Bayesian GGE model for heteroscedastic multienvironmental trials

Abstract

The dissection of genotype × environment interaction (GEI) is a crucial aspect of the final stages of plant breeding pipelines and recommendation of cultivars. Linear-bilinear models used to analyze this interaction, such as the additive main effects and multiplicative interaction (AMMI) and genotype plus GEI (GGE), often assume homogeneity of the residual variances across environments which affects the estimates and therefore, interpretations and conclusions. Our main objective was to propose a GGE model that considers heteroscedasticity across environments using Bayesian inference and to evaluate its implications in the interpretation of real and simulated data. The GGE model assuming common variance was also fitted for comparison purposes. The great flexibility of the Bayesian inference is transferred to the biplots, allowing the construction of credible regions for genotypic and environmental scores. The inference on the stability and adaptability of genotypes might change when heteroscedasticity is ignored. When real data are used, different patterns of correlations between environments also affect the representativeness and discrimination of the target environment. The modeling of heteroscedasticity allowed the clustering of environments into subgroups, with similar effects for GEI. The proposed GGE model was more adequate and realistic to deal with scenarios of heterogeneous variance in multienvironment trials, which can be useful for exploiting the GEI.