Forty-eight hybrids and nineteen parents of mung bean were evaluated in a randomized block design (RBD) with two replication during Kharif 2018, spring-summer 2019 and summer 2020 at Research farm, C.S. Azad University of Agriculture and Technology, Kanpur, Uttar Pradesh, India. Hybrids and parents were evaluated in the plot in three lines with a spacing of 30 × 10 cm. All the recommended package of practices was followed for raising the healthy crop. Individual location-wise analysis of replicated data on seed yield per plant was followed by a pooled analysis. AMMI analysis was conducted using R software package amiability (Ajay et al. 2019). The data was also submitted to an AMMI model stability study using the conventional procedure.

The equation of AMMI model is as under: Yger=μ+αg+βe+∑nλnγgnδenρgeτger

Where, Y_ger represents seed yield per genotype g in season e; μ is the grand mean of seed yield per plant, α_g represent the deviation of hybrids from the grand mean; β_e similarly represent deviation of the environment from grand mean, λ_n represent PCA n-axis eigenvalue; γ_gn and are the PCA scores of genotype and environment for PCA axis n. ρ_ge is the AMMI model’s residual and τ_ger represent random error. AMMI uses ordinary ANOVA to assess main effects, while principal component analysis is used to analyze non-additive (interaction) effects leftover by the ANOVA model. If all axes are not used, PCA decomposes the interaction into PCA axes 1 to n, leaving residuals. The interaction between genotype and environment may be inferred by multiplying the genotype’s interaction principal component axis (IPAC) score by the environmental IPCA score.

Among the many statistical methods adopted for analysis of hybrids by environment interaction (GEI) and phenotypic stability (Crossa et al. 1990). Regression based technique was widely used (Eberhart and Russell 1966; Perkins and Jinks 1968) due to its simplicity and the fact that the information on adaptive response was easily applicable to locations (Annicchiarico 1997). Zobel et al. (1988) compared the tradition statistical models such as analysis of variance (ANOVA), principal component analysis (PCA) and linear regression with AMMI analysis and showed that traditional analysis was not always effective in the interpretation of the multi-environment trait data structure.

Understanding of G×E interaction in plant species is of importance because it has implications for economic yield. In present study, ANOVA on individual location indicated the presence of significant difference among hybrids. The significant of variance due to G×E in pooled analysis indicated the presence of genotype × environment interaction. Hence, the data were analyzed for further AMMI analysis. AMMI analysis indicated significant differences among the hybrids, among seasons, and also genotype × environment interaction for seed yield per plant. In the present investigation, the analysis of variance showed significance for IPCA1 and IPCA2. Among these IPCA1 along recorded for 89.80 percent of the total variance. Hence IPCA1 alone may decide the G×E interaction within the study.

The most potent interpretative technique for AMMI models is biplot analysis. Biplots are graphed in which the genotype and environment mean are presented on the same axes (X-axis) to make the interrelationship between the two easier to see. The AMMI1 biplot depicts the significant effects (genotype mean, and environment mean) and IPCA1 scores for hybrids, parents, and environments against each other, while the AMMI2 biplot plots IPCA1 and IPCA2 scores. AMMI2 biplots do not exhibit the main effects of genotype or environment so do not show adaptation (Table 2).

PDM139 × KM2355, IPM147 × KM2355, KM2241 × MH1142 and PM1125 × MH1142 were among the hybrids with IPCA 1 scores close to zero, indicating that the environment less influenced these hybrids. Similarly, parents, IPM 147-1, KM2241, and KM2255 had IPCA 1 scores close to zero (Fig. 1).

As a result, the aforementioned stable hybrids were adaptable to all three seasons, namely Kharif, Spring Summer, and Summer. PDM139 × PM1126, IPM147 × PM1126, KM2241 × KM2355, and KM2352 × MH1142 hybrids, as well as their parents KM2328, SML1811, KM2360, and IPM147, were shown to be high yielders with high environmental interaction. As a result, these hybrids and parents were discovered to be unstable. The hybrids KM2241 × MH1142, KM2360 × KM2355, PM11125 × MH1142, and PDM139 × KM2355 produced good yields while interacting with the environment in a controlled way. As a result, these hybrids are suitable for all growing seasons. Summer was the highest yielding season, whereas the spring Kharif season had little contact with the growing seasons.

In AMMI 2 biplot, IPCA1 and IPCA2 values were plotted (Fig. 2.). This graph shows that sites with short spokes do not exert strong interactive forces, while those with longer spokes exert strong interaction. All the three seasons – E1, E2, and E3 had long spokes and exerted strong interaction. Among the three environments – E1 (Kharif season) had short spoke with the origin, which has a less interactive effect. Hybrids PDM139 × KM2355, PM1125 × MH1142 KM2360 × PM1126 and IPM147 × MH1142 and parent IPM147-1 and KM2355 were very close to the center of the origin. These hybrids and parents nearer to the origin were non-sensitive to environmental interaction forces. Hence, these hybrids can be classified as stable, and those distant from the origin were sensitive and had significant interactions.

Based on the preceding discussion, it can be concluded that hybrids PM1125 × MH1142 and PDM139 × KM2355 were found less interacting with high seed yield per plant. These hybrids may be recommended for growing in all three seasons’ viz., Kharif, sprin- summer and summer.