Adaptability and stability analyses of plants using random regression models.

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.

Combined selection in beans for cycle, plant architecture and grain yield / Seleção combinada em feijão para ciclo, arquitetura de planta e produtividade de grãos

The selection of common bean cultivars for high agronomic performance can be difficulty by genotype x environment interaction. The objectives of this work were to evaluate if common bean cultivars differ for cycle, plant architecture and grain yield in different growing seasons, and to select early, upright and highly grain yield common bean cultivars, by the use of selection index. For this, five experiments were conducted in the randomized blocks design, with three replicates. A total of 26 common bean cultivars were evaluated and the multiplicative index was used to select superior cultivars. A significant cultivar x season interaction for flowering, cycle, insertion of the first pod, insertion of the last pod, number of pods per plant and grain yield was observed. The common bean cultivars have early or semiearly cycle in rainy season and upright plant architecture. The cultivars Macanudo, BRS Campeiro, IAPAR 81, and IPR Juriti presented high grain yield in most growing seasons. The four superior common bean cultivars selected by the multiplicative index were BRS Campeiro, Macanudo, IPR Juriti, and Guapo Brilhante. The cultivars BRS Campeiro, Macanudo, and IPR Juriti presents earliness, upright plant architecture, and high grain yield and will be selected for the breeding program.

A seleção de cultivares de feijão com alto desempenho agronômico pode ser dificultada pela ocorrência de interação genótipo x ambiente. Os objetivos desse trabalho foram avaliar se cultivares de feijão diferem para ciclo, arquitetura de planta e produtividade de grãos em diferentes épocas de cultivo e selecionar cultivares de feijão precoces, eretas e altamente produtivas pelo uso de índice de seleção. Para tanto, cinco experimentos foram conduzidos em delineamento de blocos ao acaso, com três repetições. Um total de 26 cultivares de feijão foram avaliadas e o índice multiplicativo foi usado para selecionar cultivares superiores. Interação cultivar x época de cultivo significativa foi constatada para a floração, ciclo, inserção da primeira vagem, inserção da última vagem, número de vagens por planta e produtividade de grãos. As cultivares de feijão avaliadas possuem ciclo precoce ou semiprecoce no cultivo de safra e arquitetura de planta ereta. As cultivares Macanudo, BRS Campeiro, IAPAR 81 e IPR Juriti apresentaram alta produtividade de grãos na maioria das épocas avaliadas. As quatro melhores cultivares de feijão selecionadas pelo índice multiplicativo foram BRS Campeiro, Macanudo, IPR Juriti e Guapo Brilhante. As cultivares BRS Campeiro, Macanudo e IPR Juriti apresentam precocidade, arquitetura de planta ereta e alta produtividade de grãos, portanto serão selecionadas pelo programa de melhoramento.