Detection of Epistasis for Seed and Some Phytochemical Traits in Coriander under Different Irrigation Regimes

: Coriander ( Coriander sativum L.) is an annual herb mainly cultivated for its seed characteristics. Drought stress is a major problem which affects coriander behaviour through biochemical responses. This study aimed to determine the nature and magnitude of epistasis in inheritance of seed yield (SY), percent of dehulled seed (PODS), percent of seed hulls (POSH), essential oil content (EOC), essential oil yield (EOY), dehulled seed fatty acid content (DSFAC), hull fatty acid content (HFAC), fatty acid content (FAC), and fatty acid yield (FAY), and to estimate additive and dominance variance for the traits not inﬂuenced by epistasic effects. Three testers, TN-59-158 (highly drought-susceptible), TN-58-230 (highly drought-tolerant, but low-yielding), and their F 1 hybrid were each crossed for six genotypes. The experiment was performed under different levels of water deﬁcit: control (C), moderate water deﬁcit (MWD), and severe water deﬁcit (SWD) conditions. Epistasis affected the expression of SY, EOC, EOY, FAC, and FAY in all water conditions, PODS in C, POSH in SWD, HFAC in MWD, and DSFAC in both C and MWD conditions. Total epistasic effects were partitioned, showing that both [i] and [j + l] type interactions were signiﬁcant, with a prevalent inﬂuence of [i] type interactions on these traits except for POSH and FAC in the SWD condition, which exhibited a higher value of the [j + l] type. Both additive and non-additive gene actions were signiﬁcant for those traits not signiﬁcantly affected by epistasis in C, MWD, or SWD conditions. An additive type of gene action was preponderant for PODS in MWD and SWD, POSH in MWD, DSFAC in SWD, and in C and SWD conditions.


Introduction
The cost of petroleum-derived products has increased during the last decade, and considering the rapid reduction in world fossil fuel resources there is a clear need to identify alternative sources [1]. Among a broad variety of sources considered, agricultural products are potential sources of industrial raw materials. Sustainable industrial crops have thus emerged as a new source of strategic industrial raw materials. While strategies for improving the fatty acid profile and composition of oils generated by existing crops are being explored, another strategy is to look for alternative species as possible sources of specialized oils. An example of such a crop is coriander (Coriandrum sativum L.). Its oils contain a high concentration of fatty acids and essential oils [2]. The composition, stability, and extraction methods of fatty acid and essential oil are different [1]. Hydrodistillation is used to extract essential oils, whereas extraction or pressing is used to obtain fatty oils. In the case of fatty acids, seeds contain 9-21% fatty acid, of which petroselinic (C18:1n-12),

Experimental Site and Growth Conditions
The experiment was implemented at the research field of Tarbiat Modares University in Tehran, Iran (51°09′ E; 35°44′ N, at an altitude of 1265 m above sea level). Before sowing, the seeds were disinfected in sodium hypochlorite solution (10%) (Sigma-Aldrich, Saint Louis, MI, USA) for 5 min and then fixed in ethanol (96%) for 1 min and rinsed in distilled water thereafter [31]. The 9 parents, 12 single crosses, and 6 three-way crosses were evaluated with different levels of water deficit (C, MWD, SWD) with a randomized complete block design with 3 replications. In the C regime, genotypes were kept well-watered. For MWD, genotypes were well-irrigated until the commencement of stem elongation, when watering was withdrawn until the end of the flowering stage. Then, recovery water was applied once. In the SWD experiment, watering was like that of C until the commencement of the flowering stage, after which watering was cut off completely [32]. The field's soil had a sandy loam structure consisting of 15% silt, 15% clay, and 70% sand with 700 and 125 mg kg −1 K and P, respectively, as well as 0.12% N, 1.21% organic carbon and 21.1% fixed carbon. The soil had a relatively low electrical conductivity of 1.01 dS m −1 . The field daily vapor pressure deficit (VPD), corresponding precipitation, and rainy days are presented in Figure 2.
The mean relative humidity and mean temperature values were 19% and 23.5 °C at 7:00 a.m., 12% and 35.5 °C at 2:00 p.m., and 20% and 26.0 °C at 9:00 p.m., respectively. A plot size of 2 m 2 (a 2-row plot of 2 metres in length) was assigned to each entry, consisting of 14 plants in each replication. The plant-to-plant spacing between and within rows was kept at 30 cm and 40 cm, respectively, in the 3 experiments. The watering dates and frequencies are shown in Figure 3 for each of the populations.

Experimental Site and Growth Conditions
The experiment was implemented at the research field of Tarbiat Modares University in Tehran, Iran (51 • 09 E; 35 • 44 N, at an altitude of 1265 m above sea level). Before sowing, the seeds were disinfected in sodium hypochlorite solution (10%) (Sigma-Aldrich, Saint Louis, MI, USA) for 5 min and then fixed in ethanol (96%) for 1 min and rinsed in distilled water thereafter [31]. The 9 parents, 12 single crosses, and 6 three-way crosses were evaluated with different levels of water deficit (C, MWD, SWD) with a randomized complete block design with 3 replications. In the C regime, genotypes were kept wellwatered. For MWD, genotypes were well-irrigated until the commencement of stem elongation, when watering was withdrawn until the end of the flowering stage. Then, recovery water was applied once. In the SWD experiment, watering was like that of C until the commencement of the flowering stage, after which watering was cut off completely [32]. The field's soil had a sandy loam structure consisting of 15% silt, 15% clay, and 70% sand with 700 and 125 mg kg −1 K and P, respectively, as well as 0.12% N, 1.21% organic carbon and 21.1% fixed carbon. The soil had a relatively low electrical conductivity of 1.01 dS m −1 . The field daily vapor pressure deficit (VPD), corresponding precipitation, and rainy days are presented in Figure 2.
The mean relative humidity and mean temperature values were 19% and 23.5 • C at 7:00 a.m., 12% and 35.5 • C at 2:00 p.m., and 20% and 26.0 • C at 9:00 p.m., respectively. A plot size of 2 m 2 (a 2-row plot of 2 metres in length) was assigned to each entry, consisting of 14 plants in each replication. The plant-to-plant spacing between and within rows was kept at 30 cm and 40 cm, respectively, in the 3 experiments. The watering dates and frequencies are shown in Figure 3 for each of the populations.

Seed Yield Measurement
The seed yield of testers and male parents were measured using 10 plants and 20 plants for entries obtained from single and 3-way crosses, respectively. The percentages of dehulled seeds (PODS) and of seeds hulls (POSH) were measured to investigate the effect of water deficit stress.

Seed Yield Measurement
The seed yield of testers and male parents were measured using 10 plants and 20 plants for entries obtained from single and 3-way crosses, respectively. The percentages of dehulled seeds (PODS) and of seeds hulls (POSH) were measured to investigate the effect of water deficit stress.

Essential Oil Extraction
The essential oil content (EOC) of seeds was extracted using a Clevenger-type apparatus. Air-dried seeds were triturated in an electric grinder. In total, 30 grams of triturated seed samples were subjected to 250 mL water distillation for 2 h using a Clevenger-type apparatus. The EOC (%w/w) was measured as the weight (g) of EO per 100 g of seed [32]. 10

Seed Yield Measurement
The seed yield of testers and male parents were measured using 10 plants and 20 plants for entries obtained from single and 3-way crosses, respectively. The percentages of dehulled seeds (PODS) and of seeds hulls (POSH) were measured to investigate the effect of water deficit stress.

Essential Oil Extraction
The essential oil content (EOC) of seeds was extracted using a Clevenger-type apparatus. Air-dried seeds were triturated in an electric grinder. In total, 30 grams of triturated seed samples were subjected to 250 mL water distillation for 2 h using a Clevenger-type apparatus. The EOC (%w/w) was measured as the weight (g) of EO per 100 g of seed [32]. 10

Essential Oil Extraction
The essential oil content (EOC) of seeds was extracted using a Clevenger-type apparatus. Air-dried seeds were triturated in an electric grinder. In total, 30 grams of triturated seed samples were subjected to 250 mL water distillation for 2 h using a Clevenger-type apparatus. The EOC (%w/w) was measured as the weight (g) of EO per 100 g of seed [32]. Furthermore, EOY was computed as the weight (g) per plant seed sample. To evaluate the effect of water deficit stress on EOC, the primary EOC was adjusted by PODS values.

Fatty Acid Extraction
Fatty acid contents from coriander seeds and dehulled seeds with different hull contents were extracted using a Soxehlet extractor. The dehulling of seeds was done using a soft edge blade electric grinder and then the hulls were separated by an air fan. Hulls and dehulled seeds were triturated in an electric grinder. Then, approximately 2 g of Agronomy 2021, 11, 1891 5 of 17 each triturated material were extracted in a Soxehlet extractor with 250 mL of petroleum ether for 6 h. The extract was then filtered, with evaporation of the solvent under reduced pressure and temperature [10]. The FAC (%w/w) was determined as the weight (g) of oil per 100 g of hull/seeds. Furthermore, FAY was calculated as the weight (g) per plant.
2.6. Statistical Analysis 2.6.1. Analysis of Variance Analysis of variance was performed using the model suggested by Singh and Chaudhary [33] to determine the significance of treatments and to partition the treatment effect to determine the significance of variation among hybrids, parents, genotypes, testers, P 1 + P 2 vs. F 1 , P 1 vs. P 2 , genotypes vs. testers, and hybrids vs. parents for each of the traits using the MTTC technique. Excel (Excel, 2013) and SAS (SAS 9.1, 2003) software were used for data analysis and graphs, respectively.

Test for Epistasis
The detection of epistasis was performed according to Singh and Chaudhary [33]. The test of significance of the L 1j + L 2j − 2L 3j (j = genotype) provides information about the presence or absence of epistasis. Therefore, for each genotype and each replication the L 1j + L 2j − 2L 3j was calculated and then tested. The total epistasis for 6 degrees of freedom was calculated on the total replications according to Equation (1).
The total epistatic effect was divided into the [i] type (homozygote × homozygote) with 1 degree of freedom and the [j + l] type of epistasis (heterozygote × heterozygote and homozygote × heterozygote) with 5 degrees of freedom. The sums of squares of [i] and [j + l] were calculated according to Equations (2) and (3).
The sum of squares due to interaction of epistasis with blocks was calculated as the difference between the total sum of squares of epistasis and the sum of squares for the type of epistasis in question (total, [i] type or [j + l] type). Each of the 3 types of epistasis was tested against its respective interaction with blocks. However, before testing individual epistasis effects, the homogeneity of the interaction was firstly tested. Homogeneity of [i] × block and [j + l] × block interaction variances was tested using an "F" test with 2 and 10 degrees of freedom according to Equation (4).
Mean square o f i type inteaction Mean square o f j and l type inteaction (4)

Individual Genotypic Epistasis
The individual contribution of each genotype to total epistasis was determined and tested for significance from 0 for those traits in which the total epistasis was significant. The mean value ∑ L 1j + L 2j − 2L 3j /r of each genotype for a trait was tested using a "t" test with 12 degrees of freedom according to Equation (5).

t = Mean
Error mean square r For those traits in which epistasis was not detected an additive dominance was fitted to the data [29,30].

Estimation of the Additive (D) and Dominance (H) Variance Components of Variation
For estimation of the additive and dominance components, the sum (L 1i + L 2i ) and difference (L 1i − L 2i ) for each genotype was calculated replication-wise and subjected to an analysis of variance (Table 1) [33]. Table 1. Analysis of variance for estimation of the additive and dominance components.

Source of Variation df
Sum Difference

MS Expected MS MS Expected MS
Replications Where r = number of replications; n = the number of genotypes; MS r , MS s , MS d , and MS e = mean squares of replications, sums, differences, and error, respectively; and σ 2 e , σ 2 s , and σ 2 d = variance components due to error, sums, and differences, respectively. Finally, the values of D and H were calculated using Equations (6) and (7), respectively.
Average Degree of Dominance The average degree of dominance was calculated as (H/D) 1/2 , where H and D are the dominance and additive variance components, respectively.

Direction of Dominance
The linear correlation coefficient between the sums and corresponding differences (r S,D ) for all genotypes was determined as direction of dominance.

Irrigation Regime Influence on Measured Traits
WT had a significant effect on all traits (p < 0.01). Furthermore, there was a significant interaction between genotype and water treatment for all measured traits. The mean values of SY, EOY, and FAY decreased 46%, 53%, and 50% in MWD conditions, and 54%, 50%, and 50% in SWD conditions. The reduction of some genotypes in MWD conditions was greater than with SWD and vice versa for other genotypes ( Figure 4). As for SY, EOY, and FAY, EOC and FAC decreased by 10% and 14%, respectively, in MWD conditions. Furthermore, the seed hull-to-dehulled seed mass ratio significantly increased under water Agronomy 2021, 11, 1891 7 of 17 deficit stress ( Figure 5). The PODS of genotypes were differently affected in MWD and SWD conditions. The FAY reduced due to water deficit stress in all genotypes except in L 2 and H L 2 ×G6 , which had more FAY in SWD conditions. In general, the H L 3 ×G4 hybrid exposed the greatest mean value for SY and FAY in C conditions. H L 2 ×G2 and H L 3 ×G4 hybrids had the greatest mean value of FAY and SY in MWD conditions. Furthermore, in SWD conditions the H L 2 ×G2 and H L 2 ×G5 had the greatest mean value of SY and FAY, respectively ( Figure 4). As shown in Figure 5, the reduction in PODS was greater than that of the POSH, which led to an increase in the hull-to-dehulled seed mass ratio.
Furthermore, the seed hull-to-dehulled seed mass ratio significantly increased under water deficit stress ( Figure 5). The PODS of genotypes were differently affected in MWD and SWD conditions. The FAY reduced due to water deficit stress in all genotypes except in L2 and × , which had more FAY in SWD conditions. In general, the × hybrid exposed the greatest mean value for SY and FAY in C conditions. × and × hybrids had the greatest mean value of FAY and SY in MWD conditions. Furthermore, in SWD conditions the × and × had the greatest mean value of SY and FAY, respectively ( Figure 4). As shown in Figure 5, the reduction in PODS was greater than that of the POSH, which led to an increase in the hull-to-dehulled seed mass ratio.
The genotypes showed different responses to irrigation regimes for HFAC, DSFAC, and FAC ( Figure 6). In C, MWD, and SWD conditions, the greatest mean value of FAC was detected for the × , × , and L2, respectively. The EOC, adjusted essential oil content (AdjEOC), and EOY exhibited significant water treatment × genotype interactions (Figure 7). Furthermore,   MWD: moderate water deficit; SWD: severe water deficit. L 1 -L 3 : three testers, G 1 -G 6 : 6 male parents; L 1 G 1 -L 2 G 6 : 12 single hybrids; and L 3 G 1 -L 3 G 6 : 6 three-way hybrids in a modified triple test cross.   The genotypes showed different responses to irrigation regimes for HFAC, DSFAC, and FAC ( Figure 6). In C, MWD, and SWD conditions, the greatest mean value of FAC was detected for the H L 2 ×G5 , H L 2 ×G6 , and L 2 , respectively. The EOC, adjusted essential oil content (AdjEOC), and EOY exhibited significant water treatment × genotype interactions (Figure 7). Furthermore, H L 3 ×G5 in C, L 3 and H L 2 ×G2 in C and MWD, and H L 3 ×G5 in SWD conditions exhibited the greatest mean values of EOC, EOY, and AdjEOC, respectively.

Additive and Dominance Components
The ANOVA for sums indicated that mean squares due to sums were significant for all the traits in C, MWD, and SWD conditions ( Table 4). The sums × WT interactions were Figure 7. Water treatment (WT) × genotype interaction effect on essential oil content (EOC), essential oil yield (EOY), and L 1 -L 3 : 3 testers, G 1 -G 6 : 6 male parents; L 1 G 1 -L 2 G 6 : 12 single hybrids, and L 3 G 1 -L 3 G 6 : 6 three-way hybrids in a modified triple test cross. Adjusted essential oil content (AdjEOC). C: control; MWD: moderate water deficit; SWD: severe water deficit.

Detection of Epistasis
Total epistasis was significant for SY, PODS, EOC, EOY, DSFAC, FAC, and FAY in C conditions, SY, EOC, EOY, DSFAC, HFAC, FAC, and FAY in MWD conditions, and SY, POSH, EOC, EOY, FAC, and FAY in SWD conditions ( Table 2). The [i] type epistasic effect was detected for PODS in C and HFAC in MWD conditions.
For SY and EOC in MWD and SWD, DSFAC and FAC in C and MWD, and EOY and FAY in all irrigation regimes, [i] type epistasis was detected. The [j + l] type epistasis was observed for PODS and DSFAC in C, HFAC in MWD, and POSH in SWD conditions. For SY, [j + l] type epistasis was significant in all irrigation regimes. EOC, EOY, FAC, and FAY were significant in C and SWD conditions. **, *, and ns are significant at the 0.01 and 0.05 level of probability and not significant, respectively. SY: seed yield; PODS: percent of dehulled seed; POSH: percent of seed hulls; EOC: essential oil content; EOY: essential oil yield; DSFAC: dehulled seed fatty acid content; HFAC: hull fatty acid content; FAC: fatty acid content; FAY: fatty acid yield.
The combined analysis of variance exhibited significant total epistasis × WT interactions for all measured traits ( Table 3). The [i] type × WT interaction was significant for SY, PODS, DSFAC, HFAC, FAC, and FAY. The [j + l] type × WT interaction was detected in all measured traits except SY.

Additive and Dominance Components
The ANOVA for sums indicated that mean squares due to sums were significant for all the traits in C, MWD, and SWD conditions ( Table 4). The sums × WT interactions were significant for all measured traits except EOC, EOY, and HFAC ( Table 5). The mean squares due to differences were significant for POSH, HFAC, FAY, and PODS in all water treatments and FAC and DSFAC in the MWD condition ( Table 4). The differences × WT interactions were significant for all measured traits except EOC (Table 5). Table 4. Analysis of variance for additive and dominance components for different traits (within water treatments) in coriander under control (C), moderate water deficit (MWD), and severe water deficit (SWD) treatments.  For traits not significantly affected by epistasis, the additive and dominance genetic components, direction of dominance, and degree of dominance were estimated (Table 6). Both additive and dominance genetic components were significant for PODS in MWD and SWD, HFAC in C and SWD, POSH in C and MWD, and DSFAC in SWD conditions. The average degree of dominance indicated that partial dominance was detected for PODS in MWD and SWD, HFAC in C and SWD, and DSFAC in SWD. Over-dominance was found for POSH in C conditions. The correlation between sums and differences were positive and significant for PODS in MWD and SWD and POSH in MWD, and negative and significant for HFAC in C and SWD conditions, indicating that the dominant genes have decreasing effects on the PODS and POSH traits and increasing effects on the HFAC. The positive but non-significant correlation for POSH in C showed that dominance was bidirectional, and alleles for lower and higher POSH were more or less equally distributed among the coriander populations examined. The estimates of heritabilities showed that POSH in C condition had relatively high broad-sense heritability (h 2 B = 0.72) and low narrow-sense heritability (h 2 B = 0.20). In the SWD treatment, PODS, HFAC, and DSFAC exhibited higher h 2 N than in C. The average degree of dominance [(H/D) 1/2 ] was less than unity for all these traits. It ranged from 0.16 for HFAC in MWD to 0.91 for POSH in C conditions.

Source of Variation
The directions and relative magnitudes to recognize those genotypes which interacted with L 1 and L 2 to produce significant total epistasis for SY, PODS, POSH, EOC, EOY, DSFAC, HFAC, FAC, and FAY are presented in Table 7.
The genotypes TN-59-80 for PODS in C, EOC and EOY in SWD, and FAY in MWD, TN-59-160 for EOC in C and SWD, EOY in SWD, and FAY in C, TN-59-353 for SY in C and HFAC in MWD, TN-59-347 for SY, EOY, and FAY in C, POSH in SWD, EOC in C and SWD, DSFAC in MWD and FAC in MWD and SWD, TN-59-10 for SY in C, EOC in C and SWD, EOY in C and MWD, DSFAC and FAC in MWD, and commercial for POSH and EOC in SWD, EOY in C and MWD, and FAY in C conditions showed non-significant contributions towards total epistasis. The genotype TN-59-80 for SY in C and DSFAC in C and MWD as well as FAC in MWD and SWD conditions played an important negative and positive role, respectively. TN-59-160 for POSH in SWD, TN-59-353 for SY in MWD, EOY in C and SWD, and FAY in MWD and SWD, TN-59-347 for SY in SWD and EOY in MWD, and commercial for PODS in C, HFAC in MWD, and FAC in SWD accounted for high negative proportions of the total epistasis. The genotypes TN-59-80 for DSFAC and FAC in C and MWD, TN-59-353 for POSH in SWD, EOC in all water treatments, and EOY in MWD, TN-59-347 for HFAC in MWD, and TN-59-10 for SY and FAY in C accounted for the maximum positive portion to the total epistasis.

Discussion
Drought is a serious worldwide problem, influencing crop production and quality. Recent global climate change has made this situation more serious [34]. When plants are exposed to restricted environmental conditions, the production of some biochemical products, such as essential oils, can be improved [35]. However, there are reports on the negative effect of environmental constraints on other products such as SY, FAC, and FAY [8,9,32]. Therefore, the present study was undertaken to investigate the nature of the genetic controlling response of coriander to different irrigation regimes for SY, PODS, POSH, EOC, EOY, DSFAC, HFAC, FAC, and FAY.
Most of the multiple mating designs used to estimate the genetic architecture of polygenic characters assume epistasis to be absent or of little importance, and most genetic models rarely provide a reliable estimation of this assumption. Several studies in various plants using the triple test cross model have shown that epistasis is a significant component of genetic variability for polygenic traits [18][19][20]23,24,36].

Seed Yield
The SY was affected by water stress, indicating that the expression of SY depends on non-allelic interactions and that these three irrigation regimes differed in the expression of epistasis. Furthermore, epistasis × WT interactions were significant and therefore so was the sensitivity or non-consistent performance of epistasis of the SY-related loci between irrigation regimes. It is remarkable that interactions with water treatments depend on the number of loci involved in trait inheritance, i.e., the higher the number of involved loci, the greater the possibility of an environmental influence on trait expression, which is characteristic of quantitative traits. Furthermore, mechanisms involved in the expression of SY may differ according to the water treatments. Thus, if the loci that determine SY in coriander participate in adaptation and interact with the particular irrigation regimes, then epistasis will be environmentally variable, and this could therefore be a possible explanation for the strong epistasis × WT interaction detected in this study.
Changes in the relative magnitudes of the epistatic gene effects (total, i type and j + l type) between different water treatments can occur if the loci that determine the trait have different sensitivities for the water treatments considered [29]. In agreement with our results, Upadhyaya and Nigam [17] in peanut, Sood et al. [18] in linseed, Wolf and Hallauer [37] in maize, Khattak et al. [25] in mungbean, and Barona et al. [20] in soybean reported a similar instability of epistatic gene effects. As Pooni and Jinks [38] stated, [i] type epistatic gene effects are more sensitive to environmental differences than the other two types. According to the results, the [i] type of interactions were predominant as compared to the [j + l] type for SY in MWD and SWD. In the breeding program, where the purpose was to develop inbred lines, the [i] type interactions were possibly the most important because they are a fixable and linear directional component in homozygous genotypes, contributing to the superiority of elite lines [39].

Fatty Acid Content
Variable FAC in different parts of coriander was detected, with values of 9.3% in hulls and 22.65% in de-hulled seeds by Sriti et al. [40], and 17.6% and 37.60% in whole seed and e-hulled seeds, respectively, by Evangelista et al. [4]. Thus, the results of the present study are in a similar range to those found in previous reports. It was reported that water deficit led to a reduction in FAC in coriander [32] and cumin [7,13] as water stress increased, whereas in the present study genotypes showed different levels of FAC in different irrigation regimes.
Additive × additive epistatic effects were found to control (in part) the expression of FAC, DSFAC, FAY, and HFAC in C and MWD when these and the SWD treatment data were analysed together. The presence of [i] type epistasis × WT interactions indicated that breeding for DSFAC, HFAC, FAC, and FAY should be done in water conditions relevant to the target environment. The absence of significant [j + l] type epistasis for FAC, FAY and DSFAC in MWD indicated that additive × dominance and dominance × dominance types of interactions between controlling genes were either not present or of relatively smaller magnitude. Furthermore, results indicated that the relative magnitude of the [j + l] type of interaction was greater than the [i] type in SWD. Epistasis of the [j + l] type can be used in the presence of the development of hybrids [41]. Studies on genetic variation in coriander using diallel mating designs showed that dominant gene action is involved in the inheritance of FAY [32].

Essential Oil Content
Results revealed that EOC was affected by water deficit, in accordance with Bettaieb et al. [12] in Salvia officinalis and Alinian [10] in cumin and coriander [42]. Furthermore, water stress affected the EOC by PODF, indirectly, which is obvious from the difference between EOC and AdjEOC. Results indicated that the [i] types of interactions were predominant as compared to the [j + l] type for EOC in MWD and SWD, and EOY in all water treatments. Consequently, we suggest postponing the selection for EOC to later generations of inbreeding (F 5 or F 6 ) to exploit the beneficial effects of [i] type of epistasis.

Epistatic Deviations of Individual Coriander Genotypes
Overall, the six genotypes (TN-59-10, TN-59-80, TN-59-160, TN-59-353, TN-59-347, and commercial) contributed significantly towards the epistatic deviations, indicating that the presence of non-allelic interactions are determined to some extent by the genotypes included in the triple test cross design along with L 1 and L 2 testers. Therefore, this reinforces the need to include several genotypes in studies designed for the detection of non-allelic interactions and to estimate dominance and additive components of variation with equal precision through the TTC method [25,27].
In this study, extreme high vs. low testers (TN-59-158 and TN-59-230) indicated high efficiency in detecting epistasis for most traits. The experimental sample size necessary to detect allelic interactions through the triple test cross depends largely on the gene dispersion between testers [38]. However, the use of more pairs of testers and additional environments could have improved the possibility of detection of non-allelic interactions, especially for the traits which were not detected in this experiment. Several studies have reported that the manifestation of non-allelic interactions in crops occurs in diverse genotypes and is tester-dependent [22,36,43].
Since the epistasis effect was significant for traits in different water treatments, the estimates of additive and dominance components of genetic variation for these traits were biased to an unknown extent. Therefore, for given traits, additive and dominance variance components were estimated for each water treatment only if non-allelic interactions were not detected.
The higher magnitude of additive variance, as found in DSFAC and HFAC in SWD and MWD, respectively, is indicative of the relative importance of fixable types of gene action for these traits. The preponderance of additive components for DSFAC and HFAC is contrary the findings of earlier studies, where the preponderance of the dominance component for DSFAC and HFAC by a diallel mating design was reported [32].
Water deficit led to a greater decrease in PODS than POSH, which indirectly affects the whole-seed essential oil and fatty acid content. Furthermore, as discussed previously, seed de-hulling reduces the amount of material to be processed and can help to prevent considerable oil absorption by hulls in the oil-pressing extraction system [4]. The genetic control mechanism of POSH was affected by water stress and the proportion of dominance gene action decreased as water stress progressed. The genetic control of PODS was governed by partial dominance gene action in MWD and SWD water conditions because [(H/D) 1/2 ] was between 0.34 and 0.46 and h 2 B was less than 0.20 in both water treatments. Dominance variance estimated by the triple test cross method refers to different alleles between the two testers [44]. Meanwhile, if the number of those alleles is less than that of total number of segregating alleles in the population for expression of this trait, the dominance variance component will be underestimated [17]. In general, the significance of the differences in mean squares indicates that dominant gene action plays a key role in the genetic control of a given trait. Furthermore, it is specified that under the same conditions, the estimates of the additive variance component could include a portion due to dominance deviations and therefore could be biased upward [44]. Thus, in the absence of the dominance variance component, the significance of the sum mean squares provides an accurate estimate of the presence of additive variance regardless of dominance contamination and the number of alleles which differ between L 1 and L 2 .
The estimation of narrow and broad-sense heritability from the analysis of the triple test cross is uncommon because the testers are two high and low extreme selection genotypes and would not predict the response to selection [24]. However, Khan and Mc-Neilly [23] in maize, Pooni et al. [45] in rice, and Devey et al. [46] in Lolium estimated heritability from the triple test cross method, but its value was insignificant.
As discussed previously, to obtain unbiased estimates of genetic components of variance, the two testers should be extremely low vs. high for a character under consideration. However, when multi traits are considered together, achieving this purpose is not easy. Hence, the result of the present study can be considered as a tool for understanding the types of genetic control mechanisms in the involved coriander traits, rather than a tool for obtaining more realistic components of genetic variation.

Conclusions
Overall, the highly significant [i] type epistasis × WT, [j + l] type epistasis × WT, sums × WT, and differences × WT effects for measured traits suggest that different breeding strategies may be adopted in different conditions that are representative of the target environment for breeding. In the cases where [i] type epistasis was detected across water treatments we suggest postponing the selection for advanced generations and the maintenance of large segregating populations for selection to allow combinations of favorable alleles to occur for exploitation. The results also indicate the importance of dominance variance and [j + l] type epistasis in POSH and HFAC. Due to their non-directional and unfixable nature, dominance and [j + l] type epistasis can be exploited through heterosis breeding by developing hybrids. For open-pollinated plants and coriander with low inbreeding depression, breeding procedures are available for the exploitation of existing linear and non-directional components of genetic components in coriander via the development of homozygous lines and hybrid varieties, respectively.