Selection for grain size and sieve yield in F3 common bean genotypes using linear mixed models

Grain size is an essential trait in common bean breeding as it determines the acceptance of a new cultivar by producers, consumers, and the industry. The objectives of this study were to identify the ideal traits for selecting common bean lines in the F3 generation to obtain an adequate sieve yield and to identify the best lines for sieve yield by applying early generation selection. Two trials were conducted in two locations during the 2016/2017 crop season. These trials were composed of 300 F3 populations and two parents (used as checks). The experimental design used was an augmented block design without repetition for the treatments (lineages). After harvest, the grain yield, yield components, and sieve yield (SY) were evaluated. In conclusion, selection in the F3 generation can be performed for sieve yield, considering the traits SY12+13, SY14, and relative grain yield, as they present the highest values of heritability and greatest correlation between genotype and performance in the evaluated environments. Additionally, the lines selected to continue in the breeding program are composed of the 15 best lineages for traits SY12+13, SY14, and relative grain yield. Preference should be given to lines that excel in more than one of these traits.