A análise multivariada de uma forma bem geral refere-se aos métodos estatísticos que analisam simultaneamente múltiplas medidas em cada indivíduo ou objeto sob investigação. Nesse contexto, entre as técnicas de multivariadas, a análise de componentes principais (ACP) é umas das técnicas estatísticas mais utilizadas na análise de dados em diversas áreas do conhecimento, como agronomia, zootecnia, ecologia, florestal, medicina, etc. Assim, discute-se neste artigo a aplicabilidade e a interpretação da análise de componentes principais e com utilização do gráfico biplot. Também, faz-se uma discussão quanto à escolha da metodologia mais adequada, levando em consideração a informação requerida e os objetivos do pesquisador. 

SummaryThe genotype by environment interaction (GEI)) has an influence on the selection and recommendation of cultivars. The aim of this work is to study the effect of GEI and evaluate the adaptability and stability of productivity (kg/ha) of nine maize genotypes using AMMI model (Additive Main effects and Multiplicative Interaction). The AMMI model is one of the most widely used statistical tools in the analysis of multiple-environment trials. It has two purposes, namely understanding complex GEI and increasing accuracy. Nevertheless, the AMMI model is a widely used tool for the analysis of multiple-environment trials, where the data are represented by a two-way table of GEI means. In the complete tables, least squares estimation for the AMMI model is equivalent to fitting an additive two-way ANOVA model for the main effects and applying a singular value decomposition to the interaction residuals. It assumes equal weights for all GEI means implicitly. The experiments were conducted in twenty environments, and the experimental design was a randomized complete block design with four repetitions. The AMMI model identified the best combinations of genotypes and environments with respect to the response variable. This paper concerns a basic and a common application of AMMI: yield-trial analysis without consideration of special structure or additional data for either genotypes or environments.Key words: genotype environment interaction (GEI), adaptability and stability, additive main effects and multiplicative interaction model, multienvironment trials

The presence of genotype-environment interaction (GEI) influences production making the selection of cultivars in a complex process. The two most used methods to analyze GEI and evaluate genotypes are AMMI and GGE Biplot, being used for the analysis of multi environment trials data (MET). Despite their different approaches, both models complement each other in order to strengthen decision making. However, both models are based on biplots, consequently, biplot-based interpretation doesn't scale well beyond two-dimensional plots, which happens whenever the first two components don't capture enough variation. This paper proposes an approach to such cases based on cluster analysis combined with the concept of medoids. It also applies AMMI and GGE Biplot to the adjusted data in order to compare both models. The data is provided by the International Maize and Wheat Improvement Center (CIMMYT) and comes from the 14th Semi-Arid Wheat Yield Trial (SAWYT), an experiment concerning 50 genotypes of spring bread wheat (Triticum aestivum) germplasm adapted to low rainfall. It was performed in 36 environments across 14 countries. The analysis provided 25 genotypes clusters and 6 environments clusters. Both models were equivalent for the data's evaluation, permitting increased reliability in the selection of superior cultivars and test environments.Key words: genotype × environment interaction, adaptability and stability, additive main effects and multiplicative interaction model, multienvironment trials, cluster analysis, medoids

Comparison of weighted-GGE biplot and weighted-AMMI with other models of interaction genotype × environment Genotype × environment interaction (GEI) is an extremely important issue in plant breeding and production. The selection and recommendation of superior genotypes are hampered due to the occurrence of GEI and represents a major challenge for researchers. In this context, biplot analyzes have been increasingly used in analyzing agronomic data, in which data are represented by a table of two entries of means of GEI. However, the particularities in the biplot graphic hamper its interpretation, and could lead the researcher to errors. There are several models in the literature for DGE analysis (GEI data), among them, the most used are the AMMI model (Additive Main effects and Multiplicative Interaction Models) and GGE biplot (Genotype main effects + Genotype environment interaction). The AMMI model is a statistical method to understand the structure of interactions between genotypes and environments, combining the analysis of variance and principal component analysis, to adjust, respectively, the main effects (G and E) and the effects of GEI. The GGE Biplot groups genotype of additive effect with multiplicative effect of GEI, and submit these to the principal component analysis. There are two problems in using these models: i) can only be used to analyze MET data (multi-environments), which has a unique feature and ii) whose environments are heterogeneous. This paper aims to propose new W-GGE biplot models (Weighted Genotype main effects + Genotype environment interaction) and AMMI-weighted multi-environments for data analysis, and make a comparison between the existing models as AMMI and GGE biplot; mega-environment analysis; genotype evaluation, test environment within each mega-environment and understand the causes of GEI.