Indicators have advantages and disadvantages. The closer Ys (yield under stress conditions) is to Yp, the lower the sensitivity of the cultivar to water stress and, consequently, the smaller the SSI. The tolerance or susceptibility of hybrids determines drought-stress by comparing their SSI values [
23]. To evaluate drought-tolerance, some maize hybrids were estimated according to the quantitative indicators of drought-tolerance, including mean productivity (MP), geometric mean productivity (GMP), harmonic mean (HAR), Stress Tolerance Index (STI), Stress Sensitivity Index (SSI), and Tolerance Index (TOL) for mean stress levels (
Table 2). The weakness of this index is its inability to recognizing group A from group C (genotypes that have higher relative yields only in stressful conditions). According to (
Table 2), KSC260 and SC647 were the hybrids with the lowest SSI and had the lowest stress sensitivity. Also, the KSC707 and SC640 genotypes were identified as sensitive genotypes due to higher SSI than stress. The high value of the TOL index indicates the high sensitivity of the cultivar to stress, and its low value is favorable for breeders. Based on this index, KSC260 and SC647 showed the lowest sensitivity to drought stress. The highest susceptibility was related to the KSC704 genotype. The selection of hybrids based on TOL and SSI is more desirable in areas with a high yield in stress conditions and a low or medium yield in non-stress conditions. Another studied index is the average productivity index, which is obtained from the mean productivity of yield under favorable conditions and stress [
24]. A large amount of MP is a good criterion for selecting hybrids tolerant to drought stress.
According to
Table 2, SC640, KSC704, and SC647 hybrids had the highest index values and were the most tolerant hybrids. Also, the KSC707 was selected as the most sensitive hybrid based on these factors. The GMP, or geometric mean productivity, will be less skewed due to its lower sensitivity to differences between Yp and Ys. In terms of this index, SC647, SC640, and KSC704 hybrids were the most tolerant. The STI, or stress tolerance index, includes yield potential in non-stress conditions, yield in stress conditions, and intensity. According to this index, the SC647, SC640, and KSC704 hybrids were the most tolerant to drought stress, and the KSC707 hybrid was the least tolerant. The KSC707 genotype was more sensitive than other cultivars in terms of this index. According to the study of tolerance indices, SC647 and SC640 can be identified as tolerant genotypes, and KSC707 as a susceptible genotype. The results are based on the harmonic average productivity index (HAR), indicating high-stress-tolerance and high-performance potential [
25]. The highest values of water-stress-tolerance were related to SC647 and SC640 hybrids.
3.2. Drought Tolerance Indices and Yield under Stress Conditions in the Stage of Ear Emergence
The SC647 hybrid had the lowest SSI with the lowest sensitivity to stress in the ear emergence stage (
Table 4). The SC647 and KSC260 hybrids had the lowest sensitivity to drought stress in the TOL index. In terms of MP values, the SC647 and SC640 hybrids had the highest index, and they were recognized as the most tolerant hybrids at this stage. In terms of the GMP index, the SC647 and SC640 hybrid were the most tolerant. In terms of STI index, the SC647 and SC640 hybrids were the most tolerant, and the KSC707 hybrid was the least tolerant. Based on the harmonic average productivity index (HAR), the highest stress-tolerance was observed in the SC647, SC640 and KSC704 hybrids compared to other hybrids. The correlation coefficients between the estimated indices and yield under stress (Ys) and non-stress (Yp) were calculated to select the drought tolerance indices. Indices that correlate with performance in both stress and non-stress conditions are known as the best indicators [
27].
The correlation analysis of indices showed that yield under water-stress or (Ys) had the highest correlation with the STI, GMP, and HAR indices in grain yield under stress and expected conditions (
Table 5). Therefore, these indicators are the most appropriate for selecting drought-tolerant lines in maize under optimal irrigation conditions and high yield stress. The correlation between grain yield was positive and significant with STI (r = 0.86 *), MP (r = 0.84 *), and GMP (r = 0.85 *) at 0.05 level in normal irrigation conditions. Also, correlation of grain yield showed that, under stress with STI (r = 0.84 *), GMP (r = 0.85 *), HAR (r = 0.91 **) under positive and significant stress conditions. There is a positive and significant correlation of grain yield with the STI (r = 0.84), GMP (r = 0.85), and HAR (r = 0.91 **).
Some researchers have found a significant correlation at the probability level of 0.01. The correlation between drought tolerance and yield indices under mild stress conditions showed that yield under normal conditions correlated with the mean productivity index (r = 0.98 **), geometric mean (r = 0.98 **), and stress tolerance index (r = 0.97 **). The results of our study were consistent with their results [
28].
None of the above indices were significant under stress conditions or without stress in the flowering stage (
Table 6). The MP tolerance index had a positive and significant correlation with the GMP (r = 0.98 **). The STI index was significantly correlated with the MP and GMP (r = 0.99 **). The TOL (tolerance index) had a positive and significant correlation with the SSI (r = 0.91 **).
The MP tolerance index had a positive and significant correlation (r = 0.83) in conditions without Yp stress in the ear emergence stage with grain yield, and MP (r = 0.82), GMP (r = 0.89), STI (* R = 0.90), and HAR (r = 0.94 **) had a positive and significant correlation in the ear-stress stage under Ys stress conditions with grain yield (
Table 7). The HAR had a positive and significant correlation with STI (r = 0.99 **), MP (r = 0.96 **), and GMP (r = 0.99 **). The GMP index showed a high correlation with STI (r = 0.99 **) and MP (r = 0.99 **), and the MP index had a positive and high correlation with the STI (r = 0.98 **). A positive and significant correlation was observed for TOL with SSI (r = 0.93 **). Since MP-based selection increases average yield in stress and non-stress conditions, this index is not suitable for detecting group D genotypes (genotypes that do not perform well in stress and non-stress conditions). GMP is more suitable for isolating group D genotypes from other groups due to its lower sensitivity to differences between Yp and Ys. Among the studied indicators of STI, which is estimated based on GMP, it is of primary importance to selecting genotypes with high yields and greater tolerance to stress. The HAR has a significant correlation with Yp and Ys and can be a suitable index for selecting high-yield genotypes in both conditions, along with STI and GMP.
The SC647 and KSC704 hybrids had more tolerance to stress and good yield potential in stressful and non-stressful conditions than did other hybrids (
Table 7). In terms of average stress levels, the MP, HAR, and STI, which correlated with grain yield and stress conditions, were good criteria for selecting tolerance hybrids. GMP can be a suitable selection criterion in the case of ear stage under stress conditions. It concluded that the BC504 hybrid in the flowering stage and the KSC707 hybrid are the most sensitive hybrids to stress conditions in the ear stage. The KSC704 hybrid is the most tolerant hybrid in the flowering stage in stress conditions, and SC640 is the most tolerant hybrid in the ear stage in stress conditions. HAR was introduced as the best index for determining drought-tolerant hybrids due to its high correlation with grain yields. Choukan et al. [
28] showed that performance has a positive and significant correlation with mean productivity, geometric mean, and harmonic mean in severe stress conditions. A high correlation was observed with grain yield at different stress levels for the indices of mean productivity, geometric mean, and harmonic mean in normal conditions. These indices were determined as the superior index for introducing drought-tolerant hybrid [
29]. Fathi reported a significant correlation between STI and GMP and MP under normal conditions and drought stress [
30]. Mostafavi et al. reported that the reduction in maize yield under water-stress conditions at the corolla emergence and pollination stage reaches about 90%. The leaf area of maize decreased due to drought stress depending on the intensity and length of the stress period, but the final number of leaves was less affected by stress [
31]. Haji Babaei and Azizi investigated the effect of drought stress on the yield of maize hybrids. They reported that in normal and mild stress conditions, the most-used indices are GMP, MP and STI, and in normal and severe stress conditions, the most-used are the SSI and TOL [
32].
The results showed that most of the differences in the data are justified by the first and second principal components (78.95). The first principal component showed positive and high MP, SSI, and Yp coefficients. Also, the second principal component has negative coefficients for all indices except TOL and Yp. It has high coefficients for the TOL index, Ys, and by increasing these components, genotypes selected are less sensitive to stress. Therefore, selection based on the first component causes the selection of hybrids with a high yield in normal conditions. The first principal component can be called the performance potential component, and the second principal component can be called the stress sensitivity component. Therefore, the first principal component can be considered a performance component and the second principal component as a sensitivity component (
Table 8 and
Figure 2). Choukan et al. [
28] reported that principal component analysis of the first and second principal components interpreted 96.3% of the changes in drought tolerance indices for stress conditions. The first component showed a high correlation with yields in normal conditions, and MP, GMP, HAR, and STI indices with yield potential. These were able to isolate high yield hybrids in stress conditions. Many researchers have reported a significant positive correlation between Yp and Ys, suggesting that high-yielding genotypes under normal conditions can perform well under stress conditions [
33,
34,
35,
36]. Refiq et al. [
37] reported a significant positive correlation between 1000-grain weight and net grain yield in the plot. The results showed that most of the differences in the data are justified by the first and second principal components in the drought stress component in the ear stage (99.98) (
Table 8 and
Figure 2). The first principal component had positive and high coefficients in GMP, HAR, Ys, and SSI. Hybrids are selected by increasing these indices to yield in high-stress conditions. The second principal component has negative coefficients on STI, HAR, and Ys, and positive and high coefficients on TOL, Yp, and Ys. Genotypes are selected by increasing those that are less sensitive to stress. The results showed that most of the differences in the data were justified by the first and second principal components in the drought-stress component in the ear stage (99.98) (
Table 8 and
Figure 2). The first principal component had positive and high coefficients in GMP, HAR, Ys, and SSI. Hybrids are selected by increasing these indices to yield high-stress conditions. The second principal component has negative coefficients on STI, HAR, and Ys, and positive and high coefficients on TOL, Yp, and Ys. Genotypes are selected by increasing those that are less sensitive to stress.