The variation source Genotype-Environment interaction (GxE) significantly affected both groups of beans evaluated. Although the effects of genotypes were insignificant for both groups, it is important to note that the GE interaction was significant (Table 1), indicating that the effects of environments should be considered sources of variation in the joint analysis. The absence of significant effects of genotypes may be associated with experiments with contrasting environments.
Table 1
Deviance analysis for grain yield of 28 black bean genotypes (14 normal-cycle and 14 early-cycle genotypes) evaluated in Rio de Janeiro state.
Effect | Normal-cycle black beans | | Early-cycle black bean |
Deviance | Χ2 (LRT) | | Deviance | Χ2 (LRT) |
Genotype | 1,463.06 | 0.04ns | | 1,019.71 | 2.09ns |
G x E | 1,470.94 | 7.92* | | 1,020.33 | 2.71* |
Total | 1,463.02 | - | | 1,017.62 | - |
The variation in response of genotypes in contrasting environments can present challenges in selecting and recommending the optimal genotype since the ranking of genotypes based on yield can vary depending on the interaction with the environment. As evidenced in Fig. 1, the GE interaction resulted in a differentiated ranking of the genotypes in the environments evaluated. Understanding that the genetic makeup of an individual is not altered between different environments, except in cases of mutation induction, any changes in the phenotype of a specific genotype can be attributed to environmental factors, including qualitative traits.
In this sense, an interesting example of phenotypic modification is dominance reversal in Arabidopsis, where one allele controls flowering time and is recessive under continuous light but becomes dominant on shorter days (Taylor et al., 2019). In another example, wheat (Triticum aestivum L.) has a gene for cold resistance located on chromosome 5A. Under high freezing temperatures (-10°C), this resistance is dominant, while at lower temperatures (-14°C), cold sensitivity is dominant (Sutka and Veisz, 1988; Ganeva et al., 2013), demonstrating phenotypic plasticity in response to environmental variations.
The complexity of the GE interaction stems from the lack of correlation between genotypes in different environments, reflecting this interaction's intricate nature. As a result, selecting the most suitable genotype for a given environment becomes a significant challenge. To overcome this difficulty, it is necessary to perform adaptability and stability evaluations of the genotypes in different environments to obtain more precise information about their overall performance. This way, it is possible to identify genotypes with a greater potential for adaptation and stability in different environmental conditions, contributing to better planning and efficiency of breeding programs.
In selecting the genotypes with the best genotypic values (u + g), which are free of the interaction on the average of the four environments, there was the classification according to the components of the average. The genotypes that stood out were: CNFP 10794, CNFP 17489, CNFP 19263, and CNFP 17494 in the normal-cycle group and CNFP 17466, CNFP 17445, CNFP 19741, and CNFP 17459 in the early-cycle group. The cultivars BRS FP403 and BRS Campeiro, of a normal and early cycle, obtained the best values (Table 2).
Table 2
Estimates of predicted genetic gain for grain yield of 28 black bean genotypes (14 normal-cycle and 14 early-cycle genotypes) evaluated in the Rio de Janeiro state.
Normal-cycle black beans | |
Order | Genotypes | g | u + g | Gain | New Media | u + g + gem | |
1 | BRS FP403 | 22.27 | 2,381.20 | 22.27 | 2,381.20 | 2,515,76 | |
2 | BRS Esteio | 12.23 | 2,371.16 | 17.25 | 2,376.18 | 2,445,01 | |
3 | CNFP 19325 | 10.31 | 2,369.24 | 14.94 | 2,373.87 | 2,431,51 | |
4 | CNFP 17489 | 5.68 | 2,364.61 | 12.62 | 2,371.55 | 2,398,92 | |
5 | CNFP 19263 | 2.39 | 2,361.32 | 10.58 | 2,369.51 | 2,375.79 | |
6 | CNFP 17494 | 2.20 | 2,361.13 | 9.18 | 2,368.11 | 2,374.44 | |
7 | CNFP 19349 | 2.15 | 2,361.08 | 8.18 | 2,367.11 | 2,374.10 | |
8 | CNFP 19248 | 1.92 | 2,360.84 | 7.39 | 2,366.32 | 2,372.41 | |
9 | CNFP 16422 | -2.71 | 2,356.22 | 6.27 | 2,365.20 | 2,339.83 | |
10 | CNFP 17058 | -5.66 | 2,353.27 | 5.08 | 2,364.01 | 2,319.06 | |
11 | IPR Uirapuru | -6.00 | 2,352.93 | 4.07 | 2,363.00 | 2,316.69 | |
12 | CNFP 19347 | -8.80 | 2,350.12 | 3.00 | 2,361.93 | 2,296.94 | |
13 | CNFP 19266 | -13.36 | 2,345.57 | 1.74 | 2,360.67 | 2,264.86 | |
14 | CNFP 17457 | -22.62 | 2,336.31 | 0.00 | 2,358.93 | 2,199.69 | |
Early-cycle black bean |
1 | BRS Campeiro | 222.30 | 2,468.52 | 222.30 | 2,468.52 | 2,555.80 |
2 | CNFP 17466 | 206.08 | 2,452.30 | 214.19 | 2,460.41 | 2,533.21 |
3 | CNFP 17445 | 113.36 | 2,359.58 | 180.58 | 2,426.80 | 2,404.09 |
4 | CNFP 19741 | 78.59 | 2,324.81 | 155.08 | 2,401.30 | 2,355.67 |
5 | CNFP 17459 | 61.21 | 2,307.43 | 136.31 | 2,382.53 | 2,331.46 |
6 | CNFP 18310 | 46.14 | 2,292.36 | 121.28 | 2,367.50 | 2,310.48 |
7 | CNFP 19747 | 20.65 | 2,266.87 | 106.91 | 2,353.13 | 2,274.97 |
8 | CNFP 19746 | 10.22 | 2,256.44 | 94.82 | 2,341.04 | 2,260.45 |
9 | CNFP 19745 | 0.48 | 2,246.70 | 84.34 | 2,330.56 | 2,246.89 |
10 | IAC Veloz | -69.75 | 2,176.47 | 68.93 | 2,315.15 | 2,149.08 |
11 | CNFP 17456 | -74.39 | 2,171.83 | 55.90 | 2,302.12 | 2,142.63 |
12 | IPR Uirapuru | -102.20 | 2,144.02 | 42.72 | 2,288.94 | 2,103.89 |
13 | CNFP 19740 | -158.99 | 2,087.23 | 27.21 | 2,273.43 | 2,024.81 |
14 | CNFP 17435 | -353.70 | 1,892.52 | 0.00 | 2,246.22 | 1,753.66 |
u + g: interaction-free genotypic values; u + g + gem: genotypic values for the mean of the environments.
This superiority can be explained by the fact that cultivar BRS FP403 has a high yield, commercial and cooking quality of grains, and moderate resistance to Fusarium wilt and root rot. Besides its wide indication for cultivation, it corresponds to 19 Brazilian states. BRS Campeiro is recommended for the states of Rio Grande do Sul (RS), Santa Catarina (SC), and Paraná (PR), demonstrating its high phenotypic plasticity considering its performance in the state of Rio de Janeiro.
The genetic gains of the genotypes, especially the early group, were significant, reaching 9.9%, 9.54, and 8.04% for BRS Campeiro, CNFP-17466, and CNFP-17445, respectively. Such genotypic values can be useful in selecting and recommending genotypes for environments with similar GE interaction patterns. This generalizability can be attributed to using mixed models that account for genetic and environmental variability by penalizing the predicted genotypic values (Maia et al., 2009). In other words, it is possible to expect a similar performance of the genetic averages (µ + g) of grain yield when the mentioned genotypes are evaluated in different environments. This justifies the better result of the cultivar BRS Campeiro even without a recommendation for the state of Rio de Janeiro.
It is possible to see in Table 3 that the genotypic value for the mean of the environments (µ + g) generated similar results to the HMRPGV method that capitalizes on adaptability and stability simultaneously. This capitalization of the interaction is intrinsic to the choice of more stable genotypes better adapted to the range of environments assessed. The genotypes selected by the criterion of interaction-free genetic means (µ + g) were also superior for HMRPGV. This result allows us to infer that these genotypes presented greater adaptive plasticity in the analyzed environments, besides possessing good predictability, that is, yield maintenance in contrasting environments.
Table 3
Estimates of adaptability and stability (HMRPGV) of genetic values for grain yield of 28 black bean genotypes evaluated in the Rio de Janeiro state.
Normal-cycle black beans | | Early-cycle black beans |
Genotypes | HMRPGV | HMRPGV*MG | | Genotypes | HMRPGV | HMRPGV*MG |
BRS FP403 | 1.07 | 2,519.54 | | BRS Campeiro | 1.14 | 2,558.41 |
BRS Esteio | 1.04 | 2,446.79 | | CNFP 17466 | 1.13 | 2,535.68 |
CNFP 19325 | 1.03 | 2,434.66 | | CNFP 17445 | 1.08 | 2,415.73 |
CNFP 19263 | 1.01 | 2,382.63 | | CNFP 19741 | 1.05 | 2,348.79 |
CNFP 17494 | 1.01 | 2,382.23 | | CNFP 17459 | 1.04 | 2,330.85 |
CNFP 17489 | 1.01 | 2,372.49 | | CNFP 18310 | 1.03 | 2,309.59 |
CNFP 16422 | 1.00 | 2,361.84 | | CNFP 19746 | 1.01 | 2,262.67 |
CNFP 19349 | 0.99 | 2,344.60 | | CNFP 19745 | 1.00 | 2,249.44 |
CNFP 19248 | 0.99 | 2,341.57 | | CNFP 19747 | 0.99 | 2,213.33 |
CNFP 19347 | 0.98 | 2,307.91 | | CNFP 17456 | 0.96 | 2,146.67 |
CNFP 17058 | 0.98 | 2,304.24 | | IAC Veloz | 0.95 | 2,144.67 |
IPR Uirapuru | 0.97 | 2,295.44 | | IPR Uirapuru | 0.94 | 2,105.30 |
CNFP 19266 | 0.97 | 2,277.29 | | CNFP 19740 | 0.90 | 2,030.37 |
CNFP 17457 | 0.93 | 2,200.93 | | CNFP 17435 | 0.78 | 1,753.05 |
The risks in selecting stable genotypes using the results obtained by HMRPGV are minimal since the method uses mixed models and allows simultaneous selection for yield, adaptability, and stability. Thus, it has advantages in considering genotypic effects as random, dealing with unbalanced, non-orthogonal designs and variance heterogeneity, considering correlated errors within locations, and providing genetic values penalized for instability. Furthermore, the results are provided in the magnitude of the trait evaluated and can be applied to various environments (Resende and Thompson, 2004).
Based on the methodology proposed by Annicchiarico (1992), the adaptability and stability of cultivars are evaluated through the superiority of the mean in each environment, estimated from the calculation of a confidence index (I𝑖). Thus, the most stable cultivar is the one whose value is above the mean, with a confidence index equal to or greater than 100 (I𝑖 ≥ 100), indicating a response equal to or greater than the cultivar mean. This approach allows the identification of cultivars that present stable performance in different environments. Thus, it can be observed that seven normal-cycle and eight early-cycle genotypes obtained I𝑖 values higher than 100 (Table 4).
Table 4
Estimates of the stability and adaptability parameters according to the methodology of Annicchiarico (1992) and Lin and Binns (1988), modified by Carneiro (1998), referring to the grain yield of 28 black bean genotypes evaluated in the Rio de Janeiro state.
Normal-cycle black beans |
Genotypes | Annicchiarico | | Lin & Binns |
I𝑖 (%) | | Pi | Pi (+) | Pi (-) |
BRS Esteio | 106.16 | | 24,923.50 | 29,210.07 | 16,350.35 |
BRS FP403 | 111.33 | | 7,831.48 | 11,736.11 | 22.22 |
CNFP 16422 | 101.06 | | 99,519.68 | 149,279.51 | 0.00 |
CNFP 17058 | 96.21 | | 79,565.86 | 81,323.78 | 76,050.00 |
CNFP 17457 | 89.26 | | 193,356.48 | 260,850.69 | 58,368.06 |
CNFP 17489 | 101.27 | | 56,406.25 | 65,703.13 | 37,812.50 |
CNFP 17494 | 101.68 | | 52,907.99 | 70,959.20 | 16,805.56 |
CNFP 19248 | 98.94 | | 52,012.62 | 35,993.92 | 84,050.00 |
CNFP 19263 | 102.07 | | 86,082.06 | 115,316.84 | 27,612.50 |
CNFP 19266 | 94.89 | | 178,280.79 | 244,418.40 | 46,005.56 |
CNFP 19325 | 105.42 | | 27,998.73 | 39,414.06 | 5,168.06 |
CNFP 19347 | 96.74 | | 128,015.74 | 172,656.25 | 38,734.72 |
CNFP 19349 | 99.21 | | 52,917.71 | 32,070.31 | 94,612.50 |
IPR Uirapuru | 95.75 | | 87,431.60 | 79,201.39 | 103,892.01 |
Early-cycle black beans |
BRS Campeiro | 117.84 | | 7,118.06 | 4,201.39 | 10,034.72 |
CNFP 17435 | 71.96 | | 675,212.67 | 850,425.35 | 500,000.00 |
CNFP 17445 | 111.07 | | 97,656.25 | 195,312.50 | 0.00 |
CNFP 17456 | 94.52 | | 218,055.56 | 293,888.89 | 142,222.22 |
CNFP 17459 | 104.79 | | 82,573.78 | 78,342.01 | 86,805.56 |
CNFP 17466 | 116.54 | | 10,850.69 | 7,812.50 | 13,888.89 |
CNFP 18310 | 103.57 | | 93,923.61 | 90,312.50 | 97,534.72 |
CNFP 19740 | 88.03 | | 338,094.62 | 483,472.22 | 192,717.01 |
CNFP 19741 | 105.67 | | 74,904.51 | 38,967.01 | 110,842.01 |
CNFP 19745 | 100.28 | | 134,702.95 | 166,272.22 | 103,133.68 |
CNFP 19746 | 101.02 | | 125,316.84 | 151,250.00 | 99,383.68 |
CNFP 19747 | 98.53 | | 229,600.69 | 0.00 | 459,201.39 |
IAC Veloz | 94.12 | | 205,902.78 | 200,555.56 | 211,250.00 |
IPR Uirapuru | 92.05 | | 248,472.22 | 306,805.56 | 190,138.89 |
The normal-cycle genotypes with the highest Wi value were BRS FP403, BRS Esteio, and CNFP 19325; for the early-cycle genotypes, BRS Campeiro, CNFP 17466, CNFP 17445, and CNFP 19741. Comparing the classification of phenotypic stability of the genotypes obtained by the methodology proposed by Annicchiarico (1992), only with classification obtained by the HMRPGV methodology, it was observed that the genotypes indicated by Annicchiarico methodology as being of general stability coincided with the classification obtained by the HMRPGV methodology.
As for the Lin and Binns (1988) method, modified by Carneiro (1998), the most stable genotype presents the smallest deviation to the maximum yield of each environment, that is, the smallest Pi value. In the method using only Pi decomposition, the most stable/adapted genotypes, when all environments are considered, were BRS FP403, BRS Esteio, and CNFP 19325 for the normal-cycle group and BRS Campeiro, CNFP 17466, and CNFP 19741 for the early-cycle (Table 4). The genotype BRS FP403 in the normal-cycle group was the most stable/adapted to favorable environments, followed by CNFP 19349. CNFP 19747 and BRS Campeiro were the most adapted in the early-cycle group.
The CNFP 16422 and CNFP 17445 genotypes of the normal and early group showed lower Pi values in unfavorable environments when compared to favorable environments or overall Pi, indicating that these genotypes have a specific adaptation to unfavorable conditions. Thus, making its recommendation possible for producers who have low technology. A great advantage of the Lin and Binns method is the immediate recommendation of more stable genotypes due to the uniqueness of the Pi parameter and also an evaluation of the performance of genotypes as a function of environmental variation. In addition, the genotypes identified as more stable and adapted are usually among the most productive.
A study was conducted to evaluate the average performance and stability of genotypes using the WAASB method (Fig. 2). The WAASB method considers all possible combinations of IPCA to quantify stability (Olivoto et al., 2019). Genotypes in quadrants I and II are considered unstable and more likely to contribute to the GE interaction, with those in quadrant I being associated with low yield and those in quadrant II with above average yield. The genotypes in quadrants III and IV, on the other hand, present greater stability, that is, they are less likely to contribute to the GE interaction. However, considering only grain yield, the genotypes in quadrant IV are the most desirable because they present higher averages and less variation between environments, as indicated by WAASB values.
The present study found that some genotypes showed high stability but low average yield: G4, G14, G3, and G8. On the other hand, genotypes G6 and G2 showed higher averages than the general average but were considered unstable. In addition, genotypes G11, G1, G13, and G7 exhibited superior mean and stability. These results demonstrate the importance of considering stability and average yield when selecting genotypes for contrasting environments. Identifying genotypes with high stability and average yield is essential to obtain cultivars adapted to different environmental conditions, which can contribute to increasing the efficiency and sustainability of agricultural production.
The analysis of the environments by the method used allowed the identification of yield patterns and the discriminatory capacity of the genotypes. Environment E3, in quadrant III, was characterized as low yield and poorly discriminatory to the genotypes evaluated. On the other hand, environments E1 and E2, located in quadrant II, showed high yield and were considered important for evaluating the genotypes. These environments were able to generate differences in the performance of the genotypes, suggesting the existence of specific environmental factors, such as soil type, rainfall, and temperature, that significantly influenced the response of the genotypes evaluated. It is important to point out that management and fertilization were conducted uniformly in all environments, which reinforces the hypothesis that the differences observed were the result of intrinsic factors of the environments.