a graphical tool called the stability Mahalanobis trait (SMT) plot. Nine maize genotypes evaluated for grain yield across 20 environments were analyzed. The B-WAAS, B-WAASY, and SM indexes provided informative statistical inference through posterior distribution and credible intervals (highest posterior density [HPD]). HPD intervals allowed grouping similar genotypes based on stability and performance, offering reliable information for selection and recommendation. The SMT plot allows a direct comparison to an ideal scenario of high stability, facilitating the identification of genotypes aligned with breeding goals by analyzing the four quadrants. Genotypes in quadrant IV, exhibiting both high yield and high stability, are particularly valuable for breeding programs.