A Multi-Attribute Evaluation of Genotype-Environment Experiments Using Biplots and Joint Plots Graphics

In plant breeding studies, some of objectives are to study the interaction between genotype and environment (GEI), evaluating genotypic stability and adaptability. The additive model with multiplicative interaction (AMMI) has been widely used for cases in which there is only one response trait. In this work we propose the combined use of the Tucker3 model, joint plot graphics, and Procrustes analysis to analyze data from a GEI experiment with multiple responses. The joint use of these two methodologies allows a direct comparison with the results of the AMMI analysis. This method was applied to a dataset related to an experiment to evaluate the darkening of carioca bean grains by the natural grain darkening method and by the accelerated darkening method installed in the randomized complete block design, in 2016. Nineteen carioca bean genotypes in six environments in the State of São Paulo, Brazil, and eight attributes were evaluated, which consists of the measurement time in each of the grain darkening methods. The results indicated that the Tucker3 model is efficient to deal with the triple arrangement of the interaction genotypes × environments × attributes and that the use of the joint plot is advisable, because it allowed the evaluation of genotypic stability and adaptability. The use of Procrustes analysis associated with the Tucker3 model allowed the identification of general conclusions for the different attributes.