The analysis of genetic parameters of a quantitative trait is strong when many genotypes are considered. In addition, the experimental precision with incomplete block designs and the comparison between the treatments performed in this study can explain numerous hypotheses involving genetic parameters.
Genetic variation is fundamental for the selection of superior individuals (Charles Brummer et al. 2011; Ceccarelli 2015). In the case of root distribution, possible variants were found among the 64 evaluated populations (Table 2). In terms of breeding, other studies have also found significant differences in root distribution between bean accessions, cultivars and mutant populations (da Rocha et al. 2010); differences between bean strains with different growth habits were also detected (Velho et al. 2018). In the presence of genetic differences, the study on genetic parameters can be effective, since they help in the choice of the appropriate selection method (Thompson et al. 2005).
Five genetic parameters were estimated for the trait under study (phenotypic variance, genetic variance, environmental variance, broad sense heritability and average degree of dominance). All the parameters presented high values when the progeny BAF07 x BAF53 was involved (Table 3), compared to the others, mainly for the parameters of genetic variance (0.0126), heritability (74.10) and average degree of dominance (20.51). Heritability is an important tool in breeding programs because it allows estimating how much the phenotypic variation of the trait resulted from genetic effects, as well as the expected genetic gains and the genetic values of individuals from a certain population (Hill 2010). In other words, additivity is the predominant inheritance of the trait root distribution (de Melo et al. 2016).
Regarding the average degree of dominance, the results indicated that the progeny BAF07 x BAF53 rpresents non-additive allelic interactions. The average degree of dominance can be defined as the relative position of the heterozygote in relation to the mean of the homozygotes, about the type of interaction between the alleles (absence of dominance) (Thompson et al. 2005). Together, these results indicate that the hybridization between genotypes from different gene pools may increase the use of available genetic variability, which has already been observed in other species, including maize (Rovaris et al. 2017).
In contrast, estimates of the progenies of the same gene group showed high genetic similarity (Table 3). The likely common ancestry for the two gene groups is reported worldwide, and the Andean group originated from few individuals belonging to the Mesoamerican group (Bitocchi and Nanni 2012; Schmutz et al. 2014). In Brazil, the lack of studies on the origin of the genotypes and information about commercial cultivars makes it difficult to determine which types of beans were introduced, besides when, where and which human groups brought the cultivation of the species (Freitas 2006). Therefore, it is difficult to affirm or disprove that common genotypes were used during the development of commercial genotypes.
Inbreeding, or the likelihood of two randomly taken alleles, in a single locus, to be identical by descent, limits the possibility of new gene combinations in their offspring. The narrow genetic base and self-fertilization processes produce gene blocks that reduce the potential for recombination in offspring (Canci et al. 1997). Studies estimating recombination rates in Arabidopsis reported that the absence of differences between homologous chromosomes reduced the recombination rate potential (Salomé et al. 2012). Likewise, the scant evidence about the difference between parents and progenies suggests the occurrence of additive gene activity for the trait root distribution.
Evidence of heterosis expression was only detected in progenies resulting from genitors between gene pools (Table 4). In the selection of the parents for the composition of the crossing blocks, those presenting different agronomic traits were chosen from the two existing bean gene groups, Mesoamerican and Andean cultures. As stated by Shull in 1908, heterosis is regarded as the superiority of F1 hybrid progenies over the mean of their parents. This phenomenon is proportional to the genetic dissimilarity among the parents used in the directed hybridization. This fact was actually verified in only 7% of the comparisons between offspring and parents (between gene pools). The suggested heterosis model explains the variation observed only for the BAF07 x BAF53 population. As exemplified by the BAF07 x Uirapuru progeny, an inbreeding model seems to clarify the root distribution behavior (Table 7).
The traits of agronomic interest since the beginning of the domestication process have undergone intense selection in constant search for individuals that provide superior products. The introduction of breeding programs intensified the targeted selection processes by promoting changes that impacted the crops, especially for grain yield and its primary components (Bertoldo et al. 2012). In addition, the development of cultivars generally occurred in environments favorable for the development of plants (high amount of nutrients and water ad libitum). These conditions do not favor root growth, since these nutrients are available in the most superficial layer of the soil. In other words, there is a negative correlation between shoot growth and root growth. Thus, the selection pressure exerted on the aerial part of the bean may have reduced the genetic variability of the root. Thus, the genotypes were not sufficiently contrasting for the trait root distribution.
Insuficient evidence of significant differences between parents and offspring actually resulted in negative heterosis (Tables 4, 5), and only one case of superior performance for the parent was detected (Table 5). Gene interactions may be the genetic explanation for this phenomenon. Gene expression is given by the production of a certain protein, which results in the the expression of the phenotype. When a change in the genetic constitution is detected, the protein produced and its function may change or not. In the heterozygous condition, the genes in activity in the root distribution expression can be masked by other genes, which hinders root growth - also known as epistasis (Borel et al. 2016), which has already been observed in Arabidopsis thaliana (Gärtner et al. 2009; Fiévet et al. 2010). Evidence of epistatic interactions was found for grain yield and its primary components in beans (Johnson and Gepts 2002; Moreto et al. 2012; Borel et al. 2016). In these studies, progenies from bean crosses between gene pools were inferior to their parents.
Considering the common ancestry, the narrow genotype base used in breeding programs and the selection pressure exerted on shoot traits, the formation of gene blocks is one of the hypotheses for the absence of heterosis. One of the solutions to increase the genetic base for the trait root distribution is the adoption of cycles of recurrent crosses, besides the breaking of gene blocks so as to obtain a more comprehensive gene recombination. Recurrent selection cycles, together with the selection of the parents, seek to increase the frequencies of desirable alleles for quantitative traits, which results in phenotypic classes with superior performance for the specific trait. Genetic gains have already been obtained for bean culture through recurrent selection for agronomic traits and resistance to diseases (Amaro et al. 2007; Leite et al. 2017).
The results obtained in this study for the first segregant population (F2) are in agreement with the findings for other progenies studied in complete diallel, also involving the parents BAF07 and IPR Uirapuru (Toaldo et al. 2013). These authors verified the presence of heterosis for most F2 progenies, but the most common occurrences involved highly contrasting genotypes. Further studies have revealed the superiority of F2 and F3 progenies, but it was observed in the occurrence of increased contribution of additive genes throughout the segregating generations (De Melo et al. 2016). Thus, in order to obtain satisfactory gains in root breeding and displace the mean of this trait, it will be necessary to promote hybridization between more contrasting parents.