AMMI and GGE biplot analysis for yield performance and stability assessment of selected Bambara groundnut (Vigna subterranea L. Verdc.) genotypes under the multi-environmental trials (METs)

The stability and high yielding of Vigna subterranea L. Verdc. genotype is an important factor for long-term development and food security. The effects of G × E interaction on yield stability in 30 Bambara groundnut genotypes in four different Malaysian environments were investigated in this research. The experiment used a randomized complete block design with three replications in each environment. Over multiple harvests, yield component traits such as the total number of pods per plant, fresh pods weight (g), hundred seeds weight (g), and yield per hectare were evaluated in the main and off-season in 2020 and 2021. Stability tests for multivariate stability parameters were performed based on analyses of variance. For all the traits, the pooled analysis of variance revealed highly significant (p < 0.01) variations between genotypes, locations, seasons, and genotypes by environment (G × E interaction). A two-dimensional GGE biplot was generated using the first two principal components (axis 1 and axis 2), which accounted for 94.97% and 3.11% difference in GEI for yield per hectare, respectively. Season and location were found to be the most significant causes of yield heterogeneity, accounting for 31.13% and 14.02% of overall G + E + G × E variation, respectively, according to the combined study of variance. The GGE biplot revealed that the three winning genotypes G1, G3, and G5 appear across environments whereas AMMI model exposed genotypes viz G18, G14, G7, G3, G1, and G5 as best performer. Based on ideal genotype ranking genotype G1 was the best performer, with a high mean yield and high stability in the tested environment. According to the AEC line, genotypes G1 and G3 were extremely stable, while genotypes G2 and G4 were low stable, with a high average yielding per hectare. A GGE and AMMI biplot graphically showed the interrelationships between the tested environment and genotypes, classified genotypes into three categories as well as simplifying visual evaluations, according to this investigation. According to our results, breeding could improve yield production, and the genotypes discovered could be recommended for commercial cultivation.

www.nature.com/scientificreports/ yield stability across multiple locations. As a consequence, the current study aims to identify superior genotypes with stable yield performance over a wide range of environments by evaluating the efficacy of various stability analysis methodologies. Another intention of this study was to examine how GEI influenced the yield and yield components of Vigna subterranea L. (Verdc.) genotypes as well as to identify the high yielding stable genotypes for future breeding schemes in tropical and subtropical environments.

Materials and methods
Plant materials. The research work was conducted under the Institute of Tropical Agriculture and Food Security (ITAFoS), University Putra Malaysia (UPM), Malaysia. In this work, selected 30 V. subterranea accessions from the GenBank of ITAFoS, UPM were utilised. Initially, fifteen collected accessions were formal identified and investigated by Md Mahmudul Hasan Khan 3,4 under the direct supervision of Prof. Dr. Mohd. Rafii Yusop, Director, ITAFoS, UPM, Malaysia, in accordance with appropriate national and international policies. During the assessment, potentiality of high yield was considered to choose the accessions from each selfed generation of S 0 to S 5 . However, we chose 150 individual plants from the fifteen assessed landraces of generation S 0 based on the greatest number of pods and yield per plant and subjected them to subsequent selfing and selection as S 1 selfed generation. These seeds from S 1 selfed generation were cultivated for selfing and promoting the next generation as S 2 , and the top 44 performing lines were chosen. Similarly, following two rounds of selfing and selection (viz. S 2 and S 3 ), we sowed the seeds of the S 3 and S 4 generations together for a comparative and inbreeding depression assessment. Moreover, molecular characterization (https:// doi. org/ 10. 1038/ s41598-021-93867-5) also executed by Khan et al. 15 using the 44 accessions of S 4 selfed generation. However, the seeds of all potential lines are stored in GenBank, ITAFoS, UPM. Finally, we picked the 30 best-performing lines of V. subterranea from the 44 accessions of the fourth selfed (S 4 ) generation based on high yield and phenotypic uniformity and considered them to be the S 5 selfed generation. We collected the plant seeds or specimens with the proper permission of the institution's authority by following the national and international strategies as well as deposited them in GenBank, ITAFoS, UPM. We also took appropriate permission from farm or field owner during specimens' collection and experimentation in Malaysia. The name and ID of each accession were listed in Table 1.
Environments and inter-cultural practices. The field trials were directed recurrently across two locations in two cropping seasons (2020 and 2021) in Malaysia. The environments (combination of seasons and location) spanned a considerable degree of conditions varied in temperature (warm vs. moderate climate), rainfall (heavy rain vs. additional irrigation), soil structure, soil pH, and management practices (research's vs. farmer's field). Details of the environmental conditions were presented in Table 2. The soil properties of the experimental site are listed in Table 3.  www.nature.com/scientificreports/ The experiment was set up in a randomized complete block design (RCBD) with three replications in each environment. The experimental plot was divided into two rows of 1.6 m × 0.80 m each. According to Khan et al. 3 , the distance between plants was 30 cm, row to row was 50 cm, plot to plot was 1.5 m, and the distance between replication was 2.0 m. Recommended intercultural activities such as field planning, land clearing, weeding, irrigation, and fertilizer were used during the growing season. The prescribed fertilizer rates (100% N = 45 kg N/ha, 100% P = 54 kg P 2 O 5 /ha, 100% K = 45 kg K 2 O/ha) and all portions of Phosphorus and Potassium were applied during final land preparation, though, 70% N was added at five weeks after planting 3 . The field was mechanically plowed in the study places, following the usual cultural traditions of the local farmers. Where the need arose, pest and disease control was carried out. Hand weeding was done as needed, and systemic herbicide was used to control broad leaf weeds prior to land preparation and around the experimental plot.
Data collection. For this study, we considered four quantitative traits (direct and positively contributing traits with yield) such as total number of pods per plant (TNP), fresh pod weight per plant (g) (FPW), hundred seed weight (g) (HSW), and yield (kg/ha). However, data were recorded according to Bambara groundnut classification and descriptors by IPGRI, IITA, and BAMNET 33 . Data was collected from 5 randomly selected plants from each plot in each replication at various growth stages in the field and the plant physiology lab after harvest.
Statistical analysis. The quantitative traits were subjected to analysis of variance (ANOVA) to estimate the existence variations among the genotypes, locations, seasons, genotype by location, genotype by season, and genotype by location by season (genotype by environment) using SAS version 9.4. The genotypes were treated as fixed variables, while the environments were considered random variables. An additional statistical analysis was carried out if there is a significant interaction between the environment and the genotype to determine the stability level among the 30 genotypes across environments. The G × E SAS code developed by Dia and Wehner 34 was used for stability analysis which is freely available at http:// cuke. hort. ncsu. edu/ cucur bit/ wehner/ softw are. html. The G × E SAS output consists of ready to use input file in R-package for multivariate analysis. To explain the G × E interaction, the multivariate stability analysis was performed graphically based on GGE biplot and AMMI using R studio (a simplified version of R statistical software) developed by the R Core Team 35 . The GUI package of R studio was used for GGE biplots while the Agricolae package was used for AMMI 36 , involving two concepts, the biplot concepts 37,38 and the GGE concept 25 . The GGE biplots and AMMI are graphical images to exemplify G × E interaction and genotype ranking based on mean and stability. The graph generated is based on multi environment evaluation (which-won-where pattern), Genotype evaluation (mean versus stability), and tested environment raking (discriminative versus representative). The ranking of genotypes was allocated in increasing order of each stability parameter. The biplots were based on singular-value partitioning = 2, transformed (transform = 0), environment-centered (centering = 2), and standard deviation-standardized (scaling = 0).

Results and discussion
Combined variance analysis for yield and its related traits. To describe the main effect and quantify the interactions among and within the source of variations combined analysis of variance was performed. The pooled analysis of variance was displayed in Table 4. The mean square of locations, seasons, genotypes, and genotypes by locations by seasons (G × L × S; i.e., G × E interaction) showed significant differences (p ≤ 0.01, p ≤ 0.05) for TNP, FPW, HSW and yield per hectare. The genotypes by seasons (G × S) and genotypes by locations (G × L) had no significant variation for the TNP and HSW while the trait FPW and yield had a significant difference for genotypes by locations (G × L). Highly significant differences in locations, seasons, and genotypes may be attributed to changes in environment conditions and genetic makeup that differ from one environment to the next. The partitioning of the percentage of G × E interaction (% of GE) is computed from the total sum of the square shown in Table 4 which elucidates the percentages of variation for all traits. Except for the total number of pods (TNP), other traits showed a considerable extent of variation due to location that spanned from 0.15 to 14.02%. A greater difference among locations for genotype means resulting in most of the variation presence in genotype performance. Oppositely lower variation was found in genotype by location which varied from 0.61 to 7.20%. The trait total number of pods (22.9%), fresh pod weight (21.67%), and yield (22.4%) had near similar contribution towards genotype effect while hundred seed weight (7.34%) had small variation due to genotype effect. The genotype by environment interaction (GEI) i.e., G × S × L effect accounted for 9%, 8.52%, 2.52%, 1.85% of the total sum square for the traits total number of pods, fresh pod weight, hundred seed weight, and yield per hectare, respectively. The location by season effect had 68.66% variation for hundred seed weight, season effect contributed 31.13% and 42.64% variation for the trait yield per hectare and fresh pod weight respectively. Seasons contributed 31.13% variation for yield per hectare indicated that the assessed seasons in this study were different, which is highly attributed by the trait yield per hectare although G × E interaction significantly contributed 1.85%. The percent of the sum of the squares for the location by season (L × S) impact in yield per hectare is larger than the magnitude of the location effect, suggesting that there was a considerable degree of var- www.nature.com/scientificreports/ iation across the location due to two growing seasons. Similar findings were reported by Oladosu et al. 19 stated that 29.07% variation contributed by location effect for grain yield. In this current research, a significant level divergence among G × E interaction and genotype effect indicated the certainty of the presence of diverse multienvironments with different genotype as well as high yield potential 39 . Nevertheless, the variance component analysis is not enough to clarify the details of the genotype by environment interaction. Henceforth, additional statistical techniques such as multivariate analysis can be more fruitful in unfolding and understanding the GEI 19 . The genotype by environment interaction effect primarily highlights the fact that genotypes responded inversely to various locations, emphasizing the need of genotypes assessment in diverse environments. Likewise, GEI reveals the challenges that plant breeders have, when identifying a superior genotype for commercial farming before releasing it as a variety 19 . The environment's partition of variance component revealed that predictable (locations) and unpredictable (seasons) aspects were important sources of variation 19 . When GEI is subjected to the effect of predictable components, plant breeders can either choose genotypes for a specific environment or extensively adjusted genotypes across several environments 40 .
Biplot pattern for elucidation of multivariate analysis. Globally, crop farming in absence of G × E interaction is performed equally, thereby having a common result irrespective of the environment 19 . In a statement reported by Yan et al. 25 , the main effect of genotype (G) plus G × E interactions is the principal source of variation in the assessment of the genotypes under multi-environment trials (MET). Three major components can be elucidated using the biplot such as (a) 'which-won-where' pattern or MET, proposed by Yan et al. 25 is an effective approach to visualize the pattern of GEI based on the correlation between G and E; (b) stability vs mean performance over the environment for genotype evaluation; (c) representativeness and discriminating ability for test environment assessment. The prefix 'Bi' in the word biplot denotes the dual (genotypes and environment) exposing on the same graph. Biplot is a 2D visualization matrix that has two axes, first data was centered afterward sectionalizing the singular value (SV) into GE scores for individual principal components viz. PC1 and PC2 followed by intrigue the PC1 scores contrary to the PC2 scores to create a biplot 19 . The greater PC1 value indicates greater yielding ability whereas the lower PC2 value signifies stability. A biplot is made up of an asymmetrical polygon with stripes or lines running vertically from the biplot's centre to the polygon at a right angle. All the genotypes that are apart from the biplot center are linked with the polygon thus covering all genotypes in the polygon marker. The vertical stripe that runs perpendicular to the polygon from the centre of the biplot represents an expected environment in which the two genotypes on opposite sides of the polygon are expected to behave similarly 19 . Furthermore, it divides the biplot into different parts, each with its own enticing or winning genotypes 19 . The captivating genotype is always positioned at the vertex of the polygon where both sides of the polygon meet that vertical stripe, generate a borderline of that segment or section 41 . Figure 1 illustrated the polygon view of the GGE biplot pattern for total number of pods (pattern A), fresh pod weight (Pattern B), hundred seed weight (Pattern C), yield per hectare (Pattern D). The G + G × E variation was recorded as 90.41%, 98.33%, 97.33%, and 98.08% for TNP, FPW, HSW and Yield, respectively ( Fig. 1, Pattern A, B, C, D). The environmental indicators positioned into 2, 3, 2, and 2 segments or sections of biplot for TNP, FPW, HSW, and Yield, respectively with different genotype winning in each segment. This result confirming the presence of distinct interaction between genotype and environment for all the traits evaluated. Based on 30 genotypes and 4 environments the generated GGE biplot was divided into 7, 8, 7, and 9 clockwise fan-shaped sections for TNP, FPW, HSW, and Yield, respectively. The genotype G20 produced a maximum number of pods and highly stable in ENV3 while genotypes G3, G4, G7, and G11 perform best in ENV1, ENV2, and ENV3. The genotype G25 in ENV3, genotype G2 in ENV2 and ENV4, genotype G1 in ENV1 were recorded as highly stable and produce more fresh pods. For hundred seed weight genotype G26 and G12 in ENV 1, ENV 3, ENV 4 whereas genotype G1 in ENV 2 was found as highly stable and best performing line. However, the genotype G1 was recorded as high yielding and stable genotype for environment one (ENV1).  19 .

GGE biplot ('which-won-where' pattern).
Consequently, exposing the 'which-won-where' pattern of the GEI data matrix is a crucial feature of the GGE biplot that was extracted by the innermost assets or product of the biplot 39 . The genotype that attached with a vertex of the polygon in a sector where environment markers drop in suggested, such genotype provided greater yield and perform best in that environment. On the contrary, a genotype that is linked with polygon vertex where no environment indicator drops in the sector indicated that such genotype is poorly performed across the environment. The genotypes placed within the polygon are less respective to the environment than the corner genotypes. However, if multi-environments acknowledge by different winning genotypes recommends the presence of GEI in 4 environments for TNP, FPW, HSW, and Yield, this trend is validated by Gauch and Zobel 42 . www.nature.com/scientificreports/ GGE biplot pattern of 'mean vs. stability' analysis and ideal genotype assessment. The average environment coordinate (AEC) or average environment axes (AEA) line crosses through the biplot's origin if SVP = 1 (single value portioning). As a report by Yan and Rajcan 43 , the mean of PC1 and PC2 of the environmental scores is defined. The 'Mean vs. stability' view frequently stating to as AEC and SVP that helps to simplify the genotype assessment based on the mean performance and stability under a wide range of environment (Fig. 2). The two straight lines, (i) the AEC abscissa (vertical) and (ii) AEC ordinate (horizontal) comprise this biplot graph. Line one (Fig. 3: Pattern A, B, C, D) consists of a single arrow that pointed towards greater mean performance for each trait. In our investigation, the 'mean vs. stability' pattern of GGE biplot revealed 90.41% for total number of the pod (Pattern A), 98.33% for fresh pod weight, 97.33% for hundred seed weight, and 98.08% for yield per hectare of G + G × E variation (Fig. 2). The arrow sign on the AEC abscissa line directed the ranking of genotypes in increasing order with a greater value of traits evaluated. However, genotype G4 produced higher pods followed by G11 and G2 in ENV 1, ENV 2, and ENV 4 while in ENV3, the high pod producing genotype is the G3. For the trait TNP, the genotypes G2 and G8 are more stable over the tested environment though these genotypes produced lower pods ( Fig. 2; Pattern A). The highest fresh pod weight (g) was recorded for genotype G2 afterward G3 and G11 in ENV1, ENV 2, and ENV 4 but genotype G13 gave higher FPW in ENV3. Over the environment genotype G7, G10, and G15 leading to highly stable ones with lower performance Fig. 2; Pattern B). In environment one (ENV1) genotype G26 noted for HSW followed by G4 and G12 on the other hand genotype G1 showed higher HSW in ENV2, ENV 3, and ENV4 though genotype G12 and G29 considered as highly stable across the environment ( Fig. 2; Pattern C). In the case of yield per hectare genotype, G1 gave higher yield followed by G2 and G4 in ENV1 and ENV3 whereas genotype G3 followed by G5, G6, G7, and G8 produced maximum yield in the ENV2 and ENV4. Among the accessions, genotype G1, G3, and G5 gave higher yield per hectare and highly stable while G10, G13, G11, G14, G17, G18, and G20 also remarked as more stable genotypes www.nature.com/scientificreports/ but exhibited low yielding performance ( Fig. 2; Pattern D). However, these genotypes might be incorporated in the breeding strategy for crop enhancement. Aside from these, genotypes G2, G4, G6, G8, and G7 provided somewhat desired yield but shown low stability due to their position on the biplot far from the AEC line. Similar trends of observations were recorded by Oladosu et al. 19 , Hashim et al. 41 , and Sabri et al. 44 . However, the stability of each genotype measure by line two which crosses over the biplot origin, and it vertical bisects the AEA abscissa. The genotype positioned into nearness to the concentrical rings, determining the best performing genotype and the projection from AEA abscissa indicate the genotype stability. Genotypes consider being more stable when it placed on the horizontal axis (AEC abscissa) and had zero projection from the vertical axis (AEC ordinate) while the genotype with the lengthiest direction from the AEC abscissa is treated as unstable, a similar report was stated by Oladosu et al. 19 .
Genotype ranking: best and ideal genotype assessment. Through the genotype ranking biplot (Fig. 3) we can detect an ideal genotype in contrast to other genotypes evaluated. The genotypes G4, G11, and G2 could be noted as the best leading genotype due to their nearness to the arrowhead in the circle for total number of pods ( Fig. 3: Pattern A). Similarly, for fresh pod weight genotype G2, G3, G7, G8, G9, G10, and G14 ( Fig. 3: Pattern B); for hundred seed weight genotype G12, G29, and G4 ( Fig. 3: Pattern C) and for yield per hectare genotype G1, G10, G13, G5, and G3 ( Fig. 3: Pattern D) regarded as best genotype due to proximity to concentric circle. Commonly, an ideal genotype is always placed into the innermost circle and relatively nearer the head of the arrow at the center of the circular ring ( Fig. 3: Pattern A, B, c, and D). The genotype located in the inner circle is highly desirable compared to the genotypes of the outer circle. However, in some cases no genotype was www.nature.com/scientificreports/ positioned inside the inner circle, consequently, genotypes next closer to the inner circle are considered to be an ideal one 19 . Consequently, genotypes G4 and G11 for TNP; genotypes G7, G9, and G10 for FPW; genotype G12 for HSW; and genotypes G1 and G10 for yield per hectare were regarded as ideal genotypes across the tested environment because they were positioned closer to the centre of the biplot origin, indicating that they are stable genotypes. For an effective selection, an ideal genotype should have both high mean and stability properties 45 . A ring at the head of the arrow on the horizontal AEC abscissa axis generally represents an ideal genotype 19 and additionally, the idealness of a genotype refers to a small circle on the AEC abscissa line. Genotypes on the left side of the vertical line often outperform the grand mean, whereas genotypes on the right side underperform the grand mean 19 . Plant breeders used data from yield performance evaluations based on mean and stability to choose genotypes best suited to a specific environment within a multi-environment 13 , while genotypes close to the ideal genotype were also more promising or appropriate. So, the genotype ranking based on ideal genotype for yield per hectare was G1 > G10 > G13 > G5 > G3 > G6 > G14 > G17 > G11 > G12 > G8 > G2 > G4 (Fig. 3: Pattern D). Oladosu et al. 19 found similar findings across 10 settings as evidence of our result.
'Descriminitiveness vs. representativeness' pattern of GGE biplot. The determination of a best suited (ideal) test environment is crucial for a successful breeding technique in the selection of superior genotypes. The two features like descriminitiveness (the ability of an environment to distinguish genotype) and representativeness (the ability of an environment to represent all other evaluated environments) signify the idealness of the tested environments 19 . In our investigation Fig. 4 (Pattern A, B, C, D) illustrated the 'descriminitiveness vs. representativeness' of the GGE biplot study. [19]We recorded environment four (ENV4) for TNP ( Fig. 4: Pattern A), environment (ENV1 and ENV2) for FPW ( Fig. 4: Pattern B), environment two (ENV2) for HSW ( Fig. 4: Pattern C), and environment (ENV1 and ENV2) for yield ( Fig. 4: Pattern D) as an independent and unique research location due to their short vector while the environment with long vector is more influential in discriminating among the Bambara groundnut accessions. However, the environment with a long vector that forms a shorter angle with the AEC abscissa line is idyllic for the selection of superior genotypes. Thus, environment two (ENV2) for TNP and environment four (ENV4) for FPW, HSW, and yield had small-angle alongside long vector with AEC abscissa indicated that the test environment was greater representative and discriminative. Figure 5 represent the ranking of environment, exposed that environment ENV2 for the total number of pods ( Fig. 5: Pattern A), environment ENV4 for fresh pod weight (Fig. 5: Pattern B), hundred seed weight (Fig. 5: Pattern C), and yield ( Fig. 5: Pattern D) are regarded as the ideal environment. Oppositely, for TNP and FPW the environment ENV3 as well as for HSW and Yield the environment (ENV 1 and ENV 2) was noted as the poorest environment to select genotype across the environment. Thus, this study suggests that the studied genotype determined the most suitable environment to assess the mega environment based on test environments representativeness and discriminating ability. Hashim et al. 41 reported one environment is ideal for genotype selection considering yield per hectare among the tested four environments. Among the five evaluated locations, three were noted as an ideal location by Oladosu et al. 19 . The correlation coefficient between the genotype mean value over the environment and the genotype values in that environment is approximately equal to the cosine of the angle between the average environment coordinate (AEC) often refers as the average environment axis (AEA) and the environment vector 38 . The smaller angle between AEC abscissa and vector of test environment represent the better environment related to those generate greater angles. The arrow on the AEC abscissa line shows its direction and a small concentric circle denotes the average value of the environment while the length of the test environment vector guesses the discriminating ability. The length of each environment vector gives an idea of its greatness (discriminating ability) to distinguish genotypes in the environment 19 .
The relatedness among the test environments: environment assessment. Based on the biplot graph, assessment of test environment is the next important step after multi environment identification to fix the environment discriminativeness and representativeness ability, inter-relatedness, and redundant among the environments. Figure 6: Patterns (A, B, C, D) represent the discriminativeness and representativeness of tested locations. The biplot accounted for 67.19% (PC1) and 23.22% (PC2) for total number of pods, 70.24% (PC1) and 28.09% (PC2) for fresh pod weight (g), 86.65% (PC1) and 10.68% (PC2) for hundred seed weight (g) and 94.97% (PC1) and 3.11% (PC2) for yield of G + G × E interaction variation across the tested environment. In all cases, the 1st principal components showed the maximum variation for all traits evaluated. Across the location, season, and year the trait yield per hectare is largely influenced by the genotype by environment effect. The distance among each tested environment is displayed in Fig. 5 also for all evaluated traits. As a report by Lin and Binns 46 the effect of environment on genotype is highly influenced by unpredictable (e.g., weather) and predictable (e.g., soil) factors. The soil is a fixed factor due to its persistence from year after year and is noted as a predictable component. Contrary, the weather is a complex component because it includes predictable elements that are well-defined by the overall climatic region whereas the unpredictable components arise variation due to alternation of time (year to year) 46 .
However, it is effective and productive to take into consideration evaluating test environment due to it does represent proximate to multi environments, hence, can be a representative of a multi environment 38 . Based on our findings, we categorized the tested environment into three groups. The ENV4 for TNP, ENV1, and ENV2 for FPW, ENV2 for HSW, and yield per hectare are branded as the category-1 environment (short vector) which provided little or no information on genotypes also unfit for use as a test location. Environment two (ENV 2) for TNP and FPW as well as the environment (ENV3 and ENV4) for HSW, and Yield per hectare are designated as the category-2 (lower angle vs. longer vector) indicated that these environments are appropriate for promising genotypes selection because of their notable representativeness and discriminating power. Yan  Additive main effects and multiplicative interaction: AMMI 1. In additive main effects and multiplicative interaction 1 (AMMI 1), the biplot abscissa and ordinate indicated the 1st principal component (PC1) term and the trait's significant influence, respectively. In this study, Fig. 7 (Pattern A, B, C, and D) showing the additive main effects and multiplicative interaction 30 genotype and 4 environments for the trait TNP, FPW, HSW, and yield per hectare, respectively. Based on genotype mean and interaction with the environment a little similarity was found among the genotypes. For hundred seed weight (Fig. 7: Pattern C) environment three (ENV3), ENV2 for total number of pods ( Fig. 7: Pattern A), ENV4 for fresh pod weight (Fig. 7: Pattern B), and ENV2 for yield per hectare (Fig. 7: Pattern D) had a PCA1 score or vector closer to zero compared to other environments, indicates lower interaction effect which almost ensures the better performance of all genotypes www.nature.com/scientificreports/ in that environment. Moreover, these environments are treated as suitable for all genotypes evaluated. For total number of pods the genotypes G24, G10, G7, G9, G5, G26, and G12 ( Fig. 7: Pattern A); for fresh pod weight the genotypes G24, G19, G10, G15, G17, G11, G3, G27, and G29 ( Fig. 7: Pattern B); for hundred seed weight the genotypes G10, G29, G18, G21, G1 (Fig. 7: Pattern C); for yield per hectare the genotypes G18, G14, G7, G3, G1, G5, and G4 ( Fig. 7: Pattern D) had approximately zero scores on the first PCA1 axis which indicates that these genotypes were less influenced by the environment. However, some genotypes had their mean below-average performance though, in general, plant breeders are highly attracted to genotypes that are high-yielding and relatively more stable. Genotypes with PC1 scores adjacent to zero lines of biplot indicated that genotypes were suited to all environments, whereas PC1 vectors with the same sign and score but away from zero lines of biplot indicated that genotypes were adapted to a specific environment, is supported by Murphy et al. 47 . When the PCA1 score for a genotype or environment is near to zero, there is a small interaction impact; contrary, if a genotype and environment achieve the same sign on the PCA axis, there is a positive interaction; otherwise, there is a negative interaction. A report published by Mogale 11 is comparable to our findings in Bambara groundnut and Oladosu et al. 19 in rice. www.nature.com/scientificreports/ Additive main effects and multiplicative interaction: AMMI 2. Additive main effects and multiplicative interaction 2 (AMMI 2) is a principal component (PC1 and PC2) scores-based graphical representation of summarized information which gives advantages over joint regression-based analysis. The AMMI 2 divulge and inferring the complicated GEI that involves significant multi-environments and detection of genotypes with either broad or narrow spectrum adaptability. Figure 8 illustrated the first two principal component interaction of the AMMI 2 biplot model which accounted for 90.02%, 97.8%, 95.9%, and 92.6% of the G + G × E interaction variation for the total number of pods ( Fig. 8: Pattern A), fresh pod weight (Fig. 8: Pattern B), hundred seed weight ( Fig. 8: Pattern C) and Yield per hectare (Fig. 8: Pattern D), respectively. Accordingly, this proportion of variation implies that interaction of 30 V. subterranea genotypes that tested in four environments was projected by 1st two principal components of genotype and environment. Our result was consistent with the endorsement of Gauch and Zobel 42 stated that the first two PCs are sufficient for the projection of the AMMI model precisely oppositely, some researchers namely, Sivapalan et al. 48 and Tariku et al. 49 suggested 1st four PCs to report the multi-environment trail. The center of the biplot (0, 0) is divided into four distinct sectors by passing through the two-line, vertically, and horizontally (Fig. 8). Likewise, GGE biplot, genotypes that are placed apart from www.nature.com/scientificreports/ the biplot origin is regarded as winning genotypes in the environments that fall in that sector. The extent of interaction revealed by the environment over the genotype and vice versa is controlled by the distance of the environment and genotype vectors that originated from the origin of the biplot. In our study, we found ENV4 for TNP (Fig. 8: Pattern A), ENV2 for FPW ( Fig. 8: Pattern B), ENV3 for HSW ( Fig. 8: Pattern C), and yield per hectare ( Fig. 8: Pattern D) had short vector comparatively other environments. As a report by Murphy et al. 47 the environment indicator with a shorter vector i.e., nearer to biplot origin is less interactive and treated as a perfect index for selecting genotype with mean performance and adaptability. Most of the genotypes for the traits TNP, FPW, HSW, and Yield per hectare were assembled ( Fig. 8: Pattern A, B, C, D) close to the biplot origin. However, genotypes that assembled or cluster together on the biplot origin indicating that genotypes have identical feedback to all tested environments compared to the genotypes that are positioned away from each other, this statement is corroborated with the report of Akter et al. 50 . Moreover, genotypes that are placed apart for biplot origin are more sensitive to environmental interaction related to closely positioned genotypes to biplot origin. The correlation coefficient and the degree of interaction of genotype and environment can be highlighted by the angle between the vectors of environment and genotype. There was no correlation when environment and genotype form a right-angle while the severe and nearer angle between them indicates negative and positive correlation, respectively. The findings in this current investigation have authorized statements reported by Oladosu et al. 19 using two seasons five locations.

Evaluation of genotypes.
In this study, the evaluation of the selected genotype for yield and its positively correlated contributing trait's stability over a wide range of environments are justified through the result of a significant test of GE interaction.  Table 5. Over the location, all the genotypes showed significant variation for total number of pods (TNP), fresh pod weight (FWP), hundred seed weight (HSW), and Yield per hectare. The total number of pods ranged from 73 (G24) to 92 (G4) with an average of 8484.67 ± 0.46. The genotype G4 produced the highest number of pods (92) followed by G11 (91), G2, and G3 (89) though across the genotype it was 106 while the lowest was 51. The highest fresh pod weight was 684.58 g for genotype G3, followed by G2 (681.56 g), and the lowest was 58.78 g for the genotype G27.  11 . Most of the time, these traits have a strong positive association with yield. According to the findings of Khan et al. 3 and Khan et al. 4 , the traits viz. TNP, FPW, and HSW are primary component characteristics that have a dominant influence on yield due to their positive significant relationship with yield. Lowering the number of pods resulted in decreased fresh pod weight, as well as fewer dried pod weight and seeds, all of which badly influence grain yield in Bambara groundnut 3,11 . A genotype that is stable to yield in a diversified environment, on the other hand, is highly accepted by any researchers in a breeding programme to reduce the danger of yield loss owing to adverse climatic conditions 19 . In such a situation, when genotype performance is inconsistent in a diverse environment, the study of GEI followed by stability analysis is crucial which is advocated by Haldane 51 and Baye et al. 52 . www.nature.com/scientificreports/

Conclusion
The main intention of this current multi-environmental study is to evaluate V. subterranea genotypes based on mean performance under a wide range of environments in order to identify superior genotypes. The multi environmental trail (MET) of Bambara groundnut genotypes may also give information on genotype adaptability and stability to a certain environmental situation. Eventually, a genotype is proposed for commercial cultivation, its susceptibility to genotype by environment interaction (GEI) should be assessed. However, considering the multivariate (GGE and AMMI biplot) statistical result the tested genotypes are categorized into three major groups. Group one genotypes are those that are highly stable and have a high yielding potential. This group comprises genotypes of G1, G3, and G5, which are well suited to a range of environments. The basic criteria for the second category are genotypes with low stability but high yield per hectare. This group contains genotypes of G2 and G4 (perform better in ENV1), as well as G6, G8, and G7 (perform better in ENV2) that are appropriate for a specific environment. The last group worked with genotypes that had a low yield but a high stability. This group comprises genotypes of G10, G13, G11, G14, G17, G19, and G18, which are ideal for breeding schemes intended to improve certain phenotypes. This category of genotypes may have yield component compensation criteria, such as the ability to recover quickly from a wide range of environmental challenges. Genotypes G1, G3, and G5 performed well across all test locations and designated as ideal in terms of mean, stability, high yield, www.nature.com/scientificreports/ and emerged as the top genotype among those investigated. Grain yield and its contributing characteristics (total number of pods, fresh pod weight, hundred seed weight, and so on) are strongly influenced, either directly or indirectly, by a variety of environmental factors. Our findings suggested that breeding may improve bambara groundnut production efficiency, and that ideally-established genotypes could be recommended for commercial cultivation in Malaysia as well as in tropical region.