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.

中文翻译：

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异方差多环境试验的贝叶斯 GGE 模型

基因型×环境相互作用（GEI）的剖析是植物育种管道最后阶段和品种推荐的关键方面。用于分析这种相互作用的线性-双线性模型，例如加性主效应和乘性相互作用 (AMMI) 和基因型加 GEI (GGE)，通常假设跨环境的残差方差同质，这会影响估计，从而影响解释和结论。我们的主要目标是提出一个 GGE 模型，该模型使用贝叶斯推理考虑跨环境的异方差性，并评估其在解释真实和模拟数据中的含义。假设共同方差的 GGE 模型也适用于比较目的。贝叶斯推理的极大灵活性被转移到双图上，允许为基因型和环境评分构建可信区域。当忽略异方差性时，对基因型稳定性和适应性的推断可能会发生变化。当使用真实数据时，环境之间不同的相关模式也会影响目标环境的代表性和辨别力。异方差建模允许将环境聚类为子组，对 GEI 具有类似的效果。所提出的 GGE 模型对于处理多环境试验中异质变化的场景更加充分和现实，这对于利用 GEI 很有用。环境之间的不同关联模式也会影响目标环境的代表性和辨别力。异方差建模允许将环境聚类为子组，对 GEI 具有类似的效果。所提出的 GGE 模型对于处理多环境试验中异质变化的场景更加充分和现实，这对于利用 GEI 很有用。环境之间的不同关联模式也会影响目标环境的代表性和辨别力。异方差建模允许将环境聚类为子组，对 GEI 具有类似的效果。所提出的 GGE 模型对于处理多环境试验中异质变化的场景更加充分和现实，这对于利用 GEI 很有用。