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Generalizations of the AMMI and GGE models to understand the interaction between genotypes and environments and between QTL and environments In multi-environmental trials it is common for the genetic characteristics of the cultivars to be influenced by the environments. Thus, the study of tools that allow the analysis of the interaction between genotypes and environments and between QTLs (quantitative trait loci) and environments has gained more and more space among researchers in this area. However, collected data are not always suitable for use with already known models, making it necessary to search for more specific models for certain situations. In this research, we analyzed situations such as data showing heterogeneity of error variance across environments and also contaminated data, which represent data with outlying observations. In such cases, models already known in the literature, such as the AMMI (additive main-effect and multiplicative interaction) model and the GGE (genotype main-effects + genotype environment interaction) model, are not indicated. Here, we verify the use of the robust AMMI model and weighted AMMI in the detection of QTLs and in the analysis of interactions. We also propose the weighted GGE model and evaluate its effectiveness, comparing it with other models. Two data sets were used. The first data from a simulated pepper (Capsicum annuum L.) back cross population using a crop growth model report genotype to phenotype in a nonlinear way, and the second the doubled-haploid Steptoe × Morex barley (Hordeum vulgare L.) population.