**8. Results obtained in breeding programs aimed at drought tolerance**

The study was conducted by Lobato et al. [72] with six populations, with two parents P1 and P2, and F1, F2, BC1, and BC2 generations, derived from the cross between LP 97-28 (low tolerance to drought) × IPR-Uirapuru (high tolerance to drought). Regarding production components, the grain production (GP) results reveal that the evaluated plants had values between 0.01 and 9.78 g. The low and high means for all populations were 2.30 and 6.86 g, respectively (Table 1). The F2 generation showed the best performance. The low and high values for variance were obtained in the parental P1 (1.51) and F2 (8.88) generations, respectively. In relation to the average weight of 100 seeds (W100s), the values ranged between 12.56 and 29.64 g. In addition, the low and high means were 18.49 and 21.83 g, with the greatest means observed in the F1 and P2 populations (Table 1). The greatest variance of 11.12 was obtained in the F2 generation. For the number of pods per plant (NPP), the plants studied had values between 1 and 19, and the lowest and highest means were 2.70 and 7.02, respectively (Table 1). The best result was found in the F2 generation, while the lowest value was observed in the BC1 generation. The highest variance of 8.08 was observed in the F2 generation (Table 1). For the number of seeds per pod (NSP), the plants collected in this study had values between 1.0 and 6.8. The low and high means were 4.17 and 4.64 in populations P1 and BC2, respectively (Table 1). Additionally, the best result was found in generation BC2. The low and high variances were 0.38 and 1.54 (Table 1) and were obtained in the P2 and F2 generations, respectively [72].

The estimated means of the segregating generations and the existence of high genetic variation (*σ* <sup>2</sup> ) coupled with additivity indicated the presence of transgressive individuals. These findings enabled the selection of promising genotypes for drought tolerances higher than those of IPR-Uirapuru and LP 97-28, the parent lines in this study. In terms of the estimated variances in the study populations, the best performances were observed for the segregating generations (F2, BC1, and BC2), which demonstrated higher values for all traits compared to the parent (P1 and P2) and F1 generations (Table 1). These results can be attributed to the large segregation of genes and, consequently, the higher amplitude in the distribution of the drought stress tolerance values, indicating genetic variation for the evaluated traits [73]. Similar results to those found in this study in terms of the GP of the F2 generation were reported by Szilagyi [74] for experiments with the common bean grown under adequate conditions (irrigation) and drought stress. This author studied production components in six populations derived from crosses between F332 and Ardeleana.

Higher variances for GP, W100s, NPP, and NSP were observed in the F2 generation, revealing greater plant heterogeneity and suggesting great variability within this population. Genetic variability is extensively explored in breeding programs; it serves as the basis for selection and provides opportunities to establish a desired characteristic [75]. Smaller variances were obtained in the parents, confirming homozygosis in these populations due to the line and cultivar.

**Figure 5.** Seed placed into substrate (A); *V. unguiculata* seedling (B); plants with 14 days (C); trifoliate leaf (D); data

obtained during experiment (E); infra-red gas analyzer (F).

572 Abiotic and Biotic Stress in Plants - Recent Advances and Future Perspectives

Regarding genetic control, the values of the phenotypic (*σ<sup>p</sup>* 2 ), environmental (*σ<sup>e</sup>* 2 ), genotypic (*σg* 2 ), additive (*σ<sup>a</sup>* 2 ), and dominance variances (*σ<sup>d</sup>* 2 ) for grain production were 8.88, 2.97, 5.91, 5.75, and 0.16, respectively (Table 2). The genotypic variance corresponded to 66.6% of the phenotypic variance (total), and the additive variance accounted for 97.3% of the genetic variance. In W100s, the phenotypic, environmental, genotypic, additive, and dominance variances were 11.12, 2.55, 8.57, 7.66, and 0.91, respectively (Table 2). For this characteristic, the genotypic variance accounted for 77.1% of the total variance, while the additive variance corresponded to 89.4% of the existing genetic variance. In relation to NPP, the phenotypic, environmental, genotypic, additive, and dominance variances were 8.08, 2.33, 5.75, 4.73, and 1.02, respectively (Table 2). The phenotypic variance accounted for 71.2% of the genetic variance. Additionally, the additive variance corresponded to 82.3% of the genotypic variance. For the NSP, the phenotypic, environmental, genotypic, additive, and dominance variances were 1.54, 0.56, 0.98, 0.76, and 0.22, respectively (Table 2). The genotypic variance represented 63.7% of the phenotypic variance in this characteristic. The additive and dominance variances contributed to 77.6 and 22.4% of the genotypic variance, respectively [72].

The results indicate high contributions of additive variances in relation to genotypic variance and intense additive allelic interactions on all the evaluated traits. The existence of high additive variance suggests the identification of superior genotypes [76]. Typically, breeding methods that take advantage of high additive variance to obtain genetic gains are more important for the improvement of autogamous species, such as *Phaseolus vulgaris* [73].

According to this research, the use of additive variance is recommended as an indicator when studying GP, W100s, NPP, and NSP in the cross (LP 97-28 × IPR-Uirapuru), because it accounts for a significant portion of genotypic variance.

The estimates of broad-sense heritability (*H*<sup>2</sup> %) ranged between 63.6 and 77.0% (Table 2), and the high and low values were found in the W100s and NSP characteristics, respectively. The estimates of narrow-sense heritability (*h*<sup>2</sup> %) oscillated between 49.2 and 68.9% (Table 2), and the high and low values also corresponded to the W100s and NSP characteristics.

The average degree of dominance (add) values were 0.22, 0.48, 0.65, and 0.76 for the GP, W100s, NPP, and NSP characteristics, respectively (Table 2). The minimum number of genes (mng) that controlled the GP, W100s, NPP, and NSP characteristics were 4.7, 4.4, 8.6, and 5.5, respectively (Table 2).

The results related to broad- and narrow-sense heritabilities described in this study are high because studies involving populations are normally conducted under field conditions and high levels of environmental interference reduce genetic variances and produce lower heritabilities. Higher heritability coefficients may be caused by greater additive genetic variance, lower environmental variance, or minor interactions between genotype and envi‐ ronment [77]. Additionally, similar results for broad- and narrow-sense heritabilities indicate that the dominance effect is null. However, if the broad-sense heritability is higher than the narrow-sense heritability, the dominance effect is present [78].


Regarding genetic control, the values of the phenotypic (*σ<sup>p</sup>*

574 Abiotic and Biotic Stress in Plants - Recent Advances and Future Perspectives

), and dominance variances (*σ<sup>d</sup>*

contributed to 77.6 and 22.4% of the genotypic variance, respectively [72].

for a significant portion of genotypic variance.

estimates of narrow-sense heritability (*h*<sup>2</sup>

respectively (Table 2).

(*σg* 2

), additive (*σ<sup>a</sup>*

2

2

2

5.75, and 0.16, respectively (Table 2). The genotypic variance corresponded to 66.6% of the phenotypic variance (total), and the additive variance accounted for 97.3% of the genetic variance. In W100s, the phenotypic, environmental, genotypic, additive, and dominance variances were 11.12, 2.55, 8.57, 7.66, and 0.91, respectively (Table 2). For this characteristic, the genotypic variance accounted for 77.1% of the total variance, while the additive variance corresponded to 89.4% of the existing genetic variance. In relation to NPP, the phenotypic, environmental, genotypic, additive, and dominance variances were 8.08, 2.33, 5.75, 4.73, and 1.02, respectively (Table 2). The phenotypic variance accounted for 71.2% of the genetic variance. Additionally, the additive variance corresponded to 82.3% of the genotypic variance. For the NSP, the phenotypic, environmental, genotypic, additive, and dominance variances were 1.54, 0.56, 0.98, 0.76, and 0.22, respectively (Table 2). The genotypic variance represented 63.7% of the phenotypic variance in this characteristic. The additive and dominance variances

The results indicate high contributions of additive variances in relation to genotypic variance and intense additive allelic interactions on all the evaluated traits. The existence of high additive variance suggests the identification of superior genotypes [76]. Typically, breeding methods that take advantage of high additive variance to obtain genetic gains are more important for the improvement of autogamous species, such as *Phaseolus vulgaris* [73].

According to this research, the use of additive variance is recommended as an indicator when studying GP, W100s, NPP, and NSP in the cross (LP 97-28 × IPR-Uirapuru), because it accounts

The estimates of broad-sense heritability (*H*<sup>2</sup> %) ranged between 63.6 and 77.0% (Table 2), and the high and low values were found in the W100s and NSP characteristics, respectively. The

The average degree of dominance (add) values were 0.22, 0.48, 0.65, and 0.76 for the GP, W100s, NPP, and NSP characteristics, respectively (Table 2). The minimum number of genes (mng) that controlled the GP, W100s, NPP, and NSP characteristics were 4.7, 4.4, 8.6, and 5.5,

The results related to broad- and narrow-sense heritabilities described in this study are high because studies involving populations are normally conducted under field conditions and high levels of environmental interference reduce genetic variances and produce lower heritabilities. Higher heritability coefficients may be caused by greater additive genetic variance, lower environmental variance, or minor interactions between genotype and envi‐ ronment [77]. Additionally, similar results for broad- and narrow-sense heritabilities indicate that the dominance effect is null. However, if the broad-sense heritability is higher than the

the high and low values also corresponded to the W100s and NSP characteristics.

narrow-sense heritability, the dominance effect is present [78].

), environmental (*σ<sup>e</sup>*

%) oscillated between 49.2 and 68.9% (Table 2), and

) for grain production were 8.88, 2.97, 5.91,

2

), genotypic

**Table 1.** Number of evaluated plants (*n*), means (*m*), and variances (*σ* <sup>2</sup> ) from grain production (GP), average weight of 100 seeds (W100s), number of pod per plant (NPP), and number of seeds per plant (NSP) obtained in six populations (P1, P2, F1, F2, BC1, and BC2), derived from cross between LP 97-28 × IPR-Uirapuru, Maringá-PR, Brazil, 2011 [72].


**Table 2.** Estimates of phenotypic variance (*σ<sup>p</sup>* 2 ), environmental variance (*σ<sup>e</sup>* 2 ), genotypic variance (*σ<sup>g</sup>* 2 ), additive

variance (*σ<sup>a</sup>* 2 ), dominance variance (*σ<sup>d</sup>* 2 ), broad-sense heritability (*H*<sup>2</sup> %), narrow-sense heritability (*h*<sup>2</sup> %), average degree of dominance (add), and minimum number of genes (mng) related to grain production (GP), average weight of 100 seeds (W100s), number of pod per plant (NPP), and number of seeds per plant (NSP) obtained in six populations (P1, P2, F1, F2, BC1, and BC2), derived from cross between LP 97-28 × IPR-Uirapuru, Maringá-PR, Brazil, 2011 [72].In differential of selection (DS), gain by selection (GS) and predicted genetic gain, the characteristics of grain production, average weight of 100 seeds, number of pods per plant, and number of seeds per pod had differential of selection (DS) values ranging from 1.49 to 4.85 (Table 3).


**Table 3.** Mean initial in F2 generation (Mi), mean of selected plants in F2 generation (Ms), differential of selection (DS), gain by selection (GS), gain by selection expressed in percentage [(GS (%)], and predicted gain genetic (PGG) related to grain production (GP), average weight of 100 seeds (W100s), number of pod per plant (NPP), and number of seeds per plant (NSP) obtained in six populations (P1, P2, F1, F2, BC1, and BC2), derived from cross between LP 97-28 × IPR-Uirapuru, Maringá-PR, Brazil, 2011 [72].

The high and low values were obtained for the W100s and the NSP, respectively. In relation to gain by selection (GS), the GP, W100s, NPP, and NSP characteristics had values of 2.93, 3.29, 2.37, and 0.73, respectively (Table 3). When expressed as a percentage (% GS), the grain production trait had the highest value for gain by selection at 42.7%. The lowest value was found for the average weight of 100 seeds. The predicted genetic gain (PGG) values were 9.79, 24.58, 9.39, and 5.34 for the GP, W100s, NPP, and NSP characteristics, respectively (Table 3) [72].


**Table 4.** Coefficients of phenotypic correlation between grain production (GP), average weight of 100 seeds (W100s), number of pod per plant (NPP), and number of seeds per plant (NSP) obtained in six populations (P1, P2, F1, F2, BC1, and BC2), derived from cross between LP 97-28 × IPR-Uirapuru, Maringá-PR, Brazil, 2011 [72].

Regarding correlations between characteristics, results indicated that all characteristics were directly proportional (Table 4), except between the NSP and NPP, which were inversely proportional. Additionally, the results show a high correlation (0.96) between the NPP and GP. Moderate associations were found between the GP and W100s and the W100s and NSP within six generations (P1, P2, F1, F2, BC1, and BC2) derived from crosses between LP 97-28 and IPR-Uirapuru [72].
