Analysis of variance
The pooled analysis of variance (ANOVA) was used to examine the interactions between different genotypes and environments. Table 3 presents the results of the pooled ANOVA for all genotypes across various environments, focusing on yield and its components. There were significant variations observed among the different environments (E), genotypes (G) and the interaction between genotypes and environments (G×E). In fact, all the variables studied showed highly significant differences (at 5%) in terms of the environment, genotypeand genotype-environment interaction. These significant differences suggest that there is a substantial amount of genetic variation among the evaluated genotypes. Comparable findings are presented in studies conducted by
Zhang et al., (2023) on foxtail millet.
Additive main effects and multiplicative interaction (AMMI)
Analysis of variance for the additive model
AMMI analysis of variance (Table 4) for grain yield per plant (g-1) among 30 genotypes in four environments indicated substantial significance of environmental factors (ENV) (P<0.05, F= 111.558, p<0.001), accounting for 23.42% of yield variance. Replicated environments (REP(ENV)) were not significant (P<0.05, F = 1.382, p = 0.2), contributing minimally (0.56%) to variability. Genotypes (GEN) showed high significance (P<0.05, F = 19.025, p<0.001), explaining 27.94% of variability. The genotype-environment interaction (GEN: ENV) was notably significant (P<0.05, F = 4.123, p<0.001), contributing 18.17% to variance. Residuals accounted for 11.75% of variability, suggesting consistent and stable genotype performance across diverse environments.The AMMI model simplifies genotype-environment interaction (GEI) into three components: PC1, PC2and PC3, each with significant F-values (6.31, 3.55 and 2.24, respectively, all at P<0.05). PC1 dominates, explaining 54.5% of variability (SS
PC1 = 623.1). PC2 contributes 28.7% (SS
PC2 = 327.8),while PC3 explains 16.8% (SS
PC3 = 192.5). The cumulative sum of squares for these three axes is 1143.5 units, providing a comprehensive representation of GEI in the model (Table 4).
The AMMI analysis of variance revealed that environmental factors, genotypesand their interaction significantly contribute to the variability in grain yield per plant. The smaller magnitude of the GEI sum of squares compared to genotypes suggests that certain genotypes consistently perform well across different environments, making them valuable for further research or commercialization in agricultural contexts. Similar results are reported by
Madhavilatha et al., (2022).
AMMI stability biplot-1
The AMMI model generates valuable visual representations, known as biplots, which facilitate the interpretation of genotype-environment interactions. Genotype IPCA scores serve as indicators of their adaptability across diverse environments. Biplots are valid when the first two IPCAs explain most interaction variation and are often used to interpret AMMI results. However, breeders may need more than two IPCA axes for complex models, especially when stability and high yield across various conditions are sought
(Hanamaratti et al., 2009; Verma and Singh, 2024;
Balapure et al., 2016; Kumar et al., 2020; Kesh et al., 2021 and
Hooda and Hooda, 2019).
Fig 1a, displays IPCA1 scores for both genotypes and environments, plotted against the grain yield per plant in the foxtail millet dataset. Numerical markers in blue denote genotypes, while green lines indicate environments. These environments are typically represented as interconnecting axes originating from their respective averages, signifying the trait averages within those environments. The biplot has a broken vertical line at the centre, representing the experiment’s grand mean (14.65 g
-1) and a solid horizontal line at IPCA1 axis score = 0. IPCA1 was very important and explained interaction patterns better than other axes. The x-coordinate shows the main effects (means), while the y-coordinate represents the interaction effects (IPCA1). Genotypes and environments positioned to the right of this line exhibit superior yields to the overall mean, while those on the left side demonstrate yields below the overall mean. The intersection of this axis with the vertical axis divides the biplot into four quadrants. The quadrants II and IV have more potential than quadrants I and III.
In the biplot, 16 genotypes (G13, G21, G5, G19, G6, G4, G17, G18, G8, G25, G11, G9, G7, G22, G3 and G1) and one environment (E1), positioned to the right of the grand mean, were identified as high-yielding, whereas their counterparts with lower yields were on the left side of the grand mean. Furthermore, the high-potential environment (E1) was found in quadrant II, indicated by high positive IPCA1 values. Conversely, the least productive environments (E2, E3 and E4) were situated in quadrant III, with negative IPCA1 values.
Hanamaratti et al., (2009) state that genotypes with low IPCA1 values are considered more stable.
Becker and Leon (1988) propose A stable genotype will exhibit minimal variation in its phenotype
(i.e., physical characteristics) regardless of the environmental conditions in which it is grown.
In quadrant I, genotypes G24, G27, G28, G4, G16, G15, G10and G12 have positive IPCA scores but below-average yields. Quadrant III includes genotypes G29, G6, G7, G13, G30, G14, G26, G2and G11 with negative IPCA scores and below-average yields. Genotypes G10 (IPCA=0.087), G15 (IPCA=0.183), G12 (IPCA=0.283), G16 (IPCA=0.432), G13(IPCA=-0.0716), G6 (IPCA=-0.153), G7 (IPCA=-0.2316) and G29 (IPCA=-0.239) have IPCA values close to zero, signifying stability with minimal GEI interaction. However, these stable genotypes are non-adaptive and low-yielding, making them unsuitable for cultivation. Quadrant II comprises genotypes G21, G9, G17, G18, G3 and G19, characterized by positive IPCA scores and above-average yields. Quadrant IV contains genotypes G8, G23, G22, G25, G5 and G1, which have negative IPCA scores but above-average yields. G21 (IPCA=0.425), G9 (IPCA=0.432), G17 (IPCA=0.463), G8 (IPCA=-0.154) and G23 (IPCA=-0.385) thesegenotypes IPCA values are closer to “Zero (0)”, hence these genotypes consider as stable, high yielding, adaptable and exhibits minimum GEI interaction effect and recommended to general cultivation at Nagaland region. Ideal genotypes exhibit high mean yield with stability, making G8, G9, G21and G22 ideal due to their high mean yield and low IPCA scores.Similar results were observed in studies by
Khan et al., (2021) in Bambara groundnut genotypes.
AMMI-2 stability biplot
The AMMI-2 stability Biplot plotted IPCA1 scores for both genotypes and environments against IPCA2 scores for genotypes and environments. This model uses the first two interaction axes of genotype and environment scores (
Vargas and Crossa, 2000). It helps understand genotype-environment interactions and reveals which genotypes perform best in specific conditions. Genotypes near the centre of the Biplot are considered more stable (
Purchase,1997).
In the GGE biplot analysis (Fig 1b), PC1 and PC2 capture 54.5% and 28.7% of the total variation, respectively, accounting for 83.2% of the variation. In the AMMI 2 biplot, the environmental scores are joined to the origin by side lines. Sites with short spokes do not exert strong interactive forces. Those with long spokes exert strong interaction. In this AMMI Biplot-2, all environments
viz E1, E2, E3 and E4 are connected to the origin; among these environments, E2 and E3 exhibit short spokes, indicating limited interaction strength, while E1 and E4 display long arrows, indicating strong interaction forces. Polygonal biplot is used to identify MEs and superior genotypes in different environments. In this biplot, a polygon is drawn from the connection of the genotypes with the maximum distance from the coordinate origin. Genotypes G1, G11, G9, G24 and G27 were located at the farthest distance and formed a polygon (Fig 1c). These five rays divide the biplot into five sectors and environments are connected to the origin. Thus, two environments, E3 and E2, fell into a similar sector and the vertex genotype for this sector is G11, suggesting that this genotype achieves ideal performance in those specific environments. Similarly, one environment, E4, fell into a single sector and the vertex genotype for this sector was G27, while E1 fell into a single sector and the vertex genotypes for this sector were G24 and G9. Conversely, genotypes in sections without associated environments are less favourable for cultivation across the studied conditions. According to Fig 1b, G2, G25, G14, G15, G20, G23, G18 and G16 were close to the centre and considered to have high grain yield stability. Remain genotypes exhibit medium to instability. The results from this current study support the claims made by
Khan et al., (2021) using 30 Bambara groundnut varieties in four different environments.
AMMI stability value (ASV)
The AMMI stability value (ASV) for grain yield per plant is a critical metric for assessing the stability of various genotypes within this study. According to the ASV methodology, the genotype with the lowest ASV score represents the highest stability, while a higher score suggests reduced stability
(Hassanpanah et al., 2016). Consequently, when genotypes are ranked based on ASV scores, G10 emerges as the most environmentally stable genotype, securing the top position with a low ASV of 0.34 and yield is lower than mean yield. Following closely are G15 (ASV = 0.38, Rank = 2), G7 (ASV = 0.57, Rank = 3), G29 (ASV = 0.61, Rank = 4), G6 (ASV = 0.62, Rank = 5) and G13 (ASV = 0.63, Rank = 6). These genotypes demonstrate notable stability in terms of grain yield per plant, signifying their consistent performance across various environmental conditions. Theses genotypes are not suitable for cultivation due to its lower yield performance. ASV values of grain yield per plant are presented in Table 5.
