Analysis of Genotype by Environment Interactions using AMMI and GGE Biplot Methods for Soybean Germplasm Lines

Soybean [Glycine max (L.) Merrill], a self-pollinating leguminous crop of significant global cultivation, is a crucial source of food, feed, fuel and oil, valued highly in commercial markets. Approximately 5000 years ago, soybean (Glycine max) was domesticated from its wild precursor, G. soja, in China and subsequently spread globally (Du et al., 2023). Belonging to the Fabaceae family, this legume, often hailed as the “king of beans,” is esteemed worldwide for its versatility, thriving on every continent (Hossain et al., 2024). Soybean, known for its role as a supplement in livestock feed, is a photoperiod-sensitive legume crop that forms a symbiotic relationship with N-fixing rhizobia, making it a typical pod crop. Soybeans are rich in protein, healthy oils and flavones special compounds (Zhong et al., 2024). Soybean seeds, when dry, contain approximately 40% protein and 20% oil (Gunjan et al., 2016; Jin et al., 2023). The increasing demand for vegetable oils and biodiesel has led to a significant rise in soybean oil production, driven by the high oil content in soybean seeds. This has underscored the importance of improving seed composition, particularly in light of growing awareness of health concerns related to dietary fats. Soybean plants are versatile crops utilized in various applications, including soy food production, animal feed, alleviating malnutrition, improving soil fertility and serving as raw material in the processing sector.
       
In Multi-Environment Trials (MET) of soybean, understanding the influence of environment (E) and genotype-environment interactions (GEI) is crucial for effective genotype selection. Strong genotype-environment interactions can complicate the identification of superior genotypes for new environments, posing challenges for breeders and farmers who prefer high-yielding genotypes that lack adaptability and stability within specific environments. Therefore, developing versatile soybean varieties suitable for diverse agricultural settings requires a thorough understanding of environmental influences and genotype-environment interactions. Researchers and breeders have extensively studied and reported grain yield stability across multiple seasons using various soybean genotypes throughout the year (Happ et al., 2021). Regression techniques, like those developed by Eberhart and Russell, 1966, have been foundational in understanding genotype-environment interactions (GEI) patterns. However, AMMI and GGE methods have proven significantly more effective in interpreting GEI data and are widely preferred over other stability analysis methods (Ngalamu et al., 2020; Khan et al., 2021; Ngalamu et al., 2023). The AMMI method integrates ANOVA and principal component analysis to generate a biplot that crucially presents genotype means and their correlation with the first PCA component. The GGE biplot, valued for its ability to elucidate complex genotype-environment interactions in multi-environment breeding trials and agronomic studies, is widely utilized in soybean researches for its precision and adaptability (Kumar et al., 2020; Silva et al., 2021). In 2013, Hagos and Abay proposed using PCA scores and the AMMI stability value (ASV), derived from AMMI analysis, to identify stable genotypes across different locations. The ASV is calculated based on the interaction principal components axis 1 and 2 (IPCA1 and IPCA2) scores for each genotype in the AMMI model (Pramanik et al., 2024). To assess the consistent performance of genotypes, varieties, or cultivars across different seasons, it is crucial to analyze genotype interactions with various environments through GEI analysis. Genotypes with lower ASVs are generally considered broadly adapted. Additionally, genotypes with IPCA2 scores near zero exhibit greater stability, whereas those with higher IPCA2 scores are more sensitive and less stable. The primary objective of the current study was to evaluate the genotype-environment relationship, focusing on yield and trait stability, to identify lines that are broadly or specifically adapted. This research is pertinent for future breeding programs and farmer adoption, achieved through the application of AMMI and GGE biplot analyses.

The 50 advanced soybean breeding lines, derived from diverse crosses (Table 1), represent elite, high-yielding varieties developed at the seed breeding farm of Jawaharlal Nehru Krishi Vishwa Vidyalaya, Jabalpur.  These lines were chosen based on prior multi-season performance, desirable agronomic traits and genetic diversity to ensure a comprehensive evaluation of genotype-by-environment interactions (GEI). The three generations (F7, F8 and F9), of these lines were evaluated during the Kharif seasons of 2019 and 2020 and the Rabi season of 2021, designated as trials E1, E2 and E3 respectively. The experiment was carried in a randomized complete block design (RCBD) with three replications at seed breeding farm, JNKVV, Jabalpur.  The experimental layout maintained a spacing of 45 cm between rows and 7 cm between plants within a row, with each row measuring 3.0 meters in length. For the assessment of quantitative traits, five competitive plants were randomly selected and tagged from each plot in every replication. The JNKVV, located at an altitude of 411.78 m above sea level between 22^o49′ to 20^o80′ North latitude and 78^o21′  to 80^o58′ East longitude. Traits, five competitive plants were randomly selected and tagged from each plot in every replication.


       
To ascertain the genetic variance, a combined ANOVA was performed along with AMMI and GGE model, used to analyse genotype-environment interactions in soybean yield data, captures interaction components effectively through R software version 4.2.The genotype selection index (GSI) was calculated as per Farshadfar et al., (2012).
               
To assess variability in yield performance, a combined analysis of variance (ANOVA) was conducted across the three environments. Genotype-environment interactions were further analyzed using both the additive main effects and multiplicative interaction (AMMI) model and the genotype and genotype-by-environment (GGE) biplot method using R software version 4.2. AMMI was employed to partition and interpret the main effects (genotype and environment) and their interactions using principal component analysis, while GGE biplot focused on visualizing both genotype performance and stability across environments. Together, these models offer complementary insights-AMMI excels in separating interaction effects, whereas GGE provides a more intuitive graphical representation for selecting stable and high-yielding genotypes. Additionally, the genotype selection index (GSI) was calculated as per the method proposed by Farshadfar et al., (2012), combining mean yield and stability metrics to facilitate genotype ranking.

AMMI analysis
 
AMMI Analysis of Variance (ANOVA) revealed that there were significant differences (P<0.001) in the genotype, environment and G × E interactions (Table 2). The AMMI analysis of variance exhibited that 16.96% of the total sum of squares was attributable to environmental, 28.31% to genotypic and 54.66% to G × E effects (Table 2). The magnitude of the G × E interaction sum of squares was 1.93 times higher than that for genotypes, indicating that there were substantial differences in genotypic response across environments. In agreement with these results Amogne et al., (2024) and Dharshini et al., (2024) reported that the genotype by environment interaction effect accounted for the largest total sum of square, followed by genotype and environment. However, this was contrary with the findings from Silva et al., (2021) and Habtegebriel et al., (2023) who reported that the environment is the most contributing, followed by the genotype by environment interaction effect and the genotype effect. The  GEIs were further divided into two significant interaction principal components (IPCAs). The first (IPCA1) and second (IPCA2) interaction principal components were highly significant (Table 2) and they explained a total of 59.3% and 40.7% of the G × E variation respectively. Since both IPCA1 and IPCA2 were significant, best performing and stable genotypes across the three environments could be determined using ASV and GSI scores. These results were in line with the  Amogne et al., (2024) and Dharshini et al., (2024). Based on the mean seed yield (SY), the genotypes G3 (JS 22-65), G9 (JS 22-71), G39 (JS 22-101), G32 (JS 22-94) and G2 (JS 22-64) recorded mean seed yields of 14.58, 13.22, 12.90, 12.33 and 11.83, respectively, across environments. AMMI stability parameters such as the AMMI Stability Value (ASV) and Genotype Selection Index (GSI) provide additional information on genotype variation. Genotypes with ASV values close to zero are considered stable (Table 3). The range of ASV value from 0.14 (G26) to 2.94 (G3) were observed for seed yield. According to ASV, genotypes G26 (0.14), G50 (0.22) and G49 (0.23), were identified as most stable for having lower ASV values, whereas genotypes G3 (2.94), G2 (2) and G25 (1.92)  were identified as being most unstable (Table 3). To clearly define more stable genotypes, the ASV parameter was used as an ancillary. According to Yan and Kang, (2002) GSI method incorporates both stability and high performance into a single index to identify ideal genotypes and removing the problem of selecting lines solely based on yield stability, taking into account that the most stable genotypes do not always have the best yield performance. Accordingly, the GSI parameter associated with genotype classification is based on the ASV and the ranking of genotypes. Genotypes with the lowest GSI scores represent the more desirable genotypes. The most stable lines according to the GSI for seed yield across the environments were G39 (16), G26 (20) and G19 (25) showed a lower GSI value, indicating it is the most stable genotype with a high mean yield (Table 3).



                       

This finding aligns with previous studies by Mushoriwa et al., (2022) and Wodebo et al., (2023) which identified stable, high-yield genotypes through the genotype selection index based on rankings of mean yield and AMMI stability value. The first two PCs exhibited 100% of the total variation, in which PC1 contribute 59.3% and PC2 contribute 40.7%. Therefore, AMMI1 (IPCA1 vs additive main effects) biplots were generated to illustrate the genotype and environment effects simultaneously (Fig 1). The AMMI1 biplot indicated that the environment E3 was high yielding followed by E2 and E3. The genotypes G26, G12, G34, G38, G8 and G25 were located near to the environment E3 showed high yielding for that particular environment, genotypes such as G27, G44, G16, G14, G6 and G40 which were located near to the environment E2 were high yielding genotypes and the genotypes G23, G11, G31, G30 and G36 high yielding for the environment E1 (Fig 1). The AMMI model, which integrates Principal Component Analysis (PCA) and analysis of variance, enables a thorough examination of genotype and environment interactions, helping to identify interaction patterns (Gupta et al., 2023). These results align with previous research by Nowosad et al., (2016) and Mossie et al., (2024).


 
GGE biplot analysis
 
Fig 2-6 present GGE biplots for seed yield of 50 soybean genotypes, highlighting top-performing genotypes, stable genotypes across environments and representative mega-environments (Silva et al., 2022).This method simplifies complex G × E interactions into principal components, with PC1 representing average genotype performance and PC2 capturing G × E interaction and genotype instability (Khan et al., 2021; Kumar et al., 2023). In this study, PC1 and PC2 of the GGE biplot together accounted for 75.10% of the G × E variation in seed yield (Fig 2), which is significantly lower than the 95% reported in previous research. The “which-won-where” polygon view (Fig 2) illustrates the top-performing soybean genotypes in each environment. The GGE biplot analysis of 50 genotypes for seed yield explained 75.10% of the total variation, with PC1 and PC2 accounting for 30.93% and 44.8% of the variation, respectively. The GGE biplot’s polygon view highlights top-performing genotypes by connecting those farthest from the origin, with sectors dividing mega-environments. Genotypes at the polygon vertices, including G2, G3, G47, G50, G11, G32 and G31, represent the best performers in their respective environments, while genotypes closer to the origin are considered more stable across environments. These genotypes showed the highest responsiveness in their environments, with G3 achieving the highest seed yield in E3. Similarly, Habtegebriel et al., (2023) found that the polygon view of the biplot grouped test environments into three sectors and genotypes into four, with three sectors lacking test environments. Fig 3 shows the ranking of genotypes based on mean performance and stability. In a GGE biplot, PC1 reflects genotype main effects, while PC2 represents G × E effects, serving as a measure of genotype instability. The Average Environment Coordinate (AEC) axis, extending from the biplot origin to the average environment circle, is determined by the average scores of PC1 and PC2 across all environments, with the arrow pointing to the highest yield value. In our study, the AEC method, using average principal components, assessed genotype yield stability. The GGE biplot revealed that 75.10% of yield variation was due to genotype and G × E interaction (Fig 3). A line from the biplot origin to the average environment indicates stronger genotype main effects. Moving away from this line, either towards or away from the origin, signifies increased G × E interaction effects. The length of genotype projections onto the AEA (dotted lines) estimates their contribution to G × E interaction, with longer projections indicating greater instability and lower yield stability across environments. The line divides genotypes into below-average and above-average performers. Genotypes G3 (14.58), G9 (13.22), G39 (12.9), G32 (12.23),  G41 (10.95) and G4 (10.58) and showed higher yield performance than the average (Figure 3), a finding also reported by Silva et al., (2021, 2022),  and Habtegebriel et al., (2023).The GGE biplot effectively evaluates a test environment’s ability to differentiate genotypes and represent the broader mega-environment. In this study, E3 and E2 had the longest vector lengths (Fig 4), identifying them as the most discriminating environments. E1 had the shortest vector length, indicating it is the least discriminating environment, providing limited information on genotype differences. Similar findings were reported in soybean studies by Habtegebriel et al., (2023). The ideal genotype is the one that with the highest mean performance and absolutely stable (Yan and Kang, 2002). This is assumed to be in the centre of the concentric circles is an ideal genotype across the tested environment. It is more desirable for a genotype to be located closer to the ideal genotype. Hence, the GGE biplots (Fig 5) shows that genotype G9 was ideal in terms of higher-yielding ability and stability as compared to the other genotypes across the environment. The GGE biplot identifies ideal environments as those near the center of concentric circles with longer vectors, indicating high discriminating power and representativeness of average target growing conditions. Therefore, based on the GGE biplot, E2 followed by E1 might be ideal environments in this study, reflecting Yan and Kang, (2002) emphasis on discriminating power and target environment representativeness. Likewise, Arega et al., (2018) also observed similar result by using GGE biplot analysis.



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The grain yield of soybean varieties varied significantly due to environmental factors, variety differences and their interactions (GEI). Environmental factors had the largest impact on yield variability, with notable genotype-by-environment interactions. AMMI analysis identified genotypes G26 (JS 22-88) with 20 and G39 (JS 22-101) with 16  as the most stable and high-yielding genotypes across different environments. And GGE biplot analysis highlighted G9 (JS 22-71) as the most productive and consistent genotype.

The authors say that there is no conflict of interest.