The evaluation of cultivars using multi-environment trials (MET) is an important step in plant breeding programs. One of the objectives of these evaluations is to understand the genotype by environment interaction (GEI). A method of determining the effect of GEI on the performance of cultivars is based on studies of adaptability and stability. Initial studies were based on linear regression; however, these methodologies have limitations, mainly in trials with genetic or statistical unbalanced, heterogeneity of residual variances, and genetic covariance. An alternative would be the use of random regression models (RRM), in which the behavior of the genotypes is characterized as a reaction norm using longitudinal data or repeated measurements and information regarding a covariance function. The objective of this work was the application of RRM in the study of the behavior of common bean cultivars using a MET, based on Legendre polynomials and genotype-ideotype distances. We used a set of 13 trials, which were classified as unfavorable or favorable environments. The results revealed that RRM enables the prediction of the genotypic values of cultivars in environments where they were not evaluated with high accuracy values, thereby circumventing the unbalanced of the experiments. From these values, it was possible to measure the genotypic adaptability according to ideotypes, according to their reaction norms. In addition, the stability of the cultivars can be interpreted as variation in the behavior of the ideotype. The use of ideotypes based on real data allowed a better comparison of the performance of cultivars across environments. The use of RRM in plant breeding is a good alternative to understand the behavior of cultivars in a MET, especially when we want to quantify the adaptability and stability of genotypes.

The Mauritia flexuosa L.f. tree is of immense socioeconomic significance in the Brazilian Middle North Region for its manifold benefits, but mainly for its fruit. However, the potential of this species has still not been extensively studied. The objectives of this work were to study the phenotypic and genotypic correlations between the characteristics of the M. flexuosa fruits and to establish the direct and indirect effects of the secondary characteristics of the fruit on the pulp yield. Samples of ten fruits per genotype were gathered from four natural populations, from 240 different genotypes. These samples were assessed in terms of the fruit, almond and hull weights, equatorial and polar fruit diameters, and the fruit, almond and pulp, volumes, as well as the pulp yield. The genotypic correlations showed greater magnitude, higher than the phenotypic correlations, and both were significant and revealed equal signs. The indirect selection of the M. flexuosa genotypes with greater fruit weight and almond volume favored the increase in the pulp yield in this fruit species.