Core Ideas Partitioning of the progenies effect within populations has several advantages. FAI‐BLUP index capitalizes the progenies × growth seasons interaction. The selected inbreed progenies showed favorable genotypes for the target traits. Genetic breeding towards the common bean ideotype can accelerate the cultivar release. ABSTRACTThe goal of breeding programs is selection toward the ideal plant type. In this study, field experiments were performed to select common bean inbred progenies that maximize the probability of extracting superior lines. A total of 124 inbred progenies of three consecutive generations (F2:3, F2:4, and F2:5) were conducted in field experiments over three different environments (one generation in each environment). Seven different traits, related to disease severity, commercial acceptance grain, and yield, were evaluated by best linear unbiased prediction. This work underscored the importance of incorporating population information into the statistical model as a means of comparing progenies from different populations with higher efficacy, even when kinship information between populations is not available. Toward the common bean ideotype, 20 inbred progenies of greater potential were selected using the factor analysis and genotype‐ideotype distance (FAI‐BLUP) index. This index is based on the structural equation models by joining the factor analysis technique (exploratory factor analysis) with the ideotype design (confirmatory factor analysis). The predicted genetic gain was increased for all the traits in all generations. Selection strategies that capture the multitrait information capitalize the progenies × growth season interactions and are based on the ideotype, such as as the FAI‐BLUP index, have the potential for use in genetic breeding toward the common bean ideotype and can accelerate the release of more adapted cultivars.

Correlated information from different genetic sources is absent in most of annual self-pollinated crops using the recurrent selection strategy, which is a breeding strategy that improves crop traits consistently over years. In common bean (Phaseolus vulgaris L.) breeding programs, progenies coming from multiple biparental populations are evaluated across generations of inbred plants with the assumption that the data are not correlated. In this paper, in addition to the effects of progeny, we evaluate the effects of populations and generations and provide information for the selection process in a self-pollinated recurrent selection breeding program. Nineteen progenies were extracted from 20 breeding populations and evaluated at different sowing times across F 3:4 and F 3:5 generations. The evaluated traits were plant architecture, angular leaf spot resistance, grain appearance, and grain yield. Progenies were selected using three methods: means of progenies regardless of generation and population effects; the multigeneration index (MI), which considered the generation effect; and the selection index with parents, populations, progenies, and generations (SIPPPG). We showed that adding variation among progenies correctly weighted for different generations as well as variation among populations yield for an increase in genetic gain. Therefore, selection accuracies of the SIPPPG were the highest for all traits compared with those of MI and when generation and population effects were not considered.

Choosing breeding populations in a common bean (Phaseolus vulgaris L.) breeding program via recurrent selection is a crucial step since it maximizes the effort to find superior inbred lines. The application of the mixed models methodology (REML/BLUP) in predicting breeding values has shown good results in animal and perennial crops breeding programs. Conversely, studies on the application of this methodology to annual crops are still scarce. The present work aimed to use the REML/BLUP methodology to select breeding populations of a common bean breeding program via recurrent selection. Thirty-five F 3 populations were evaluated. Individual plants data were assessed for grain yield and hypocotyl diameter, and the genetic potential of the population was estimated via the mixed models and the Jinks and Pooni's methodologies. A selection index was applied to the selection among and within population, considering both characters simultaneously, using the population and individual BLUP means. REML/BLUP has shown to be a feasible methodology to predict and select the potential of breeding populations, considering more than one character. Selecting individual plants within population provides positive genetic gain estimates for both characters. BLUP breeding values are fundamental to the choice of the number of populations and single plants to be conducted in a common bean breeding program via recurrent selection.