Heterogeneity of variances in the Bayesian AMMI model for multienvironment trial studies

Abstract

In analyses of multienvironment trials, it is common to assume homogeneity of variances in additive main effect and multiplicative interaction (AMMI) models for further inferences about the genotypes × environment interaction (GEI). However, it is not always reasonable to adopt such an assumption because it could mislead the evaluation and selection of the best genotypes. In this context, modeling the heterogeneity of variance jointly with GEI models has been of particular interest in plant breeding, since the experimental accuracy may float across the trial network. In this study, we used the Bayesian AMMI model in real and simulated frameworks to study GEI effects in the presence of heterogeneous variances (BAMMI‐H) across environments, highlighting the differences that can arise when this scenario is neglected. The findings indicate that neglecting the differences among the experimental variances across environments can influence the biplot precision and the conclusions regarding adaptability and stability. The main differences observed between the naive AMMI (assuming homogeneity) and BAMMI‐H biplots were related to the biplot precision for the genotypic and environment scores and the ability to recover information about experimental differences among the trials in the biplot. The results observed in this study suggest the importance of taking the heterogeneity of variance into account in the AMMI analysis to select genotypes for stability and adaptability.