Introduction

Maize, wheat and rice provide approximately 30% of calories for more than 4.5 billion people in the world (Von Braun et al. 2010). Indeed, demanding for maize will be nearly twice in the developing countries by 2050 (Ray et al. 2013). Drought is a multi-dimensional stress for plants that can influence various levels of their growth and development over space and time. Therefore, physiological responses are unpredictable and complex (Sari-Gorla et al. 1999). As a matter of fact, drought stress in maize causes rolling of the leaves and makes change in color from green to green gray. Meantime, with closing of stomas, photosynthesis is being dramatically decreased and so growth slows down (Edmeades 2013). Since maize yield is very susceptible to abiotic stresses, study of maize tolerance to the abiotic stress such as drought, salinity, flooding and pollutants is important (Wattoo et al. 2009).

Chlorophyll content is a key indicator of crop photosynthesis, and it reflects the level of crop stress (Nagy et al. 2015). Chlorophyll a and b are the most important pigments of the total chlorophyll that almost vital to convert light energy and then store the chemical energy that powers the biosphere (Cannella et al. 2016). During vegetative growth under drought stress, the concentration of chlorophyll a and b and likewise total chlorophyll content significantly decrease. Strong correlation between higher chlorophyll contents and carotenoids and stress tolerance was reported in different plant species (Khaleghi et al. 2012; Hailemichael et al. 2016). The chlorophyll content or index as an important physiological parameter in agronomy is used to evaluate photosynthetic efficiency in breeding programs (Fernandez-Marin et al. 2015). Ganji et al. (2012) revealed that drought resistant genotypes had the highest chlorophyll content. Therefore, the measurement of chlorophyll content as a new tool (indicator) was useful to assay effects of different stress such as heat, drought and salinity on crop yield (Shah et al. 2017).

Generation mean analysis is a biometrical method developed that greatly helps in the estimation of various components of genetic variance. This method gives information on the value of average additive, dominance and non-allelic (epistasis) gene actions in determining genotypic values of the generations and as a consequence. In the most of methods, evaluation is based on a generation, but this method is used to calculate the genetic effects of the mean of different generations (Kearsey and Pooni 2004; Said 2014). Estimation of the gene action types, level of the additive effect and dominance degree are very important in designing a plant breeding for improving the trait of interest (Mather and Jinks 1982). The major role of additive and non-additive effects in the genetic controlling of quantitative traits in maize and different crop plants revealed by many researchers (Mbogo et al. 2015; Harakotr et al. 2016; Prabhu et al. 2017). Efficiency of selection majority depends on genetic variances of additive and environment and interaction effect of genotype × environment, and this causes breeders to understand what extent of the variation is heritable and how much of this variation is genetically. Knowledge of interact and gene act determine which breeding system can improve gene action and illustrate the role of this system in the crop plants evolution (Hallauer et al. 2010). Information about the inheritance mechanism and additive genetic variance in maize for the traits related to drought tolerance is effective breeding strategy for developing water deficit tolerant varieties (Mather and Jinks 1982; Zaidi et al. 2010).

The aims of this study were to determine the effective breeding strategy for genetic improvement of grain yield, physiological traits and genetic assessment of these traits in maize using seven generation models including P1, P2, F1, F2, F3, BC1 and BC2 under full irrigation and two water deficit conditions. However, there are no reports or studies on the gene action of physiological traits in maize under water deficit conditions by the generation mean analysis. Furthermore, we implemented multivariate analysis to understand the relationships of grain yield and physiological traits under the experimental conditions.

Materials and methods

Field evaluation and experimental design

Seeds of maize inbred lines including B73 (maternal line of cytoplasmic male sterile, tall and late), MO17 (paternal line, dwarf and early), SC704 (F1 hybrid derived from across parents inbred lines), F2, BC1, BC2 and F3 generations were evaluated in a randomized complete block design (RCBD) with twenty replications under full and deficit irrigation. Three experiments were performed under field conditions at 38° 5′ N latitude and 46° 17′ E longitude in the agricultural research station at University of Tabriz, Tabriz, at an average altitude of 1360 m above sea level. The climate of the region is defined as cold semi-arid based on Domarton classification. The mean wind speed in 2 m above ground level was 5.93 m s−1. Seeds were hand-sown during the second half of May and two seeds per each pipe (U-PVC), 20 cm in diameter and one meter height, which was filled with loamy sand soil (83.67% sand, 10.97% silt and 5.36% clay). At tillering stage, thinning was undertaken and one plant per pipe was maintained till physiological maturity. The growing season mean temperature was 37.5 °C with 29% relative humidity at 28.20% FC (field capacity) and 13.80% PWP (permanent wilting point). The seeds were grown under natural sunlight with a bulk density (ρb) of 1.41 g cm−3. For protection of the crops from rainfall, a plastic cover was used under the water deficit conditions. Weeding and fertilizing were performed throughout the growing season under all three irrigation conditions. After hand harvesting, grain yield per plant based on (14% moisture per g) was measured.

According to standard method of FAO (Allen et al. 1998) and using class A evaporation pan daily, plant water requirement and evaporation daily were measured. The stresses were applied at three levels of full irrigation (100% FC), mild stress (55% available water depletion) and severe stress (75% available water depletion). The application of stress began after 5–6th leaf stage and continued until the silking stage. By measuring the relative humidity, wind speed and position of the pan, the pan coefficient (KP) was calculated, and with its application, ETO (reference crop evapotranspiration) was achieved. Then, the KC curve was plotted using the three values of the maize crop coefficient (KC) in initial, mid-season and the end of the season. The crop evapotranspiration (ETC) was determined using KC and ETO (ETC = KC ETO). When the amount of ETC was equal to stress treatments level, irrigation was applied. Available water (AW) was calculated on volume basis using the following equation:

$$AW = \left( {\frac{{\theta_{{{\text{FC}}}} - \theta_{{{\text{PWP}}}} }}{100}} \right)D\frac{{\rho_{{\text{b}}} }}{{\rho_{{\text{w}}} }}$$

where \(\rho_{{\text{w}}}\): density of water (1 g cm−3), D: root depth of maize.

Leaf chlorophyll index and photosynthetic pigments

Leaf chlorophyll index was measured using chlorophyll meter (Minolta SPAD 502). The data were collected at the first leaf below the flag leaf from the midrib to the leaf margin. Three times per plant were measured to get an average. The contents of chlorophyll and carotenoid were quantitatively estimated by Lichtenthaler and Welburn (1983) method. The chlorophyll a and b, total chlorophyll and carotenoid contents were estimated by the following equations:

$$\begin{aligned} {\text{Chlorophyll-}}a\,\left( {\text{mg/g}} \right) & = \left( {12.21 \, \times \, A \, \left( {663} \right){-}2.81 \, \times \, A \, \left( {646} \right)} \right) \times \, v/1000 \times \, w \\ {\text{Chlorophyll-}}b\,\left( {\text{mg/g}} \right) & = \left( {20.13 \, \times \, A \, \left( {646} \right){-}5.03 \, \times \, A \, \left( {663} \right)} \right) \times \, v/1000 \times w \\ {\text{Total chlorophyll}}\,\left( {\text{mg/g}} \right) & = {\text{Chlorophyll-}}a + {\text{Chlorophyll-}}b \\ {\text{Carotenoid}}\,\left( {\text{mg/g}} \right) & = \left( {1000 \times A \, \left( {470} \right){-}3.27 \, \left( {{\text{chla}}} \right){-}104 \, \left( {{\text{chlb}}} \right)} \right)/229 \\ \end{aligned}$$

where V: final volume of 80% acetone (10 ml), W: weight of sample taken (0.1 g).

Statistical and genetic analysis

Analysis of variance and mean comparison of the traits were performed using Statistical Analysis System (SAS 9.2). Pearson’s correlation was undertaken using SPSS (IBM SPSS Statistics 23), and principal component analysis was undertaken by CANOCO software for Windows 4.5 (Lepš and Šmilauer 2003) to describe relationships among the traits under experimental conditions.

Generation mean analysis was done by Mather and Jinks (1982) method using Microsoft Excel program. In this model, the overall average for each trait is shown as follows:

$$Y = m + \alpha \left[ d \right] + \beta \left[ h \right] + \alpha^{2} \left[ i \right] + 2\alpha \beta \left[ j \right] + \beta^{2} \left[ l \right]$$

where Y: the generation mean, m: F∞ metric, d: additive effects, h: dominance effects, i: additive × additive interaction, j: additive × dominance interaction, l: dominance × dominance interaction and α, β, α2, 2αβ and β2 are the coefficients of genetic parameters.

The calculation was carried out for each character separately in three irrigation conditions via weighted least squares method. At first, additive-dominance model was conducted and the joint scaling test was used to verify the goodness-of-fit model (Cavalli 1952). All genetic parameters were estimated after adequacy testing of three-parameter models by joint scaling test. Then parameters were tested for significance using a t test. If the Chi-square value was significant, other models which included epistatic components were fitted. The model which had significant results of all parameters, non-significant chi-square value and high adjusted R2 was the best fit model. For test of the additive-dominance model validity, four scaling tests were used and the variance of the tests was calculated as following equations:

$$\begin{array}{*{20}l} {A \, = {\text{ 2BC}}_{{1}} {-}{\text{ P}}_{{1}} {-}{\text{ F}}_{{1}} } \hfill & {{\text{VA }} = {\text{ 4V}}_{{{\text{BC1}}}} + {\text{ V}}_{{{\text{P1}}}} + {\text{ V}}_{{{\text{F1}}}} } \hfill \\ {B \, = {\text{ 2BC}}_{{2}} {-}{\text{ P}}_{{2}} {-}{\text{ F}}_{{1}} } \hfill & {{\text{VB }} = {\text{ 4V}}_{{{\text{BC2}}}} + {\text{ V}}_{{{\text{P2}}}} + {\text{ V}}_{{{\text{F1}}}} } \hfill \\ {C \, = {\text{ 4F}}_{{2}} {-}{\text{ 2F}}_{{1}} {-}{\text{ P}}_{{1}} {-}{\text{ P}}_{{2}} } \hfill & {{\text{VC }} = {\text{ 16V}}_{{{\text{F2}}}} + {\text{ 4V}}_{{{\text{F1}}}} + {\text{ V}}_{{{\text{P1}}}} + {\text{ V}}_{{{\text{P2}}}} } \hfill \\ {D \, = {\text{ 4F}}_{{3}} {-}{\text{ 2F}}_{{2}} {-}{\text{ P}}_{{1}} {-}{\text{ P}}_{{2}} } \hfill & {{\text{VC }} = {\text{ 16V}}_{{{\text{F3}}}} + {\text{ 4V}}_{{{\text{F2}}}} + {\text{ V}}_{{{\text{P1}}}} + {\text{ V}}_{{{\text{P2}}}} } \hfill \\ \end{array}$$

The significance of the scaling tests caused to compute the epistasis (non-allelic) interaction using the six parameters genetic model of Mather and Jinks (1982). Variance components including additive, dominance and environmental, broad sense (\(h_{{\mathrm{b}}}^{2}\)) and narrow sense (\(h_{{\mathrm{n}}}^{2}\)) heritability were calculated as the following equations, respectively:

$$\begin{aligned} {\text{V}}_{{\text{A}}} &= {\text{ 2V}}_{{{\text{F2}}}} {-}{\text{ V}}_{{{\text{BC1}}}} {-}{\text{ V}}_{{{\text{BC2}}}} \hfill \\ {\text{V}}_{{\text{D}}} &= { 4}\left( {{\text{V}}_{{{\text{BC1}}}} + {\text{ V}}_{{{\text{BC2}}}} {-}{\text{ V}}_{{{\text{F2}}}} {-}{\text{ V}}_{{\text{E}}} } \right) \hfill \\ {\text{V}}_{{\text{E}}} &= \, 0.{25 }\left( {{\text{V}}_{{{\text{P1}}}} + {\text{ V}}_{{{\text{P2}}}} + {\text{ 2V}}_{{{\text{F1}}}} } \right) \hfill \\ h_{{\text{b}}}^{2} &= \left( {{\text{V}}_{{\text{A}}} + {\text{ V}}_{{\text{D}}} } \right) / \left( {{\text{V}}_{{\text{A}}} + {\text{ V}}_{{\text{D}}} + {\text{ V}}_{{\text{E}}} } \right) \hfill \\ h_{{\text{n}}}^{2} &= \left( {{\text{V}}_{{\text{A}}} } \right) / \left( {{\text{V}}_{{\text{A}}} + {\text{ V}}_{{\text{D}}} + {\text{ V}}_{{\text{E}}} } \right) \hfill \\ \end{aligned}$$

Degree of dominance was calculated as follows, based on the additive and dominance variance components estimated from the within-generation variances:

$${\text{Degree of dominance }} = \sqrt {2{\text{V}}_{{\text{D}}} /{\text{V}}_{{\text{A}}} } .$$

Results

Statistical and genetic analysis

Analysis of variance revealed that significant differences among seven generations in full irrigation and water deficit conditions for all studied traits (Table S1). The generation × stress levels interactions were also significant except for chlorophyll a, b and total chlorophyll. Therefore, the significant difference between generations makes possible generation mean analysis.

The mean values for grain yield, carotenoids and SPAD value are shown in Fig. S1. The highest grain yield and SPAD value were for SC704 under full irrigation. The lowest grain yield and carotenoids were observed in B73 under severe stress. The highest carotenoids and the lowest SPAD value were belong to F3 in normal and sever stress conditions, respectively. Grain yield and carotenoids of MO17 33.79% and 10.99% reduction, while in the B73 56.06% and 26.03% reduction (Table S2). However, for SPAD value the reduction was 22.18% in MO17 and 14.81% in B73.

Pearson’s correlation matrix between the grain yield and physiological traits (Table S3) revealed that the most positive correlation between total chlorophyll and chlorophyll-a, and chlorophyll-b significantly (r ≥ 0.8 and r ≥ 0.5, respectively) under all three conditions. Moreover, there was a positive and significant correlation between grain yield and carotenoids (r = 0.579), and SPAD value (r = 0.598) under severe stress condition. The PCA biplot performed on the grain yield and physiological traits indicated 98.60% of variation for PC1 and 1.40% of variation for PC2 under all water regimes (Fig. S2). The PCA results showed a positive correlation among grain yield, carotenoids and SPAD value which grain yield and carotenoids strongly associated with PC1.

Scaling tests were significant for all studied traits in full irrigation (Table S4). Hence, non-allelic or epistasis interactions were involved in the genetic controlling of these traits in normal condition. In the mild and severe stress conditions, scaling tests were significant for all traits except for grain yield and carotenoids, respectively.

The estimation of genetic effects and their standard errors (SE), Chi-square (X2) and its degree of freedom (df) is presented in Table S5. For all grain yield per plant and physiological traits, m was significant which indicates a significant difference between two parents. In all traits under full and deficit irrigation, the value of the MO17 was greater than the B73 and the superior parent (MO17) was considered as the second parent, considering that the sign of additive effect was negative. Furthermore, negative sign of additive effect showed that the superiority of the reduction alleles of studied traits.

Variance components of all traits are given in Table S6. For some traits in different environmental conditions, variances of dominance and additive were estimated negative and these negative values were set to zero in the corresponding table, and in the case of zero additive variance, the degree of dominance was non-estimated.

Grain yield per plant

Both additive and dominance gene effects were involved in the inheritance of grain yield because dominance and additive gene effects were significant (Table S4). In addition to, the interactions of additive × additive and dominance × dominance were significant. In both stress conditions, additive and dominance gene effects were significantly negative and positive, respectively. Under full irrigation and mild stress condition, VA had high value, but in severe stress condition VD was high (Table S5). The degree of dominance was greater than unity in all three conditions.

Chlorophyll-a

The results of generation mean analysis showed that dominance effect and dominance × dominance interactions were significant in the full and severe stress irrigation. In addition to, additive × additive effect was also significant for chlorophyll-a under severe stress condition. In all three conditions, VA was higher than VD.

Chlorophyll-b

The gene effects of dominance, additive × additive and dominance × dominance were significant in the inheritance of this trait under the mild stress condition. Under severe stress condition additive, dominance and additive × dominance interaction effects were involved in the genetic control of this trait. The significance of chi-square (X2) in the three conditions indicated that trigenic interaction, genetic linkage and maternal effects play a role in the inheritance of this trait. In full and water deficit irrigation, VA was high.

Total chlorophyll

In the inheritance of this trait under full and mild stress irrigation, the gene effects of dominance and dominance × dominance were significant. In the severe stress condition dominance, additive × additive and dominance × dominance effects were significant. Degree of dominance was higher than unity under full irrigation that showed the over-dominance gene action in controlling of this trait. Under full and water deficit irrigation, VD and \(h_{{\mathrm{b}}}^{2}\) were high.

Carotenoids

Both types of additive and dominance effects were involved in the genetics of carotenoid under normal condition. Furthermore, the interaction effects of additive × additive, additive × dominance and dominance × dominance were significant that involved in the genetics of this trait and dominance effect was higher than additive effect. Under mild stress condition, dominance main effect and epistasis effects of additive × additive and dominance × dominance were significant. Degree of dominance under water deficit irrigation was greater than unity for carotenoids indicated that over-dominance gene action for this trait.

SPAD value

Dominance × dominance and additive effects were significant under full irrigation. In both water deficit conditions, four-parameter model [ m −  d  −  h −  l] was determined as the best model for the chlorophyll index. Both main effects of dominance and additive were involved in the genetic control of this trait, but dominance effect was higher than additive effect. Furthermore, dominance × dominance interaction effect was significant and involved in the genetics of chlorophyll index. Degree of dominance was greater than unity, indicating over-dominance gene action for this trait under full irrigation.

Discussion

The average of traits in SC704 derived from the crossing of two parents in grain yield per plant and chlorophyll index was more than parents, which indicates that there is an over dominance in these traits (Fig. S1-A and -C). Moreover, the average of SC704 hybrid was more than F2 generation in all grain yield per plant, carotenoids and chlorophyll index, which can be attributed to adverse effects of inbreeding (Fig. S1-A, -B and -C). In the terms of studied traits, MO17 was superior parent compared to B73 (Moharramnejad et al. 2015; Kravić et al. 2016). In general, these traits among seven generations were decreased by increasing of stress levels. Similarly, many studies documented the reduction in the grain yield, carotenoids and chlorophyll content (SPAD value) under watering regimes (Steidle Neto et al. 2017; Li et al. 2019), while according to Chen et al. (2016) drought stress had no significant effect on the carotenoids which is opposite with our results.

Correlation matrix and PCA biplot as the efficient tools for the plant breeders could improve the selection process (Beiragi et al. 2012). PCA and correlation matrix revealed strong associations among grain yield, carotenoids and SPAD value. Hence, these traits could be selected in maize breeding programs for improvement of grain yield and water deficit tolerance. Many similar investigations have been shown by Ali et al. (2017) and Qaseem et al. (2019), and they observed that physiological traits such as chlorophyll content (SPAD) had a strong positive correlation with grain yield and yield components of maize and wheat, respectively.

The results of the genetic analysis revealed that the digenic epistatic model was adequate to explain variation of generations mean for all studied traits expect carotenoids under stress condition. This analysis for all of the characters showed the importance of additive, dominance and types of epistasis gene effects.

The signs of (h) and (l) were opposite for grain yield suggesting duplicate type of epistasis in this trait under full irrigation. Negative sign of additive effect showed that the superior parent (MO17) is considered as the second parent and the superiority of the reduction alleles of the grain yield, while the positive dominance effect revealed that dominance exists toward increasing this trait in both water deficit conditions. The findings indicated that the grain yield was governed by both main effects, but dominance effects were higher than additive effects. According to Wolf and Peternelli (2000), the F2 population derived from across lines of MO17 and B73 showed that for grain yield dominance effect was more important than additive effect, but for other characteristics related to yield it was the reverse. In severe stress condition, VD and broad-sense heritability highly indicated that breeding of this trait can be effective with the later generation selection. Degree of dominance value in the grain yield indicated the presence of possible over-dominance gene action in controlling of this trait or the accumulation of many genes effects with partial or complete dominance. However, the results may be affected by the epistasis effects and linkage disequilibrium. Linkage disequilibrium could be the estimation of degree of dominance, mostly in the early segregation generations, so that an incomplete or complete dominance is estimated falsely as over dominance genetic effect (Hallauer et al. 2010). Linkage disequilibrium has been alluded as the possible cause of over dominance or pseudo-over dominance (Bersabe et al. 2016). Our observations are in agreement with the findings of Singh and Roy (2007) and Irshad-ul-Haq et al. (2010). Also, Shahrokhi et al. (2013) in the study of the genetic components of maize varieties using six basic generations observed that additive, dominance and epistatic genes play a significant role in controlling of grain yield.

The opposite signs of dominance and dominance × dominance effects in the chlorophyll-a confirmed duplicate dominant epistasis under normal condition. This type of epistasis, decreasing diversity in the F2 generation and subsequent generations, disrupts the process of selection. Under mild stress condition, additive × dominance non-allelic interaction effect had a main role in the genetics of this trait. Significance of additive × dominance effect indicated that selection through self-fertilizing is not to be effective for improving of this trait (Farshadfar et al. 2008). Therefore, among the epistasis effects, additive × dominance type is more fixable and useful for plant breeders. Comparison between \(h_{{\text{b}}}^{2}\) and \(h_{{\text{n}}}^{2}\) indicated that equal importance of additive and non-additive effects in the genetic controlling of the chlorophyll-a. In both water deficit irrigation, degree of dominance was less than unity then breeding of this trait can be effective with the parents inbred lines selection.

Negative and significant values of [i] parameter under mild stress condition showed that alleles dispersion in parents for the chlorophyll-b (Jayasekara and Jinks 1976; Mather and Jinks 1982). Positive and negative signs of the dominance gene effect indicated increasing and reductive alleles involving dominant phenotype, respectively (Mather 1973; Crusio 2006). Negative sign of dominance × dominance interaction shows ambidirectional dominance. In this study, for most traits, it is found that dominance direct was unidirectional dominance and reductive alleles were involved in the inheritance of studied traits. Comparison between \(h_{{\text{b}}}^{2}\) and \(h_{{\text{n}}}^{2}\) indicated that additive effects were governed in genetic controlling of this trait. Therefore, breeding of this trait can be effective with the parents’ inbred lines selection. Zhang et al. (2009) in wheat reported that the heritability of chlorophyll-a and b was high and additive effects were significant for these traits. Also, these results are consistent with reports published by Kumar (2015) in wheat and dos Santos Pessoa et al. (2018) in pepper.

Dominance and duplicate type of non-allelic interaction effects had a main role in the inheritance of total chlorophyll under all three conditions. Therefore, breeding of this trait can be effective with the later generation selection and hybrid production. Negative sign of additive × additive interaction effects under severe stress condition indicated it is possible to fix decrease by selection genotypes on the basis of the total chlorophyll. Also, negative sign for dominance effect revealed that there was dominance toward decreasing this trait in all three conditions. Total chlorophyll content in crops (wheat, cotton, rice) was controlled by dominance gene effects reported by Naroui Rad et al. (2012); Song et al. (2014) and Makwana et al. (2018), respectively.

The opposite signs of [h] and [l] parameters in the carotenoids under normal and mild stress conditions indicated duplicate type of epistasis. The significance of additive × dominance interaction effect revealed that this type of epistasis by selection through self-fertilizing was not fixed. The same signs of [d] and [i] indicated that an obvious role of additive effects in the inheritance of carotenoids. Negative and significant values of [i] parameter showed alleles dispersion in parents for carotenoids. Under severe stress condition, negative sign of additive effect showed that the superiority of the reduction alleles of this trait. In all three conditions, VD and broad-sense heritability were high. Hence, breeding of this trait can be effective with the later generation selection. Genetic analysis of the spring durum wheat showed that the content of carotenoids was controlled by additive gene effects (Bebyakin and Starichkova 1992). However, study on African marigold (Sreekala and Raghava 2003) and capsicum (Naresh et al. 2016) indicated that the carotenoids were governed by dominance gene action.

In the chlorophyll index, high dominance × dominance non-allelic interaction effect revealed that this epistasis had a main role in controlling of this trait. Positive sign of [l] parameter showed that unidirectional dominant under full irrigation. The dominance × dominance effect had a negative sign indicated that ambidirectional dominant under both water deficit conditions. Under full and water deficit irrigation, VD and \(h_{{\text{b}}}^{2}\) were high. Therefore, breeding of chlorophyll index can be effective with the later generation selection and hybrid production. This is revealed by Said (2014) who reported that genetic analysis of chlorophyll index in wheat showed dominance effects under drought stress. Contrary to these results, Dai et al. (2016) reported that the additive gene effects in rapeseed were the mainly genetic effects for this trait.

Conclusion

In conclusion, grain yield, carotenoids and SPAD value were decreased significantly under two water deficit conditions. Multivariate analysis of grain yield and physiological traits indicated positive stronger correlation between grain yield and carotenoids, and SPAD value under the severe stress conditions. Thus, the selection according to these traits could be used in breeding programs to screen for high yield and water deficit tolerance in maize. The results of genetic analysis emphasized the major role of non-additive genetic effects (dominance and epistatic) in justifying the genetic variation of the traits. All of the studied traits were controlled by epistatic effects suggested that for breeding high performance of maize hybrids, selection of favorable epistasis compounds can be effective. Our findings showed that under full and water deficit irrigation in all studied traits, except chlorophyll a and b, the dominance variance and broad-sense heritability were high. Thus, the selection for these traits should be undertaken in more advanced generations and hybridization would be more effective. Clearly, use of the carotenoids and chlorophyll index as indicators of grain yield in maize could be deserve to further study. Also, quantitative trait loci analysis can be useful to identify water deficit resistant traits in maize.