The AMMI model is comprised of additive main effects of genotype and environment, and the multiplicative effect of GxE interaction, and thus can explain more information compared to other methods (Gauch 2013). AMMI analysis as such does not make provision for a quantitative stability measure that is deemed useful to quantify the ranking of studied genotypes according to their yield stability. AMMI stability parameters permit to evaluate yield stability after reduction of the noise from the G×E interaction effects (Zhang et al. 1998). Highly significant effects of environment (E), G×E interaction and genotypes (G) had been observed by AMMI analysis (Table 3). Environment explained about significantly 21.6% of the total sum of squares due to treatments indicating that diverse environments caused most of the variations in genotypes yield (Table 3). Significant proportion of G>E interaction deserves the stability estimation of genotypes over environments (Veenstra et al. 2019). Genotypes explained only 18% of total sum of squares, whereas GxE interaction accounted for 21.5% of treatment variations in yield. More of GxE interaction sum of squares as compared to genotypes indicated the presence of genotypic differences across environments and complex GxE interaction for wheat yield. Further partitioning of GxE interaction revealed that the first six multiplicative terms (IPCA1, IPCA2, IPCA3, IPCA4, IPCA5 and IPCA6) explained 47.1%, 17.9% , 14.7%, 9.4%, 8.2% and 1.9 % of interaction sum of squares, respectively. Total of significant components were 99.3 % and remaining 0.7% is the residual or noise, which is not interpretable and thus discarded (Adjebeng et al. 2017).

Low absolute value of IPCA1 expressed by G7, G5, G9 and higher value achieved by G3 (Table 5). Minimum values of (EV) associated with stable genotype accordingly, the genotype G9 followed by G5 G4 and G12 had the maximum value of EV measure. SIPC measure identified G9 followed by G5, G4 possessed lower value, whereas G2 would be of least stable behaviour. Za measure considered absolute value of the relative contribution of IPCs to the interaction revealed G8, G12 and G5 genotypes as most stable in descending order of stability, whereas G2 genotype with the least stability. ASTAB measure observed genotypes G9 G5 and G12 as most stable and genotype G2 was least stable in this study (Rao and Prabhakaran 2005). ASV measure showed that genotypes G9, G7, G5 possessed lower values would express stable performance and G3 be of least stable type. Values of ASV1 selected G7 G5 G9 for their stable behaviour whereas G3 would express unstable performance. Measures MASV and MASV1 consider all significant IPCAs. Values of MASV showed that the genotypes, G9,G5 and G8 were most stable and G12 G8 & G9 would be stable by MASV1measure respectively (Ajay et al. 2019). The lower values of WAASB associated with stable nature of genotypes as G9, G5, G12 for considered locations of the zone at the same time maximum value obtained by G2, that is, the one that deviates maximum from the average performance across environments. Lower value of Superiority index had observed for G2 G3 and G8 whereas large value by G7. Genotypes G8 G2 and G6 were identified for their more stable yield performance by MHPRVG as well as by PRVG measures and G1 with least stable yield. Maximum yield expressed by G1 G7 followed by G2 and G10 as good variation had been observed from 26.9 to 35 q/ha among genotypes.

Stability alone is not a desirable selection criterion as stable genotypes may not be a high yielders, simultaneous use of yield and stability in a single measure is essential (Kang 1993; Farshadfar et al. 2008). Simultaneous Selection Index also referred to as genotype stability index (GSI) or yield stability index (YSI) (Farshadfar et al. 2011) was computed by adding the ranks of stability measure and average yield of genotypes. Ranks for IPCA1 measure selected MACS 6695, HI 1605 & HI 8805 for stable high yield performance, whereas high values suggested as least stable yield for GW 1346 (Table 7). EV measure identified HI 1605, HI 8805 & MACS 6696 whereas by SPIC favoured genotypes were HI 1605, HI 8805 & DBW 93. Genotypes HI 1605, MACS 6695 & HI 8805 possessed lower value of Za measure. WAASB measure observed suitability of HI 1605, HI 8805 & HI 8802 genotypes. Superiority index while weighting 0.65 and 0.35 for yield & stability found MACS 6695, HI 1605 & NIAW 3170 as of stable performance with high yield. Analytic measures MASV and MASV1 consider all significant principal components of interactions. MASV HI 1605, HI 8805, MACS 6696 genotypes of choice for these locations of the zone as and MASV1 settled for HI 1605, HI 8802. MACS 6695. Least magnitude of ASV and ASV1 pointed towards MACS 6695, HI 1605 and HI 8805 wheat genotypes (Oyekunle et al. 2017). PRVG and MHPRVG measures observed suitability of NIAW 3170, MACS 6695 & MACS 6696 wheat genotypes. Moreover, the average yield of genotypes ranked NIAW 3170, MACS 6695 & MACS 6696 as of order of choice. In the present study, all measures identified genotypes HI 1605, MACS 6696 and HI 8805 as stable and high yielders.

Loadings of stability measures as per first two significant principal components for evaluated wheat genotypes were reflected in table 9. Biplot graphical analysis based on two significant principal component analysis (PCA) as these PCAs accounted for 91.4% of variation of the original variables (Balestre et al. 2019). The stability measures of wheat genotypes grouped into three major groups (Fig. 1). SI clubbed with MASV and EV. Yield clubbed with PRVG & MHPRVG measures. Large group consisted of ASTAB, ASV, IPCA1, ASV1, SIPC, Za, MASV1. Measure WAASB maintained distance from stability measures and observed as outlier in graphical analysis.

Average yield expressed only significant positive correlations with SI, ASTAB, MHPRVG, PRVG & EV (Table 11). SI expressed only negative values of correlations most of other stability measures except of MHPRVG, PRVG, yield. Only indirect relations were observed with stability measures (EV, SIPC) by SI measure otherwise positive values of correlation were seen. WAASB measure exhibited direct relationships with other measures analogous of negative values with MASV, SI, MHPRVG, PRVG, yield.

Analytic measures MHPRVG & PRVG had only positive values with SI, and yield remaining stability measures maintained negative values. AMMI based measures Za, SIPC, SV, ASV1, MASV1 and ASTAB achieved only positive correlation values among themselves and with others (Ajay et al. 2019). More over MASV had maintained only negative relationships with all measures. Negative correlations of SIPC with SI, PRVG, MHPRVG and yield were of low magnitude. Indirect relations of Za observed with PRVG, MHPRVG and yield of moderate negative values. Same behaviour of negative correlations had displayed by IPCA1, ASV1, MASV1, ASV, MASV also.

Highly significant effects of environment (E), G×E interaction and genotypes (G) had been observed by AMMI analysis. Environment explained about significantly 33.7% of the total sum of squares due to treatments indicating that diverse environments caused most of the variations in genotypes yield (Table 4). Significant proportion of G×E interaction deserves the stability estimation of genotypes over environments (Veenstra et al. 2019). Genotypes explained only 10.7% of total sum of squares, whereas GxE interaction accounted for 20.5% of treatment variations in yield. Partitioning of GxE interaction revealed that the first six multiplicative terms (IPCA1, IPCA2, IPCA3, IPCA4, IPCA5 and IPCA6) explained 37.8%, 25.4% , 16.2%, 8.5%, 7.9% and 3.5 % of interaction sum of squares, respectively. Total of significant components were 99.3 % and remaining 0.7% is the residual or noise, which is not interpretable and thus discarded (Adjebeng et al. 2017).

Wheat genotypes G5, G10, G1 expressed least value of IPCA1 and higher value achieved by G3 (Table 6). The genotype G8, G6 followed by G10 had expressed lower and G9 showed the maximum value of EV measure. The lower value SIPC measure identified G6 followed by G8, G10 as the most stable genotypes, whereas G9 would be of least stable behaviour. Za measure revealed G4 G6 and G5 would be stable genotypes in descending order of stability, whereas G8 genotype with the least stability. ASTAB measure observed genotypes G7 G8 and G10 as most stable and genotype G1 was least stable in this study (Rao and Prabhakaran 2005). ASV and ASV1measures showed that genotypes G5, G7, G6 possessed lower values would express stable performance as compared to G3. Analytic measures MASV and MASV1 consider all the significant IPCAs. Values of MASV showed that the genotypes G8 G10 and G2 were most stable while MASV1 measure suggested the stable behaviour of G10, G8 & G2 genotype (Ajay et al 2019). Stable nature of genotypes as G6, G5, G10 confirmed with the lower values of WAASB measure for considered locations of the zone at the same time G3 deviated maximum from the average performance across environments. Lower value of Superiority index had observed for G8 G9 and G2 whereas unstable performance of G5 by large value. Genotypes G8 G2 and G6 were identified by MHPRVG and PRVG measure along with least stable yield of G5. Maximum yield expressed by G5 followed by G4 and G3 as good variation had been observed from 22 to 27.5 q/ha among genotypes.

Least ranks of IPCA1 measure considered MP1358, NIAW3170 & NIDW1149 were as stable with high yield, whereas high values suggested as least stable yield for UAS446 (Table 8). EV measure identified MACS4087, MP1358 & NIAW3170 whereas SPIC favoured MACS4087, MP1358 & NIAW3170 genotypes. MACS4087, MP1358 & HI1605 possessed lower value of Za measure. WAASB measure observed suitability of MP1358, NIDW1149 & NIAW3170 genotypes. Superiority index while weighting 0.65 and 0.35 for yield & stability found MP1358, NIAW3170 & MACS4087 as of stable performance with high yield. Composite measures MASV as well as MASV1 selected NIAW3170, HI1605, MACS4087 genotypes of choice for these locations of the zone. Values of least magnitude of ASV and ASV1 pointed towards MP1358, HI8805 and NIAW3170 wheat genotypes (Oyekunle et al. 2017). PRVG and MHPRVG measures observed suitability of MP1358, HI1605 & MACS4087 wheat genotypes. More over the average yield of genotypes ranked MP1358 , MACS4087 & HI1605 as of order of choice. In the present study, all measures identified genotypes MACS4087, MP1358 & NIAW3170 as stable and high yielders.

Loadings of stability measures as per first two significant principal components for evaluated wheat genotypes were reflected in table 10. Biplot graphical analysis based on two significant principal component analysis (PCA) the simultaneous ranks (Fig. 2). These two PCAs accounted for 81.8% of variation of the original variables (Balestre et al. 2019). The stability measures of wheat genotypes grouped into three major groups. MASV1 clubbed with Za and yield grouped with PRVG & MHPRVG measures. Larger group comprises of ASTAB, MASV, ASV, IPCA1, ASV1, SIPC. Measure WAASB maintained distance from stability measures and observed as outlier in analysis.

Mean yield showed mostly positive correlations and only negative values expressed towards Za and IPCA1. Similar behaviour of MHPRVG & PRVG measures seen with other stability measures (Table 12). SI expressed mostly negative values other measures except of weak direct relation with MASV1, MASV along with strong with yield, MHPRVG & PRVG measures. WAASB measure exhibited direct relationships with other measures and indirect with only MASV1 & SI. AMMI based measures SIPC, SV, MASV1, MASV and ASTAB achieved only positive correlation values among themselves and with others (Ajay et al. 2019). More over Za and EV had maintained positive relationships with other non AMMI based measures. ASTAB, ASV, ASV1, SIPC, Za had indirect relation with SI measure.