Using genotypes adapted to different regions is one of the main ways to increase Brazilian bean yield. The aim of the present study was to assess the genotypic performance of Carioca beans through mixed models. Fourteen Carioca bean genotypes were assessed in four locations in Pernambuco State (Arcoverde, Caruaru, Belém de São Francisco and São João counties) in 2015. The experiments followed a completely randomized block design, with three repetitions. Genetic parameters were estimated according to the REML/BLUP methodology, whereas genotype selection was based on the harmonic mean of relative performance of genetic values method (MHPRVG). The mean genotype heritability had moderate magnitude, high selective accuracy, besides allowing selection of agronomically superior individuals. Genotypes ‘BRS Notável’, CNFC 15480 and ‘IPR 139’ showed good adaptability and grain yield stability. There was agreement among the statistics μ ̂ + g ̂…, stability (MHVG), adaptability (PRVG), and stability and adaptability of genetic values (MHPRVG) in the discrimination of the most productive genotypes, which presented high adaptability and stability. This outcome indicated that these genotypes can be part of the selection criteria regularly used in bean breeding programs.

The objective of this work was to determine the efficiency of a simultaneous selection for yield, stability, and adaptability of bean genotypes of the carioca and black groups. In the 2016 harvest, two experiments were carried out in the state of Pernambuco, Brazil: one for the carioca group, with 20 genotypes, in the municipalities of Caruaru, Arcoverde, and Belém de São Francisco; and the other for the black group, with 12 genotypes, in the municipalities of Caruaru and Arcoverde. The parameters were estimated by mixed models, and selection was performed by the harmonic mean of the relative performance of genetic values, using three strategies: selection based on the predicted genetic value, without interaction; selection based on the predicted genetic value, considering each location; and simultaneous selection for grain yield, stability, and adaptability. The environments affected the phenotypic expression of the carioca bean genotypes, indicating specific adaptation. The average heritability for grain yield showed high values for black bean genotypes, which is a favorable condition for selection, and low values for carioca bean genotypes. The black bean genotypes CNFP 15684, 'BRS Esteio', CNFP 15678, CNFP 15697, CNFP 15695, and 'IPR Uirapuru' show the best performances in the studied environments, simultaneously considering grain yield, adaptability, and stability.

The genotype x environment interaction represents one of the major selection challenges due to the difficulty in identifying effectively superior genotypes. The present study aimed at estimating genetic parameters and selecting genotypes of early Carioca beans by analyzing simultaneous attributes, including yield, adaptability, and stability. In the agricultural year of 2015 and 2016, three trials were conducted, using a randomized block design, with three repetitions each, in the Agreste and Sertao regions of Pernambuco State. The genetic parameters were estimated using the mixed model procedure, and the selection was based on the harmonic mean of the relative performance of genetic values (MHPRVG, abbreviation in Portuguese) method. The environments influenced the phenotypic expression of the bean genotypes during both years, setting a specific adaptation. The mean heritability of the genotypes regarding yield exhibited low magnitude values  in the trials of 2015 (5.78%) and 2016 (13.77%), indicating costly conditions for the selection of the improved genotypes. Genotype CNFC 15856 was selected, considering the genetic gain predicted for yield, by the average and specific performance in the three environments, and by the simultaneous attributes of yield, adaptability, and stability. The MHPRVG method enables the optimized selection of genotypes considering yield, stability, and adaptability; therefore, it should be included in the recommended selective criteria for agronomically superior genotypes in commercial plantations.

Changes in the relative performance of genotypes have made it necessary for more in-depth investigations to be carried out through reliable analyses of adaptability and stability. The present study was conducted to compare the efficiency of different informative priors in the Bayesian method of Eberhart & Russel with frequentist methods. Fifteen black-bean genotypes from the municipalities of Belém do São Francisco and Petrolina (PE, Brazil) were evaluated in 2011 and 2012 in a randomized-block design with three replicates. Eberhart & Russel’s methodology was applied using the GENES software and the Bayesian procedure using the R software through the MCMCregress function of the MCMCpack package. The quality of Bayesian analysis differed according to the a priori information entered in the model. The Bayesian approach using frequentist analysis had greater accuracy in the estimate of adaptability and stability, where model 1 which uses the a priori information, was the most suitable to obtain reliable estimates according to the BayesFactor function. The inference, using information from previous studies, showed to be imprecise and equivalent to the linear-model methodology. In addition, it was realized that the input of a priori information is important because it increases the quality of the adjustment of the model.