Twelve of drought tolerance indices for sugar beet were calculated for genotypes based on root yield using the following equations as shown in Table 1.

Correlation analysis among drought tolerance indices was performed to determine the best drought-tolerant genotypes and indices. Principal component analysis (PCA) was performed based on the observations. Correlation analysis and principal component analysis (PCA), based on the rank correlation matrix and biplot analysis were performed by SPSS ver. 18, and Excel 2013/XLSTAT Version 2015.4.01.21575 (Copyright Addin soft 1995-2018).

To determine the most desirable drought tolerance criteria, the correlation coefficient between YP, YS and other quantitative drought tolerance indices in moderate and severe stressed conditions were calculated (Table 4,Table 5). There was a positive significant correlation between Yp and Ys (r=0. 50) and (r=0.65) in the severe stress (50%) and moderate stress conditions (75%), respectively (Table 4 and Table 5). This indicates that high root yield performance under favorable condition resulted in relatively high root yield under stress conditions.

Both Yp and Ys in the control-50% analysis (severe drought stress) have significantly positive correlation (P<0.05) with MP (r=0.80 and 0.92), GMP (r=0.73 and 0.95), YI (r=0. 50 and 1.00), HM (r=0.67 and 0.98) and DI (r=0.32 and 0.98), while the YSI and RDI had significantly positive correlation with Ys (r= 0.90 and 90). This indicates that these indices were more effective to identify high yielding genotypes under drought stress as well as non-stress conditions (Table 4). The correlation between Yp with TOL, YSI, SDI, RDI and SSP was negligible (r = 0.17, r = 0.07, r = -0.07, r = 0.07 and r = 0.17 respectively). On the other hand the correlation between Ys and either SSI, TOL. SDI and SSPI indices were significantly negative values with r = -0.47, r = - 0.77, r = -0.90 and r = -0.77, respectively.

The observed relationship between YP, MP, STI, YS, MP and STI are in consistent with those reported by 47 in sorghum and 48 in wheat crop. 49 Introduced STI, MP and GMP as the best indices for yield predicting. 50 Reported that GMP, MP STI indices were significantly positive correlation with stress on yield. 51 Mentioned that, the validity of selection index for screening genotypes for stress conditions depends on its good correlation with yield under normal and stressed wheat. Similarly, three indices (STI, GMP and MP) had the highest positive correlation coefficient with yields under normal and drought stress conditions and introduced as selection indices for post water stress tolerance in sorghum and wheat 52, 53 .

The PCA showed that the first two components (PC1 and PC2) explained about % 77.206 and 99.980 of the total variance in moderate stress (75%) and 70.871and 91.304 for severe stress (50%) analyses (Table 6 and Table 7). Therefore, the bi-plot was drawn based on the first two components (Figure 1 and Figure 2).

For the moderate stress (75%) analysis (Table 6), the PC1 explained 77.206% of the obtained variation with a positive correlation with all indices except SSI, TOL, SDI and SSPI. This component had a highly positive correlation (0.979) with the yield under the stress environment and mild correlation (0.478) with the yield under the non-stress environment. However, the PC2, which explained only 22.774% of the total variation had a positive correlation with all indices except YSI (-0.243), DI (-0.042) and RDI (-0.243) (Table 6), and this component was highly positive correlated (0.979) with Ys and positively correlated (0.478) with Yp.

In the severe stress conditions (50%) analysis (Table 7), the first PC1 explained 70.871% of the obtained variation , and had positive correlation with Yp (0.121), Ys (0.315), MP (0.273), GMP (0.288), YI (0.315), YSI (0.301), HM (0.298), DI (0.316) and RDI (0.301) indices. Thus, the first dimension can be named as the yield potential and drought tolerance. This component separates drought tolerant genotypes with high yield in both environments. The PC2 explained 20.433% of the total obtained variation, and showed high coordination with SSI (0.356), YSI (0.185), DI (0.034) and RDI (0.185) (Table 7). This component had negative correlation (-0.127) with yield under stress conditions (YS) thus it can be named drought sensitive dimension with high yield under non-stressed and low yield under stressed environment (Table 8). The relationships among the indices were graphically presented in biplots of the PC1 and PC2 (Figure 1 and Figure 2). Genotypes that possessed high PC1 and low PC2 values are more stable under both drought stress and favorable conditions (Golabadi et al. 2006) 54. Based on the first two components in the control-50% analysis, genotypes 6 and 7 were identified as the most stable high yielding genotypes in both environments. On the other hand, the genotypes 5, 8 and 2 were classified as drought-sensitive genotypes (Figure 1). In the control-75% analysis, the Genotypes 4 and 6 were more stable than the other genotypes; however, genotypes 1 and 9 were most sensitive (Figure 2).

Stable genotypes under both favorable and drought conditions are vital for plant breeding programs in areas prone to drought stress. However, the level and time of drought stress events are not predictable; for this reason, it is better to evaluate sugar beet genotypes under various levels of drought stresses. Therefore, a genotype that shows low fluctuations of yield under various levels of drought stress conditions can be considered drought tolerant. Further, drought indices could be good indicators of genotypes stability.

In the present study, we found highly significant correlation between some indices, indicating that some of them measure similar aspects of drought tolerance. Farshadfar et al. (2012) 55 and Dehghani et al. (2009) 56 obtained similar results in multivariate analysis of drought tolerance in different crops. Yan et al., 200057, suggested using biplot, three-dimensional plots and cluster analysis as the most appropriate techniques for analysis the multi-location trials data, for identifying drought tolerant genotypes and for elucidating the relationships of drought tolerance attributes with yield in non-stress and stress conditions.