AMMI Analysis of variance
The AMMI analysis of variance for the pooled means of five yield traits across three environments (E1, E2 and E3) of seven cotton genotypes is presented in Table 2. The results revealed that the greatest proportion of variation was explained by the environmental sum of squares, followed by the genotype sum of squares and the GEI sum of squares for traits such as the number of bolls per plant (56.9), seed cotton yield (48.39) and lint yield (40.40). However, for the trait ginning percentage, the GEI contribution to the sum of squares is greater than the environmental sum of squares and the genotypic sum of squares. This clearly indicated the varied response of genotypes across environments. The presence of a considerable amount of GEI sum of squares necessitates studying the stability of cotton genotypes in different environments. The partitioning of the GEI by the AMMI revealed two multiplicative axes, namely, PC1 and PC2. These two principal components cumulatively accounted for a cent percent of the GEI interaction sum of squares for all the five traits studied.
Table 2
AMMI Analysis of variance for seed cotton yield and related traits across three environments
Source
|
DF
|
SCY
|
LY
|
BN
|
|
|
SS
|
MS
|
% V
|
SS
|
MS
|
% V
|
SS
|
MS
|
% V
|
ENV
|
2
|
4717992
|
2358996***
|
48.39
|
462766.9
|
231383***
|
40.40
|
393.47
|
196.67***
|
56.9
|
GEN
|
6
|
2750548
|
458424.6***
|
28.21
|
344510.6
|
57418***
|
30.07
|
170.98
|
28.50***
|
24.73
|
GEN*ENV
|
12
|
2281099
|
190091.6***
|
23.39
|
338043.6
|
28170***
|
29.51
|
126.92
|
10.58**
|
18.36
|
PC1
|
7
|
2049790
|
292827.1***
|
89.85
|
289289
|
41327***
|
85.57
|
81.74
|
11.68**
|
64.40
|
PC2
|
5
|
231308.8
|
46261.76
|
10.14
|
48754.6
|
9751**
|
14.42
|
45.17
|
9.04*
|
35.59
|
Residuals
|
42
|
1742857
|
41496.6
|
|
82862
|
1973
|
|
137.44
|
3.27
|
|
Contd.. |
AMMI-I and AMMI-II
The AMMI model adopts a unified strategy that combines principal component analysis of G×E interactions with analysis of variance for genotype and environment main effects. The results are illustrated graphically in a biplot that allows concurrent visualization of genotype stability and mean performance by plotting the main effect means on the abscissa and PCA 1 values (interaction effects) on the ordinates. The horizontal line shows the interaction PC1 score of zero, and the vertical line indicates the mean of the genotype effect. The abscissa (X-axis) is divided into two parts by the ordinate (Y-axis), thereby separating the genotypes with below-average means from those with above-average means.
Analysis of variance revealed that E, G and G × E explained 48.39%, 28.21% and 23.39%, respectively, of the total sum of squares respectively for the trait seed cotton yield (Table 2). AMMI analysis revealed an interaction component IPCAI, with 89.86% of the total interaction sum of squares. Genotypes, G3 and G2 were the top yielders, and exhibited above average performance with positive interactions in quadrant I with environment E1 (Fig. 2A). However, genotype G1, with above average performance but with negative interactions, was present in quadrant IV with environment E2, and the remaining genotypes, G4, G5, G6 and G7, with yields less than the grand mean and negative interactions, were confined to quadrant III with E3. Genotypes with IPC scores close to zero exhibit less GEI and better adaptation to all environments. The G7 and G4 scores of the genotypes were close to zero, and the plants were better adapted to all the environments. However, neither of the two entries had a yield higher than the average yield (1352.68 kg/ha) (Fig. 2B, Table 3). This indicates that an adapted and stable variety might not always be a high yielder. A similar result was observed in the AMMI 2 biplot, where genotypes G7 and G4 were close to the center of the biplot, indicating their stability over other genotypes. The AMMI 2 biplot also revealed that E1 was a highly interactive environment where the G3 genotype exhibited a high yield ability; similarly, G1 and G4 performed well in E2 (Fig. 2B). There is no provision for quantitative stability measurement in the AMMI model. A measure of this kind is necessary to quantify and rank genotypes according to the stability of their traits. Accordingly, the AMMI stability value (ASV) is used to study the stability of traits. The variety with the lowest ASV determined by the IPCA axis and IPCA scores is considered the most stable. The lowest ASVs were recorded for G7, G4 and G6, which are considered to be stable. However, the parameter yield stability index blends yield and stability across environments, suggesting that the genotypes that exhibit lower YSI (G7, G3 and G4) are preferred because they have high and stable yield performance (Table 3).
Table 3
IPCA components of genotypes along with ASV (AMMI Stability Value) ranks for different characters
S.No.
|
Entry
|
Code
|
Seed Cotton Yield (Kg/ha-1)
|
E1
|
E2
|
E3
|
Mean
|
RYi
|
IPC1
|
IPC2
|
ASV
|
ASV rank (RASVi)
|
YSI
|
1
|
GBHV-193
|
G1
|
1411.0
|
1805.8
|
1059.4
|
1425.4
|
3
|
-0.33
|
-0.24
|
2.99
|
4
|
7
|
2
|
RAH 1075
|
G2
|
2261.7
|
1472.6
|
1024
|
1586.1
|
2
|
1.00
|
0.25
|
8.87
|
7
|
9
|
3
|
NDLH 2035-5
|
G3
|
2000.4
|
1895.0
|
1084.1
|
1659.8
|
1
|
0.34
|
-0.40
|
3.07
|
5
|
6
|
4
|
BGDS 1033
|
G4
|
1383.6
|
1600.3
|
823.3
|
1269.1
|
5
|
-0.09
|
-0.31
|
0.86
|
2
|
7
|
5
|
SURAJ
|
G5
|
1028.0
|
1483.6
|
1016
|
1175.9
|
6
|
-0.58
|
0.31
|
5.16
|
6
|
12
|
6
|
SAHANA
|
G6
|
1005.8
|
1305.7
|
738.3
|
1016.6
|
7
|
-0.32
|
0.11
|
2.85
|
3
|
10
|
7
|
SIVANANDI
|
G7
|
1483.6
|
1495.0
|
1029.1
|
1335.9
|
4
|
-0.01
|
0.28
|
0.31
|
1
|
5
|
|
|
|
|
|
|
1352.68
|
|
|
|
|
|
|
E1 = Environment 1 (2018-19); E2 = Environment 2 (2019-20) and E3 = Environment 3 (2020-21) |
contd.. |
The results showed that E, as the main component, explained 56.90% of the variability in the number of bolls per plant, whereas G and GE explained 24.73% and 18.36%, respectively (Table 3). AMMI analysis revealed that IPC A1 interacted with 64.41% of the total interaction sum of squares (Fig. 3A). Genotypes G2 and G1, with above average performance and negative interactions, were in quadrant IV, while G7 and G5, with below average numbers of bolls per plant and positive interactions, were in quadrant II. The IPC1 values of four genotypes, viz., G4, G7, G2 and G1were closer to zero and hence stable across all the environments. However, G2 and G1 exhibited means above the overall mean, therefore, these genotypes were found to be stable combined with an increased number of bolls (Fig. 3B, Table 3). AMMI II revealed that G4 and G7 were close to origin indicating that they were less responsive to the environment had greater stability and general adaptability to all the other environments. Genotypes G5 and G3, which were scattered from biplot origin exhibited specific adaptations to E2 and E3, respectively. Among the three environments, E1 was found to be highly interactive with longer vectors compared to the others for the trait number of bolls per plant. In the present study, genotypes G4 (0.28) and G7 (0.40) exhibited the lowest ASVs and were considered as highly stable for the trait number of bolls per plant.
The environment explained 35.50% of the variation in boll weight, the genotype genotype explained 30.44% and the contribution of the GE interaction to the total treatment variation was 34.04% (Table 3).The first two principal components (IPCA1: 73.49% and IPCA2: 26.51%) explained the maximum portion of the GEI. Single genotype G3 exhibited above average performance, and a positive interaction was detected in quadrant I with environments E1 and E2. Similarly, genotypes G1 and G4 which exhibited below average average performance coupled with negative interactions, were present in quadrant III with environment E3 (Fig. 4A). Genotypes G3 (NDLH 2035-5) and G5 (SURAJ) exhibited IPC1 values closer to zero and a mean above the overall mean indicating greater stability for BW across all the test environments (Fig. 4B). Genotypes G5, G3 and G4 had the lowest ASvs and were therefore considered stable for this trait (Table 3).
For the trait lint yield, the effect of E explained 40.40%, while G and G × E explained 30.07% and 29.51%, respectively, of the total sum of squares Table 3). Furthermore, the first two IPCs were highly significant and explained a major portion of the genotype and environment interactions. The genotypes with above average performance coupled with positive interactions, viz., G2 and G3, were present in quadrant I with environment E1 (Fig. 5A). In the AMMI 2 biplot, genotypes G1 and G6 were found close to the origin, indicating their stability and adaptability. However, genotype G2, which was highly scattered from biplot origin and had an IPCA1 value equal to one, is considered a highly unstable genotype and sensitive to environmental conditions for trait lint yield (Fig. 5B). The ASVs suggests that genotypes G1, G6 and G3 have ASVs close to zero; hence, they are stable (Table 3).
The environment as the main effect explained 32.58% of the total sum of squares, whereas G × E and G explained only 39.74% and 27.66% respectively of the variation in the percentage of the trait ginning (Table 3). The first two IPCs explained most of the GE interaction. The single genotype G3 present in quadrant I with environment E3 exhibited above average performance and positive interaction effect. Similarly, genotypes G5, G6, G1 and G2 which are present in quadrants IV with E1, also showed above average performance but negative interaction effects. However, the remaining two genotypes, G4 and G7 which had below average performance and positive interaction effects were present in quadrant II with E2. The genotype G5 had an IPCA 1 score equal to zero and hence was highly stable (Fig. 6A). Analysis of the AMMI 2 biplot also revealed that only G5 was close to its origin and therefore was less sensitive to the environments and stable. G2 is considered to be highly unstable because it is far from the center of the biplot, while entries G3 and G5 performed well in E2, and E3 was beneficial for G4 and G7; likewise, genotypes G1 and G6 interacted favorably with E1 (Fig. 6B). Based on the ASV values, the lowest values were recorded for G5 and G7, indicating that these two varieties exhibit stable trait ginning percentages across environments (Table 3).
GGE biplot (‘whichwonwhere’ pattern)
The ability of a GGE biplot to display the which-won-where/what-won-where pattern of a genotype by utilizing an environment dataset is one of its most fascinating features. In this approach, a polygon is first constructed by joining the genotypes far from the origin consisting of all the other genotypes inside the polygon. Then, starting from the biplot origin, perpendicular lines are drawn to each side of the polygon. The G + GXE variation was 96.55%, 89.48%, 97.14%, 97.92% and 89.59% for the number of bolls per plant, boll weight, seed yield (kg/ha), lint yield (kg/ha) and ginning percentage, respectively, (Fig. 7, Patterns a,b,c,d and e). The environmental indicators were positioned into two, two, two, two and three segments or sections of the biplot for BN, BW, SCY, LY and GP, respectively, with different genotypes winning in each segment. The results confirmed the presence of distinct interactions between genotype and environment for all the traits evaluated. Based on seven genotypes and three environments, the generated GGE biplot was divided into four, seven, five, five and four sections in the clockwise direction for BN, BW, SCY, LY and GP, respectively. For trait BN, genotype G1 in ENV 1 and genotype G3 in ENV 2 and ENV 3 were highly stable, with a greater number of bolls. For the trait BW, genotype G7 in ENV 3 and genotype G3 in ENV 1 and ENV 2 were the best performers with high boll weight. Compared with those of other genotypes, the G2 genotype in ENV 1 and the G3 genotype in ENV 2 and ENV 3 exhibited greater SCY with high stability. For the trait LY, the G3 genotype in ENV 2 and ENV 3 and the G2 genotype in ENV 1 exhibited greater lint yields. In the case of GPs, the G3 genotype in ENV2, the G6 genotype in ENV 1 and the G2 genotype in ENV 2, the G6 genotype in ENV 1 and G2 genotype in ENV3 exhibited increased ginning percentages and stability.
GGE biplot pattern of ‘mean vs. stability’ analysis
The mean vs. stability' view is often referred to as the AEC view with SVP = one, since it aids in genotype evaluations based on mean performance and stability across environments feasible. Genotypes are ranked based on their performance in an environment by drawing a line that passes through the biplot called the “average environment axis,” or the axis of the AEC abscissa. The AEC ordinate passed through the biplot origin and was perpendicular to the AEC abscissa. In this study, the average principal component will be used in all environments and is presented with a circle and single arrow pointing in the direction of higher mean performance for each trait. Stable genotypes are those that fall on the AEC abscissa (horizontal axis) and have almost zero projection onto the AEC ordinate (vertical axis). The mean vs. stability pattern of the GGE biplot revealed 96.55% for BN, 89.48% for BW, 97.14% for SCY, 97.92% for LY and 89.59% for GP (Fig. 8, Pattern, a,b,c,d and e). For the trait BN, genotype G3 was found to be a good performer with a greater number of bolls in ENV 3 and ENV 2, followed by G2 in ENV1. Genotype G5 had the lowest number of bolls per plant. In the case of the trait boll weight, genotypes G3 followed by G5 exhibited the greatest boll weight. The entry 5 reported increased boll weight combined with high stability. Genotypes G2, G6, G1 and G4 were unstable and had lower boll weights. For economic traits such as seed cotton yield (kg/ha) and lint yield, genotype G3 had a greater yield. However, genotypes G4 and G7 exhibited relatively low yields and high stability. For the trait GP, genotype G6 exhibited a higher ginning percentage coupled with increased stability, while genotypes G4 and G7 showed lower GP% with high stability.
Genotype ranking: best and ideal genotype assessment:
An ideal genotype is the one with the highest mean performance and maximal stability. The genotype ranking or comparison with the deal genotype is a biplot view with concentric circles. The ideal genotype is always located in the inner circle, and the head of the arrow is at the center of the circle. In certain instances, such as for trait LY in the present study, if none of the genotypes were located inside the inner circle, genotypes that were located next to or closer to the inner circle were considered ideal. Therefore, genotypes G2, and G1 for BP, genotypes G5,G3 for BW, genotype G3 for LY, genotype G6 for GP were considered as ideal. Genotypes close to the ideal genotype were also more promising and appropriate. Therefore, the ranking of genotypes for the SCY trait was as follows: G3 > G7 > G4 > G1 > G2 > G5 > G6 (Fig. 9, Patterns a, b, c, d and e).
‘Descriminativeness vs. representativeness’ pattern of the GGE biplot
The identification of the best ideal test environment is crucial for a successful breeding technique that eventually helps in the selection of superior genotypes. Two aspects namely, discrimitiveness (the ability of an environment to distinguish genotypes and representativeness (the ability of an environment to represent all other evaluated environments) denote the idealness of the tested environments. The average environmental coordinates (AECs) and test environments are capable of visualizing type-1 environments, type-2 environments and type-3 environments. The type-1 environments are represented by short vectors with average discriminative power indicating the average performance of genotypes. The type-2 environments are shown as the longest vectors with the highest discriminative powers, and are capable of discriminating the performance of genotypes. Type-3 environments are represented as the longest vector with large angles, and are suitable for the negative effects of environments. The ideal environments are those having the longest genotypic vector and located on or at acute angles to the AEC.
Based on this classification, as suggested by Yan et al., 2007, the results of the present study inferred that ENV 2 for BP and BW, and ENV 3 for SCY, LY and GP have short vectors representing the average or similar performance of the genotypes; hence, not much information is available about the genotype differences. The environments with a long vector that forms a shorter angle with the AEC abscissa line are ENV 2 for BP, ENV 1 for BW SCY, LY and GP indicating that the test environments were more representative and discriminative (Fig. 10, patterns a,b,c,d and e).
Relationships among environments:
To illustrate the interactions among environments, lines are drawn from the test environment to the center of the biplot; these lines are otherwise called “ environment vectors”.The cosine of the angle between the vectors of two environments reflects their correlation. In the present study, acute angles (< 90º) were reported for ENV2 and ENV 3 for BN, ENV 2 and ENV 1 for BW, ENV 2 and ENV 3 for SCY, and ENV 1 and ENV 3 for LY and ENV 1 and ENV 3 for GP, indicating the presence of a positive correlation between these environments. This demonstrates that genotypes exhibiting the best performance at ENV 2 can also exhibit the same performance at ENV 3 and vice versa for trait SCY. If the angle between two environmental vectors is an obtuse angle (> 90º), then these environments exhibit negative correlations, such as ENV3 and ENV2 for BW and GP, indicating that there is a negative association; genotypes that performed well in ENV3 do not perform similarly at ENV2 and vice-versa. The third situation, where the angle between two environmental vectors is right angle (90º) or closer to 90º exhibits no correlation or is unrelated, suggesting that each environment has unique genotypic performance. ENV3 and ENV1 for BW, ENV3 and ENV2 for LY and ENV1 and ENV2 for GP exhibited zero correlation for their respective traits (Fig. 11, Patterns a, b, c, d and e).
Ranking of environments:
Based on the ranking of environments, in the present experiment, the environments are ranked ENV 1 and ENV 3 for BP, ENV 1 for BW, and ENV 1 for SCY, LY and GP are considered ideal environments. The center of the concentric rings is the "ideal test environment". Conversely, ENV 2 for BP, ENV 3 for BW, ENV 3 and ENV 2 for SCY and LY, ENV 2 for GP were regarded as the poorest environments for selecting the genotypes across the environment (Fig. 12, Patterns a,b,c,d and e).