Testing multiplicative terms in AMMI and GGE models for multienvironment trials with replicates

Key messageFor analysing multienvironment trials with replicates, a resampling-based method is proposed for testing significance of multiplicative interaction terms in AMMI and GGE models, which is superior compared to contending methods in robustness to heterogeneity of variance.AbstractThe additive main effects and multiplicative interaction model and genotype main effects and genotype-by-environment interaction model are commonly used for the analysis of multienvironment trial data. Agronomists and plant breeders are frequently using these models for cultivar trials repeated across different environments and/or years. In these models, it is crucial to decide how many significant multiplicative interaction terms to retain. Several tests have been proposed for this purpose when replicate data are available; however, all of them assume that errors are normally distributed with a homogeneous variance. Here, we propose resampling-based methods for multienvironment trial data with replicates, which are free from these distributional assumptions. The methods are compared with competing parametric tests. In an extensive simulation study based on two multienvironment trials, it was found that the proposed methods performed well in terms of Type-I error rates regardless of the distribution of errors. The proposed method even outperforms the robust FR test when the assumptions of normality and homogeneity of variance are violated.