The TTSS of ANOVA due to G+E+GEI was partitioned into G, L, Y, GLI, GYI, LYI, and GLYI variances attributed 15.1, 20.9, 25.5, 15.9, 5.5, 5.2, and 8.8%, respectively (Table 3). The largest variance was explained by E (51.6%) consisted L, Y, and LYI effects. The GEI variance was also almost twice than the G that explained 30.2% of G+E+GEI variance. The interaction is not ignored for such large GEI than G (Yan and Kang, 2002). This large GEI effect was suggested by the differential responses of genotypes and possibility of ME existence with different winning genotypes (Yan and Kang, 2003; Fayeun et al., 2016). The larger GEI variance also indicated both predictable and unpredictable effects leading to specifically or broadly performing genotypes developing (Dehghani et al., 2006).

 

 

The ANOVA due to G+L+GLI also provided G, L, and GLI variances (Table 4). The G and GLI variances were 28.3 and 50.3%, respectively, out of the 94.4% for 2015. The G and L effects were also 27.1 and 50.1%, respectively, from total 96.9% variance for 2016. The GLI variance in comparison with G effect suggested the possibility of ME existence. This large variation due to  G, L, and GLI effects suggested the suitability of SREG model for stability analysis (Gauch and Zobel, 1996). The GGE model is efficient for G vs. cross-over-type GEI effect interpretation (Karimizadeh et al., 2013). This model is also effective to identify highly stable vs. specifically adapting genotypes via GEI variance demonstrating vs. ME's delineating (Santos et al., 2016). Moreover, Kang et al. (2006) confirmed that the GGE biplot strength for stability vs. superiority was determined. The limitation of GGE biplot is the capturing of small portion of total variability (Yang et al., 2009).

The ANOVA of site regression model was significant (p<0.001) for G, E, and GEI variances (Table 6). The E (53.23%) and GEI (31.15%) effects took the largest proportion of the TTSS variance. The GGE MS variance was strongly significant for PC1, PC2, and PC3 with 81 df, cumulatively accounted 81.95% of the TSS. The 1st and 2nd PC axes with 40.35 and 26.38%, respectively and df of 29 and 27, respectively, effectively partitioned the existed GEI (Table 6).  This  66.73%  attributes  was predicted on the 1st and 2nd PC axes of the total G+GEI derived by G+GE centered to SVD for existed GEI variance visualizing. The results are in accordance with that of Edmore et al. (2015) who explained 36.8% (PC1) and 29.5% (PC2) of the GGE SS. This justifies the efficiency of GGE model in exploiting the G plus GEI variability. Similar reports were confirmed by Yan et al. (2000); Gauch (2013) captured 67% variation with the first two PCs. The positioning of G vs. GEI effects on PC1 vs. PC2 of GGE biplot is as shown in Figure 3. The GGE biplot is an effective method for which-won-where pattern and superiorly performing stable genotypes displaying via

GEI vs. ME's visualizing (Yan et al., 2007; Atnaf et al., 2013; Massaine et al., 2018). The results of GGE biplot showed that G3, G5, G4, G12, G9, and G10 were the highest and poorest located at the vertexes of polygon responding either positively or negatively for seed yield (Figure 3). G3 and G5 were the best winning at A15, B15 and B16, G5 and G4 are the highest, so niche at A16 and K16, while G4 and G12 are also well performing at K15 (Figure 3). The G3 and G12 were specifically adapted at favorable sites; contributed maximum MS to GEI SS  due to high values for 2st PC (Figure 3). The polygon vertices are markers for highly projected genotypes indicating specific adaptability (Melkamu et al., 2015; Pavel et al., 2015). G8, G9, G10, G14, and G16 were the poorest that lied in opposite side of the vectors of all environments; not performed at all testing sites. The polygon vertexes G9 and G10 are the poorest genotypes that lied in opposite side of all vectors. Similar results were reported by Ashraful et al. (2017). Moreover, Figure 3 also provides  a  summary  of  E   vs.   G  relationship.   These variables were represented by vectors and markers, respectively. The correlation between vectors was determined by drawing a lines passed across origin aligned perpendicular to each polygon's sides. The line segments divided the polygon into sites and genotypes sectors. The environments were categorized into three major growing sectors based on the angles related with correlation coefficient (Figure 3). The first group was A15 and B15 with G3 and G5 as the most favorable genotypes. The second sector also includes B16, A16 and K16 where B16 is with G3 and G5, while A16 and K16 are with G5 and G4. The third one is K15 with G4 and G12 as favorable genotypes. The correlation for adjacent vectors was determined by cosine of the angles (Yan and Tinker, 2006). A15 and K15 were higher than 90° projected highly to positive and negative coordinates, respectively, witnessed negative association (Figures 3 and 7). A16, B16, and K16 showed less than 90 which implied strong correlation. This less than 90° indicates high correlation (Yan and Holland, 2010). The positive and negative relations were observed for Ls vs. ys combination analysis (Santos et al., 2016).

 

 

 

The horizontal axis drawn to pass via biplot origin and average genotypes was average tester coordinate (ATC) line used for visual displaying of both means vs. stability (Figure 4). The oval sign of an arrow is showing the positive end of ATC line. The average yielding capacity was estimated by mean projection onto ATC x-axis (Pavel et al., 2015; Ashraful et al., 2017). The double arrowed ATC lines passed via biplot midpoint divided the genotypes into the poorest (below average) vs. the highest (above average), and stable vs. unstable based on means and stability (Figure 4). The G5 is the highest, while G10 is the lowest for mean. The double arrowed ATC lines show the lowest vs. highest and stable vs. unstable genotypes (Fayeun et al., 2016). The stability was also explored by projection onto ATC vertical axis. For instance, G4, G12, G13, G23, G3, and G14 were strongly deviated from ATC line. These genotypes were unstable contributed high MS for GEI effect. The smaller distance between ATC line and genotypes markers also indicates high stability (Figure 4). For example, G5, G17, G25, G26, G15, G7, G16, and G8 were consistent for yield response showing slightly little projection. These shorter absolute deviations witnessed high stability (Melkamu et al., 2015; Fayeun et al., 2016; Ashraful et al., 2017). The term high stability is desirable only when associated with high means (Yan and Tinker, 2006). Moreover, the yield performance consists of both means and stability. Accordingly, the highest scores for PC1 (3.03, 2.25, 3.93, and 2.36%) and near zero absolute values for PC2 (0.77, -0.02, -0.93, and 0.13%) were recorded for G5, G17, G19, and G25, respectively (Table 1). The GGE biplot is effective to evaluate and rank the genotypes based on the means vs. stability (Yan et al., 2007; Amira et al., 2013; Pavel  et  al.,  2015).  The  GGE biplot was also used to integrate both superior means vs. stability (Kang, 2002; Kang and Magari, 1996). According to Yan (2001), Yan and Hunt (2001, 2002) and Yan and Kang (2003), the first two PCs of GGE biplot are completely partitioning the GEI by visual displaying of G vs. GEI effects distribution, both poor vs. superior, and which-win-where vs. stability pattern for identifying and integrating of superior vs. stability as well as discriminating vs. representing ME mapping.

 

 

The ATC line drawn to pass via average genotypes vs. biplot origin serves as reference to compare the genotypes based on means and stability. This ATC performance line was used for genotypes ranking according to the mean and stability (Yan and Kang, 2003). The average means for genotypes were estimated by projection onto ATC horizontal axis (Figure 5). The projection is equal to the longest vectors of all genotypes. The center of concentric circles is showing the virtual ideal genotypes (Figure 2). The ideal genotypes could be high yielding and absolutely better for stability (Yan and Kang, 2003; Pavel et al., 2015). The smaller distance from ideal genotype indicates absolute stability. The highest yielding G5 following G19, G17, and G25 was high for both means and stability. The closely positioned genotypes were highly desirable due to high means and stability (Pavel et al., 2015; Richmond et al., 2015; Fayeun et al., 2016). The genotypes located near to ideal genotype were also highly productive and stable (Olayiwola et al., 2015; Ashraful et al., 2017; Massaine et al., 2018). The G10, G8, and G9 were highly projected from the center of concentric circles to unstable. Moreover, the G13 and G18 are not different from apparently inferior G20 and G1 (Figure 5). These highly projected genotypes were found to be the poorest and unstable (Edmore et al., 2015; Massaine et al., 2018). There were different genotypic groups observed from overall inter-relationship among all 26 tested genotypes (Figures 5 and 7). The G17, G19, and G25 were found to be positively and moderately correlated with most favorable G5 (Figure 5). There are high correlation among the best genotypes namely G5, G17, G19, and G25 (Figure 5). The G6, G19, G25, G26, and G21 had shown positively strong association with the most favorable genotypes (G17 and G5) (Figure 7). Similar results of strong correlation among the genotypes were reported by Ashraful et al. (2017). They confirmed that the genotypes being positioned close to each other on GGE biplot responding together similarly to the environments were found near to these genotypes.

 

 

The average environment coordination (AEC) line was passed via average environment vs. origin for ideal environment position delineation. The average means was estimated by projection onto AEC horizontal axis. The projection is equal to the longest vectors of all environments. The center of concentric circles shows virtual   ideal   environments.    The   deviation    is    zero indicating absolutely representative for average environments. The representing vs. discriminating ability was also explored by length of projection (Figure 6). The AEC concentric circle GGE biplot method is best to estimate the discriminating vs. representing ability for assessing the genotypes (Yan and Tinker, 2006; Yan et al., 2007; Atnaf et al., 2013). For instance, the suitability of B16 and K16 were high in representing all genotypes. The concentric circles nearest sites were high for their stability  in  representing  the  genotypes  (Fayeun  et  al., 2016; Ashraful et al., 2017). The discriminating ability was significant and positive for A15 and K15 where they deviated strongly from the center of the concentric circles (Table 7 and Figure 6). The closer it is the better it will be as virtual ideal environment to all tested soybean genotypes. The K16 is highly favorable in representing all the tested genotypes considering both mean vs. stability. The ideal environments are close to ATC x-axis and zero projection onto ATC y-axis (Ashraful et al., 2017). Moreover, Blanche and Myers (2006) also witnessed  the efficiency of GGE for ideal genotypes vs. highly representing optimum environment identification for widely adapted genotypes selection.

 

 

The yield data vs. PC coordinates plotting for additive and interaction effects was done on the same biplot for yield variation efficiently partitioning. The A16 and B16 exhibited nearly additive effect on genotypes (Figure 7). The yield performance at A16 and B16 was associated with overall mean confirmed average responses to genotypes. The strongly projected sites were highly discriminated to all genotypes. The A15 and K15 were the longest which showed high yield variation for genotypes. The genotypes consistencies were better at A16 and B16 than inconsistent responses at A15 and K15 (Figure7). Environments with longer vectors are high in discrimination capability to all tested genotypes (Yan et al., 2007; Massaine et al., 2018). The results of the present study were strongly allied with Fayeun et al. (2016) who noticed little variation to genotypes for short vectors, while high variation for strongly projected testing sites. Similarly, the entries positioned near to the biplot origin were taken as an average means (Figure 7). For instance, G1, G18, G15, G21, and G26 showed average response for their yield means. G4, G5, G12, and G13 were the highest for their means being strongly projected from the center of the biplot. G3, G8, G9, and G10 were the poorest genotypes being deviated negatively (Figure 7). These polygon vertexes positively vs. negatively responding genotypes were unstable, adapted specifically at favorable environments (Melkamu et al., 2015). These two variables projection showed that the GEI which resulted from regressing of G over E as well as E over G contributed high MS for GEI variance. This resulted in inconsistency of the genotypes for mean performance due to strongly significant GEI effect in MEVT.

 

 

The angles present between the average tester axes vs. biplot vectors indicated the environmental stability (Figure 7). The distance between the biplot vectors represented the similarity vs. differences in discriminating vs. representing to all tested genotypes (Fayeun et al., 2016). The environments near to AEC are high for their stability. Accordingly, K16, B16, and A16 were less than 90° that deviated little from AET axes (Figure7). These averagely responding environments were suitable for widely adapted soybean genotypes selection. Smaller angles for vectors showed strongly positive correlation (Massaine et al., 2018). The results of the present study were also in accordance with Marcin and Krzysztof (2016).  A15  and  K15 were  highly  projected  from  AET showing high discriminating ability to all genotypes. Similar results were reported by Fayeun et al. (2016) and Bhartiya et al. (2017).