3.1 AMMI (Additive Main Effect and Multiplicative Interaction) model analysis
Table 2
Analysis of variance of Grain Yield using AMMI models
| SS | Percent explained | Percent accumulated | DF | MS | F | PROBF |
ENV | 47570701 | 83.03 | 83.03 | 1 | 47570701 | 134.5187 | 0 |
GEN | 4721944 | 8.24 | 91.27 | 19 | 248523.4 | 0.70277 | 0.79395 |
ENV*GEN | 5001274 | 8.73 | 100 | 19 | 263224.9 | 0.74434 | 0.75231 |
PC1 | 5001274 | 100 | 100 | 19 | 263224.9 | 3.03839 | 0.00691 |
PC2 | 0 | 0 | 100 | 17 | 0 | 0 | 1 |
Residuals | 14145450 | 0 | 0 | 40 | 353636.3 | NA | NA |
ENV = Environment; GEN = Genotypes; SS = Sum of squares; DF = degree of freedom; MS = Mean Sum of squares; PC1 = Principal component 1; PC2 = Principal component 2; ENV*GEN = Environment*Genotypes.
The AMMI model ANOVA showed, 83.03%, 8.24%, 8.73% is marked to environment, genotype and environment*genotype interaction (Table 2.). This means the grain yield is significantly (p < 0.05) affected by environment. Likewise, PC1 explained 100% of the sum of squares which means there is 100% interaction between the environment and genotype with DF 19 of PC1 and DF 17 of PC2.
AMMI model has been used as a statistical tool for fixed effect multiplicative models analysis to find the GE interaction by implying genotypes clusters based on the similarity of their response (Bocianowski et al., 2019). X-axis of AMMI model denotes environment and genotype main effect and effect of interaction is represented by Y-axis (Tekdal & Kendal, 2018). If genotypes are closer to the X-axis, then they are more stable than the farthest from the same axis. The genotypes located on the right of the Y-axis are the above average yielding genotypes and that located left to the Y-axis are below average yielding genotypes(Hamurcu, 2023).
Figure 1 shows AMMI biplot of 20 genotypes in two environments (heat drought and irrigated) for grain yield. Genotypes that are cluster together shows the similar characteristics and adaptation. NL 1386 and BL 4407 shows the same response in the environment. The genotypes NL 1368, NL 1381 and NL 1404 are adaptive genotype across drought environment and NL 1179 being the highest yielding genotype in heat drought environment. Similarly, NL 1412, NL 1413and NL 1417 are the adaptive line in irrigated environment with genotype NL 1384 being the highest yielding genotype and is unstable in irrigated environment. Similarly, the lowest yielding genotype under irrigated environment is NL 1386 and BL 4407 and heat drought environment is NL 1369.
Table 3
Interaction Principal Components of AMMI (PC1and PC2) with Yield of 20 elite wheat lines.
S.N. | NAME | Yield | PC1 | PC2 |
1 | 1 (Bhrikuti) | 1930 | -0.03466 | -2.2*10− 08 |
2 | 10(NL 1369) | 1350 | 0.473417 | 2.95*10− 10 |
3 | 11(NL 1376) | 1615 | 0.371802 | -1.1*10− 09 |
4 | 12(NL 1381) | 1702.5 | 0.179459 | 1.36*10− 10 |
5 | 13(NL 1384) | 2295 | -1 | -1.3*10− 09 |
6 | 14(NL 1386) | 1795 | -0.10724 | 7.41*10− 11 |
7 | 15(NL 1387) | 1432.5 | 0.106877 | -7.9*10− 11 |
8 | 16(NL 1404) | 1487.5 | 0.295591 | 9.31*10− 10 |
9 | 17(NL 1412) | 1855 | -0.10724 | 7.41*10− 11 |
10 | 18(NL 1413) | 2137.5 | -0.43749 | 1.83*10− 10 |
11 | 19(NL 1417) | 2092.5 | -0.46652 | -2*10− 10 |
12 | 2(BL 4407) | 1802.5 | -0.13264 | 4.87*10− 10 |
13 | 20(NL 1420) | 2100 | -0.2016 | 3.2*10− 10 |
14 | 3(BL 4669) | 1672.5 | 0.360915 | -1.2*10− 09 |
15 | 4(BL 4919) | 1952.5 | -0.35039 | 1.34*10− 09 |
16 | 5(Gautam) | 1730 | -0.15805 | 1.49*10− 10 |
17 | 6(NL 1179) | 1742.5 | 0.266558 | -9.6*10− 10 |
18 | 7(NL 1346) | 1810 | 0.262929 | -1*10− 09 |
19 | 8(NL 1350) | 1687.5 | 0.310107 | -3.8*10− 10 |
20 | 9(NL 1368) | 1497.5 | 0.368173 | -1.1*10− 09 |
3.2 GGE biplot analysis – “which-won-where model”
The farthest genotypes from the origin are joined to form the Which-won-where graph, containing all other genotypes within the polygon with one genotype in the polygon’s vertex. Next perpendicular lines are drawn from the biplot origin on each side of the polygon, dividing the biplot into several sector (Sciences et al., 2017). In which-won-where model of GGE biplot analysis, a polygon was made by joining the elite lines of wheat in two tested environments. This model shows 6 sectors where two tested environment lies in two sectors.
The vertex genotype in each sector represent the highest yielding genotypes in the location that was within that specific sector, according to the polygonal view of the biplot which revealed which genotype performed best in which environment(Oyekunle et al., 2017).
Genotypes NL 1346, NL 1179, NL 1350, BL 4669 lies in the drought environment sector (1) and are responsive in this environment with NL 1346 having the farthest vertex from the origin and is the winning elite line of drought environment. Likewise, Fig. 2 indictes genotypes NL 1384, NL 1413, NL 1417, BL 4919, NL 1386, BL 4407 are responsive to irrigated environment (2) with genotype NL 1384 being the winning elite line for this environment as it lies the farthest from the origin. Genotypes NL 1420, Bhrikuti, NL 1376, NL 1381, NL 1368, NL 1404, NL 1369, NL 1387, Gautam lies beyond the sector of tested environment, so these lines are not adapted in either environment. Genotype NL 1412 which lies in the center is stable in both the environments.
3.3 Mean VS stability of the genotypes
The GGE model gives plant breeders a lot of discretion for yield and stability selection simultaneously. It is effective for method for achieving high mean yield genotypes with acceptable stability(Kendal et al., 2019). The identification of genotypes with high average performance and stability across a variety context is made possible through mean and stability analysis by GGE biplot, graphically through Average Environment Coordinates (AEC) with the arrowhead. The other line running through AEC and origin is called AEC abscissa.
Above Fig. 3 shows that genotypes Bhrikuti, BL 4407, NL 1386, NL 1420, NL 1412 are both above average yielders and stable whereas genotypes NL 1384, NL 1346, NL 1413, NL 1417, NL 1381 are above average yielders but are less stable. Genotypes BL 4407, NL 1387, Gautam are below average yielders and are stable but NL 1179, NL 1350, BL 4669, NL 1376, NL 1368, NL 1404, NL 1369 are both less stable and below average yielders.
3.4 Evaluating the idealness of the environment (Discriminativeness VS Representativeness)
The biplot was useful tool for evaluating the environment, something that the AMMI model was unable to do because of its lack of discriminative power and representativeness (SOLONECHNYI et al., 2018). Discriminativeness is the capacity of an environment or location to define genotypes, whereas representativeness is the capacity of the tested environment to reflect the other tested environment(Hasan et al., 2022). The cosine of the angles between the environment vectors indicates the correlations between test environments, with acute angles denoting the strong positive correlation, obtuse angle denoting a significant negative correlations or a cross over GEI of genotypes, and right angle denoting no association (SOLONECHNYI et al., 2018).
The vector length of the environment represents the discriminating ability. In the Fig. 4 the vector of irrigated environment is longer than that of the drought environment, implying that the irrigated environment has a greater standard deviation and thus higher discriminative ability than the drought-stricken environment. The cosine angle between the environment vector represents its representative ability; Larger the angle, less representative the environment is. The cosine of the vector between the environment was perpendicular meaning that there is no correlation between the environment or they are not associated.
3.5 Ranking genotypes
A biplot tool called Ranking genotypes, is used to test the best ideal variety from among the tested kinds. The most suitable variation is that which is located near the arrowhead in the innermost circle(Khan et al., 2021). Other tested variations can be graded in relation to the innermost variety based on how closely they resemble the innermost ideal variety(Bishwas et al., 2021).
If genotype is found closer to the ideal genotype, it is considered to be more desirable. As per Fig. 5, NL 1420 is the ideal genotype with which other genotypes are tested. Genotypes NL 1413, Bhrikuti, NL1417, BL 4919 are the desirable ones.
The general ranking from the biplot is given below:
NL 1420 > NL 1413 > Bhrikuti > NL 1417 > BL 4919 > NL 1412 > NL 1386 > BL 4407 > NL 1346 > Gautam > NL 1179 > NL 1381 > NL 1350 > BL 4669 > NL 1384 > NL 1376 > NL 1368 > NL 1404 > NL 1387 > NL 1369
Below is the comparison of 20 elite wheat line positions on mean yield and biplot ranking for both drought and irrigated environments:
Table 4
Comparison of the rank of 20 elite wheat lines based on mean yield and biplot ranking
Genotype rank | Mean Yield Ranking | Biplot Ranking |
1. | NL 1384 | NL 1420 |
2. | NL 1413 | NL 1413 |
3. | NL 1420 | Bhrikuti |
4. | NL 1417 | NL 1417 |
5. | BL 4919 | BL 4919 |
6. | Bhrikuti | NL 1412 |
7. | NL 1412 | NL 1386 |
8. | NL 1346 | BL 4407 |
9. | BL 4407 | NL 1346 |
10. | BL 4669 | Gautam |
11. | NL 1179 | NL 1179 |
12. | Gautam | NL 1381 |
13. | NL 1381 | NL 1350 |
14. | NL 1350 | BL 4669 |
15. | BL 4669 | NL 1384 |
16. | NL 1376 | NL 1376 |
17. | NL 1368 | NL 1368 |
18. | NL 1404 | NL 1404 |
19. | NL 1387 | NL 1387 |
20. | NL 1369 | NL 1369 |