It was found that the progenies variation source was significant (p ≤ 0.01) for all traits, indicating the presence of genetic variability (Table 1). The environments (locations-generations) were very contrasting as it can be seen by the significance of the environment’s variation source.
The progenies x environments interactions were significant (p ≤ 0.01) for all traits, except for the diameter. It shows that the progenies behavior did not match in the different analyzed environments.
Table 1
Significance of P-values obtained in evaluating 62 common bean progenies across three generations (S0:1, S0:2 and S0:3) and three sites of the joint variance analysis, for the following traits: height at flowering (Height1, cm), height at harvest (Height 2, cm), stem diameter (Diameter, cm), mass of 100 grains (M100, g), plant architecture score at flowering (Score 1), plant architecture score at harvest (Score 2) and grain yield (Yield, kg ha− 1).
Source of variation | DF | Mean Square |
Height1 | Height2 | Diameter | M100 | Score1 | Score2 | Yield |
Environment (E) | 7 | 11449.67** | 29080.47** | 96.28** | 1828.53** | 52.51** | 72.07** | 57641338.50** |
Treatment (T) | 63 | 2245.95** | 1560.77** | 5.34** | 108.15** | 18.33** | 22.99** | 863988.60** |
Among progenies (P) | 61 | 1895.07** | 1459.57** | 4.39** | 97.33** | 13.81** | 17.70** | 873074.10** |
Controls (C) | 1 | 465.16 | 279.50 | 10.45** | 82.37 | 42.72* | 102.67** | 884277.42 |
(P) x (C) | 1 | 25430.62** | 9015.63* | 58.16** | 793.70** | 269.51** | 265.62** | 289482.18 |
T x E | 441 | 302.17** | 266.54** | 1.31 | 38.91* | 1.41** | 1.65** | 324757.20** |
P x E | 427 | 276.55** | 246.84** | 1.31 | 39.65** | 1.33** | 1.58** | 321356.10** |
C x E | 7 | 336.15** | 409.72** | 0.26 | 19.40 | 3.56** | 1.60** | 351530.96** |
P x Wi x E | 7 | 1830.96** | 1324.88** | 2.67* | 13.41 | 4.09** | 5.96** | 505435.91* |
Mean Error | 840 | 153.24 | 131.27 | 1.30 | 33.69 | 0.75 | 1.13 | 239892.59 |
**, *: significant at 1% and 5% probability, respectively, according to the F test.
An alternative to providing a guideline for the recurrent selection program is to try to identify the traits, to be subjected to selection, that have greater heritability. The higher the h2 estimate of the trait, the more likely it is to predict which trait or traits are most likely to gain from recurrent selection. It can be seen in Table 2 that when considering selection based on the average of the progenies, the estimate of this parameter varied between traits. The lowest value was 59.2% for the mass of 100 grains. Initially, the h2 estimates were obtained in the broadest sense. However, the contribution of dominance variance (\(\:{\sigma\:}_{D}^{2}\)) to the total genetic variance in autogamous plants is small (Ramalho et al. 2024). Additionally, as inbreeding progresses, there is a reduction in the frequency of heterozygous loci, and evidently the participation of \(\:{\sigma\:}_{D}^{2}\) decreases. Thus, the h2 estimates, among the average progenies, in this situation can be considered in a strict sense, that is, with a practically integral response to selection.
Comparing the h2 estimates available in the literature is not easy because it depends on the variability between the progenies evaluated, the number of replications and the environments, and experimental precision. The literature presents numerous reports of h2 estimates for grain yield in bean crops. Ramalho et al. (2024) presents a compilation of results from the literature. Estimates ranged from 10.6 to 88%. Most grain yield estimates were lower than those obtained in the present study. Pires et al. (2014) used eighth cycle progenies from the same recurrent selection program and found h2 estimates for grain yield in the average progenies very similar to those obtained in the present study. It indicates that recurrent selection of plant architecture did not affect grain yield variability.
Height, stem diameter and plant architecture estimates from h2 estimates were greater than 70%. Some estimates of h2, referring to traits linked to plant architecture, are relatively frequent in the literature. The values found varied from 51.7–87% (Paula et al. 2020; Pereira et al. 2017). Therefore, the h2 obtained here are above or within the range of variation reported in the literature.
Table 2
Estimate of heritability, gain with selection based on index Z (\(\:\varSigma\:\)Z) and expected gain with (SG) for the following traits: height at flowering (Height1, cm), height at harvest (Height 2, cm), stem diameter (Diameter, cm), mass of 100 grains (M100, g), plant architecture score at flowering (Score1), plant architecture score at harvest (Score2) and grain yield (Yield, kg ha− 1). Data obtained from the 62 progenies from S0:2, S0:3 and S0:4 generations assessment in Lavras-MG, Lambari-MG and in Patos de Minas-MG.
Parameters | \(\:\varSigma\:\)Z | Height1 | Height2 | Diameter | M100 | Score1 | Score2 | Yield |
h2(%) | 74.61 | 85.41 | 83.09 | 70.24 | 59.26 | 90.34 | 91.09 | 63.19 |
LL | 63.80 | 77.29 | 73.99 | 57.44 | 43.05 | 85.42 | 86.74 | 47.02 |
UL | 83.15 | 89.41 | 87.87 | 80.16 | 73.45 | 93.20 | 93.82 | 75.30 |
SG(%) | 5.47 | 23.81 | 5.82 | 7.25 | 8.07 | 9.85 | 11.54 | 7.54 |
RX(Z)(%) | - | 9.5 | - | 4.63 | 2.3 | 8.74 | - | 2.44 |
LL; UL: lower and upper limit, respectively, of the confidence intervals, at 5% probability of the heritability (h2) in the mean of progenies; RCX(Z): response correlated to the traits according to the selection done in the index Z (\(\:\varSigma\:Z).\)
The main focus of this research was to verify whether early selection, that is, carried out at the time of plant flowering, was efficient in relation to traits related to plant architecture. The main alternative to evaluate what is found is through estimates of correlations between traits at different times.
The estimates of phenotypic and genetic correlations showed behavior that was in principle coincident at different times (Table 3). It is worth highlighting the phenotypic and genetic correlation between the different heights in the two evaluation periods. It was of great magnitude (rF =0.90 and rG= 0.97). High rG for height at both ages (j and j') is expected, as one of the causes of genetic correlation is the pleiotropic effect of genes (Ramalho et al. 2024) which occurs in this case as this correlation involves the same trait at two ages. Obviously, the genes are the same, rGjj’ must be 1.0. As it was not exactly one, the most likely explanation would be the error associated with the estimate. Another explanation is that the genes are the same and they express at different times, which would contribute to the progenies x evaluations age interaction. Which doesn't seem to be the case at the moment.
As an early selection strategy, what matters is the correlation of the phenotype of the same trait at age j and the genotype at age j' (r(FjGj')). Bernardo (2020), comments that it is obtained by the expression r(FjGj') = h2j raj’. Where, h2j is the heritability of the trait at the time of evaluation j and rGjj' has already been defined, rGjj' must be 1.0 or close to this value, will be the heritability of this trait obtained at the flowering of the plant. The estimate of h2, for this trait, was of great magnitude (Table 2).
The architecture of the plant, in reality, is the trait of greatest interest for carrying out selection and at the same time recombination during flowering. In this condition, the recurrent selection gain per unit of time would be double that achieved at the end of the cycle. The architecture is an index that involves some traits among them, the height, the number of branches and the angle of insertion of the branches, among others. This assessment is subjective and carried out visually. In this case, the genes that are expressed at flowering for architecture are also expected to be the same ones that are expressed closer to harvest. Estimates of genetic correlation for architectural leakage confirm this fact (rGjGj’ = 0.97) (Table 3). In this case, even though the evaluation was visual, the estimate of h2j was high. Therefore, early assessment is expected to work and the selection of individuals to be recombined can be carried out at the beginning of flowering at the site itself.
The estimates of the phenotypic correlation between stem diameter and plant architecture scores showed medium magnitude. They were significant and near 60% in both cases.
Table 3
Estimates of phenotypic (above the diagonal) and genetic (below the diagonal) correlations obtained from the mean of the progenies in all evaluated environments, for the following traits: height at flowering (Height1, cm), height at harvest (Height 2, cm), stem diameter (Diameter, cm), mass of 100 grains (M100, g), plant architecture score at flowering (Score1) and at harvest (Score 2) and grain yield (Yield, kg ha− 1).
| Height1 | Height2 | Diameter | M100 | Score1 | Score2 | Yield |
Height 1 | 1 | 0.9** | -0.23 | 0.12 | -0.51** | -0.47** | -0.28* |
Height 2 | 0.93 | 1 | 0.03 | 0.16 | -0.27* | -0.28* | -0.27* |
Diameter | -0.31 | 0.00 | 1 | 0.27* | 0.62** | 0.57** | -0.16 |
M100 | 0.15 | 0.24 | 0.37 | 1 | 0.17 | 0.13 | -0.12 |
Score1 | -0.58 | -0.32 | 0.73 | 0.23 | 1 | 0.93** | 0.03 |
Score2 | -0.53 | -0.32 | 0.68 | 0.18 | 0.97 | 1 | 0.03 |
Yield | -0.45 | -0.45 | -0.25 | -0.26 | 0.04 | 0.03 | 1 |
**, *: Significant at 1% and 5% probability, respectively, according to t-test.