The experiment was conducted at the Algerian National Institute of Agronomic Research (INRAA), Setif Unit, Algeria (36°12'N, 05°24'E, 981 m asl). The climate is of a semi-arid type, with a total rainfall from September to June of 427.4 mm for the 2012-2013 cropping season. The soil is a calcisol of fine-grained texture (38.4% clay, 42.7% silt, 18.7% sand) and carbonate bearing (26.6% CaCO₃), with a pH of 8.2 and 1.35% organic matter (Kribaa et al., 2001). Plant material utilized was generated from crosses among nine bread wheat varieties (Table 1), chosen on the basis of differences in adaptation and morpho-physiological characteristics (Fellahi et al., 2013). These varieties were divided into two contrasting groups and crossed in 2011 in a partial diallel scheme. Group 1 was composed of five lines: Acsad₉₀₁, Acsad₈₉₉, Acsad₁₁₃₅, Acsad₁₀₆₉ and Ain Abid, and group 2 consisted of four lines, Mahon-Demias, Rmada, Hidhab and El-Wifak. The F₀ resulting seeds were grown in 2011-2012 crop season to develop the F₁ generation. The 20 F₂ hybrids, were planted along with their parents in 2012-2013 season in a randomized complete block design with three replications. The plots consisted of two rows of 10 meters with a spacing of 0.2 m between rows and 0.2 m between plants in the row. Thirty competitive plants were tagged before heading and data were recorded in each plant. The following traits were evaluated: number of calendar days from emergence to 50% heading (DHE, days); flag leaf chlorophyll content (Chl, CCI), estimated with a CCM-200 chlorophyll meter (Opti-Sciences, Tyngsboro, MA, USA); plant height (PHT, cm), measured from the ground level to the tip of spike excluding awns; number of spikes per plant (SN, No.), counted at physiological maturity; spike weight (SW, g), obtained by weighting each individual selected plant; number of grains per spike (GN) present in the plant; thousand-kernel weight (TKW, g), recorded by counting four 250 grain subsamples from each plant; above-ground biomass (BIO, g) and grain yield (GY, g), by individually threshing of each plant.

Table 1

The data collected for each trait were tested for the normal distribution of frequency using Kolmogorov-Smirnov test. The statistical procedures adopted for the analysis of variance involved the partitioning of the genotype source of variation into the parents, crosses and the contrast parents vs. crosses according to Viana et al. (2000). The means were grouped by the Scott and Knott (1974) test at a 5% probability level. The traits showing significant differences were further subjected to diallel cross analysis. Analysis of the partial diallel was performed according to the model proposed by Viana et al. (1999, 2000, 2001), adapted from the method of Hayman (1954) using parents and the F₂ generation. The following non-genetic and genetic parameters were estimated and their statistical significance was tested via t test.

D ₁ = Genetic variation due to additive genetic effects of group 1 D ₂ = Genetic variation due to additive genetic effects of group 2 D ₃ = Genetic variation due to additive genetic effects in both groups of parents H ₁ = Genetic variation due to dominant genetic effects of group 1 H ₂ = Genetic variation due to dominant genetic effects of group 2 h ² = Dominance effects over all loci F = Mean of covariance between additive and dominant genetic effects E = Expected environmental component of variation

From the genetic components estimates, the following genetic parameters were determined, and their interpretations are related exclusively to the parental genotypes used in this study.

(H ₁ /D) ^1/2 = Average degree of dominance over all loci H ₂ /4H ₁ = Proportion of positive and negative alleles K _D /K _R = Proportion between dominant and recessive genes in all parents (K ⁺ - K ^- ) ² /K = Direction of dominance h ² /H ₂ = Number of effective factors h ² _ns = Narrow sense heritability

The additive-dominant model validity was performed based on testing the values of the coefficient of regression of offspring parent covariance (Wr) on parental array variance (Vr), against zero and against one for each trait. All statistical analyses were performed using the program Genes, version 2014.6.1 (Cruz, 2013).

The results of the analysis of variance indicated significant differences between genotypes for nearly all traits, except for GY, which was not significant (Table 2). Partitioning the genotype effect indicated significant differences between all parents, between genotypes within each group of parents, and among groups of genotypes (Table 2). The contrast Parents vs. F₂, was highly significant for HD, PHT and SN, while the F₂ populations exhibited significant differences for almost all evaluated traits, except for SW, BIO and GY, which were not significant at the 5% probability level.

Table 2

The Scott-Knott means grouping test revealed significant differences between and within the two parental groups (Table 3). Within group 1, Acsad₈₉₉ had the highest average for Chl (40.38 unit) and for TKW (39.47 g), while Acsad₁₁₃₅ was the tallest parent (73.10 cm) with 6.93 spikes per plant. The parent Ain Abid showed the highest means for HD, PHT, SW, GN, BIO and GY, with mean values of 138.67 days, 76.60 cm, 22.79 g, 63.57 g, 30.79 g and 15.09 g, respectively (Table 3). In group 2, Mahon-Demias had the longest vegetative cycle (142.00 days) and was the tallest (104.81 cm) parent, expressing higher tillering ability (9.23 spikes), heavier grain weight (40.78 g). This parental line also showed the highest SW (19.48 g), BIO (38.93 g) and GY (12.46 g). Hidhab had the highest mean for Chl (38.98 unit) with more grains (52.22 grains) (Table 3). In general, group 2 parents were taller with higher SN and TKW, fewer GN and more BIO. The two groups of parents were similar in Chl, HD, SW and GY. Compared to their parents means, the F₂ hybrids varied depending on the cross and the trait; being shorter, late, expressing lower tillering capacity and more grains.

Table 3

The data collected on the traits were subjected to two adequacy tests to check the validity of the additive-dominance model. The first test was carried out by joint regression analysis of Vr and Wr. According to Mather and Jinks (2013), the data will be only valid for genetic interpretation if the value of regression coefficient b must deviate from zero but not from unity. The second test was the t² test which is an F after rotation by 45°. The results of two scaling tests indicated that the hypotheses of the genetic analysis were partially satisfied for all traits under study considering both parental groups (Table 4). ANOVA of grain yield did not show significant difference among genotypes (Table 2), this result does not justify the further genetic analysis of the considered trait. Partial failure of the assumptions described by Hayman (1954) indicates a more complex genetic system implicated in the inheritance of the said traits. However, it is possible to make estimates of the population parameters and genetic components of these traits, even though such estimates will be less reliable than they would have been if all the assumptions were satisfied. Results of genetic analysis studies showing partially adequate model were reported in wheat (Farooq et al., 2011), rice (Mahmood et al., 2004), sorghum (Wilson et al., 1978), cotton (Ali and Awan, 2009) and Soybean (Fronza et al., 2004).

Table 4

The estimates of the genetic and non-genetic parameters for the traits under study are shown in Tables 5 and 6. Chl genetic components of variation (D ₁, D ₂ and D ₃) showed positive and significant values at 5% probability, indicating the presence of additive effects in the inheritance of this trait (Table 5). The estimate (D ₁ - D ₂) was less than zero (-1.4), suggesting greater variability in group 2. Genetic components due to the dominance effects (H ₁ and H ₂) were positives but only H ₁ parameter was significant, suggesting the presence of dominance effect in the group 1. These results were confirmed by the significance of F estimates for the parents Acsad₉₀₁ and Acsad₁₁₃₅ (Table 5). However, the positive and significant estimate of F value in group 2 for Mahon-Demias suggested the predominance of dominant alleles for this parent. The average degree of dominance (H ₁ /D) ^1/2, was greater than unity, suggesting over-dominance in both parent groups (Table 6). The proportion of dominant genes with positive or negative effects in the parents H ₂ /4H ₁ was lower than 0.25 in both groups of parents, assuming unequal distribution of dominant genes with positive or negative effects (Table 6). This result was confirmed by the dominance-recessive ratio K _D /K _R which estimated the proportion between dominant and recessive genes, indicating the prevalence of dominant alleles in both parental groups. The direction of dominance (K ⁺ - K ^- ) ² /K had a value close to zero, revealing the occurrence of bidirectional dominance (Table 6). According to Viana et al. (1999), (K ⁺ - K ^- ) ² /K value would it be close to zero when the frequencies of the dominant genes with positive and negative effects were similar.

Table 5

Table 6

The graphical analysis based on the regression of Wr on Vr (Figures 1, 2, 3, 4, 5, 6, 7 and 8) revealed that the parents Acsad₈₉₉ and Hidhab, with the highest number of recessive alleles, had also the highest values for chlorophyll content in group 1 and group 2, respectively (Table 3). For HD, the results show that the components associated with additive ef fects (D ₂ and D ₃) were more relevant than those associated with dominance effects (H ₁, H ₂ and h ²) at 5% probability (Table 5). Even though D ₁ was not significant for group 1, the joint assessment (D ₃) proved the occurrence of additive gene effects for this trait. Considering the two parental groups, the covariance of additive and dominance effect F was important in the first group, suggesting the prevalence of dominant alleles in this group.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

There was asymmetric distribution of favourable and unfavourable alleles in the par ents under study. This result was confirmed by the K _D /K _R ratio (Table 6). (H ₁ /D) ^1/2 estimates were 3.22 and 1.36, respectively for group 1 and group 2. This result shows the existence of over dominance among the alleles in the control of this trait (Table 6). The (K ⁺ - K ^- ) ² /K values showed evidence of unidirectional dominance (Table 6).

For PHT, the components associated with the additive effects were predominant in relation to those associated with the dominance effects (Table 5). The estimate of (D ₁ - D ₂) was lower than zero, proving greater variabil ity in group 2. Over-dominance was evidenced in the expression of plant height in group 1, while partial dominance was present in group 2 (Table 6). Average value of the allelic frequency products H ₂ /4H ₁ was lower than 0.25 in both groups of parents, suggesting unequal distribution of dominant and recessive alleles (Table 6). The ratio K _D /K _R indicated that both groups of parents carry more dominant alleles. Dominance acted in the direction of increasing value plant height. Additionally, the individual estimates (Table 3) in rela tion to the graphical analysis (Figure 3), suggested that the parents Acsad₁₁₃₅, Acsad₁₀₆₉, Ain Abid and Mahon-Demias had the highest number of dominant alleles.

The components (D ₂ and D ₃) for SN were significant at 5% probability, indicating a greater importance of additive gene effects in the determination of this trait. Over-dominance was involved in the genetic control of this trait in the first group, whereas partial dominance controlled this trait in group 2. The ratio K _D /K _R, estimating the proportion between dominant and recessive genes, indicated that more recessive alleles were present in both parental groups (Table 6). Group 1 showed symmetric distribution of the alleles with favourable and unfavourable effects in the parents (Table 6), but the H ₂ /4H ₁ estimate was probably biased, since the maximum parametric value expected was 0.25. However, group 2 illustrated the occurrence of asymmetry distribution, its estimate was 0.07. Mean values analysis indicated that Acsad₁₁₃₅ had the highest average among the parents of group 1, while Mahon-Demias, in group 2, recorded the highest value. These two parents carried also the highest number of recessive alleles (Table 5). This result indicates that high SN values are determined by recessive genetic factors.

TKW additive genetic components (D ₁, D ₂ and D ₃) were positive and significant at 5% probability, D ₂ was greater than D ₁ (D ₁ < D ₂), indicating more genetic variability in group 2 (Table 5). Nevertheless, only H _1, from the parameters related to dominance effects, was significant, suggesting the presence of both additive and dominance effects in the determination of this trait in group 1. These results were supported by the positive and significant values of F component (Table 5). The average degree of dominance took a value greater than one, suggesting over-dominance in both parental groups (Table 6). Mean value of the allelic frequency products H ₂ /4H ₁ was close to zero in both groups, suggesting unbalanced distribution of dominant genes with positive or negative effects in the parents under study (Table 6). This was confirmed by the K _D /K _R ratio, which showed the preponderance of dominant alleles in both parental groups. Dominance was unidirectional for this trait and acted in the direction of increased value (Table 6).

The diallel analysis revealed significant role of additive and dominant genetic effect in the inheritance of SW (Table 5). Relative magnitude of dominant components (H ₁ and H ₂) were higher than additive component (D ₁, D ₂ and D ₃), suggesting the preponderance of dominant gene effects controlling the inheritance of this trait. In addition, unequal H ₁ and H ₂ genetic component (H ₁ < H ₂), indicated that positive alleles are not proportional to negative alleles at all loci, among parents (Table 5). Positive and significance H ₂ component estimates were determined for Acsad₁₁₃₅ and Hidhab, showing evidence of dominance for spikes weight in these parents. F parameter exhibited positive and significant estimates for Acsad₈₉₉, Ain Abid and Mahon-Demias revealing the predominance of dominant alleles. These three parents recorded the highest values for SW. Therefore, selection of dominant alleles will improve this trait. The genetic factors that determine SW trait exhibited over-dominance for both groups of parents, as indicated by (H ₁ /D) ^1/2 estimates (Table 6). The gene frequency seemed to be unequal as the range of the H ₂ /4H ₁ component were less than 0.25 in both groups of parents. The estimates of the consistency of expression of the degree of dominance across all segregating loci K _D /K _R indicated over-dominance level over all loci.

The components of additive effects (D ₁ and D ₂) predominated the dominance effects for the GN trait, suggesting that genes controlling this trait acted additively. The difference (D ₁ - D ₂) was negative, attesting greater variabil ity in group 2 (Table 5). Absence of dominance in the genetic control of GN is also suggested by the non-significant estimates of the component F, at 5% probability (Table 5). Value of H ₂ /4H ₁ ratio was close to 0.25 in group 1, denoting equality of distribution of increasing and decreasing alleles. However, unequal gene frequency was observed in group 2 (Table 6). The K _D /K _R ratio indicated predominance of recessive genes in group 1 and dominant alleles in group 2 (Table 6). Over-dominance effect was apparent in the control of GN, the dominance was bidirectional and acted toward increased values of this trait, as shown by the (K ⁺ - K ^- ) ² /K estimate (Table 6).

Estimation of genetic components of variation for BIO trait revealed significant additive gene effects (Table 5). Distribution of array points (Figure 8) depicted that the genotypes Ain Abid (group 1) and Mahon-Demias (group2) contained maximum dominant alleles while Acsad₁₁₃₅ and El-Wifak being farthest from the origin hold the least dominant genes. Average degree of dominance in both parental groups (2.72 and 1.39, respectively) depicted over-dominance for this trait (Table 6). As the H ₂ /4H ₁ deviated from its expected value of 0.25, therefore, the gene distribution was asymmetrical. The K _D /K _R ratio estimates suggested that more dominant alleles were present in the parents and dominance acted in the direction of increasing value of this trait (Table 6).

The environmental component E was not significant for all the traits under study (Table 5), indicating that these characters were not affected by environmental variations. The lack of significance of the statistic h ² was found for all the traits (Table 5), suggesting that pedigree selection could be rewarding for these traits (Ali et al., 2008). The h ² /H ₂ measuring the number of groups of genes which control the traits suggested that there were one, two or more pairs of genes affecting the inheritance of these (Table 6). These results indicated that there has been at least one genetic group involved in the genetic control of the traits under study. Heritability is an important genetic parameter in crop breeding. It provides information about traits transmissibility from parents to their progeny, and how this is affected by genetic and environmental factors.

High narrow sense heritability h ² _ns was observed for PHT and intermediate values were recorded for HD, TKW and BIO, indicating that selection to improve these traits would be effective. Narrow sense heritability for Chl, SN, SW and GN was low due to the dominance gene effects involved in the genetic control of these traits. These results suggested that delaying selection to improve these traits would be more effective.

Genetic components of variations for HD, PHT, SN, GN and BIO revealed that only additive gene effects were significant in both groups of parents. Thus, improvement of these traits by selection could be done in early generations. Genetic components of variation for Chl, TKW and SW showed that both additive and dominance variations were significant. However, dominant components were preponderant to additive components for these traits. Similar findings were reported by Farooq et al. (2011). H ₂ /4H ₁ ratio values, for all traits under study in both groups except for SN and GN in group 1, indicated unequal distribution of positive and negative alleles among the parents. These results were in accordance with those previously reported by Yao et al. (2014) and Afridi et al. (2017). Except for PHT and SN in group 2, average degree of dominance (H ₁ /D) ^1/2 for all the traits suggested the presence of over-dominance. Shehzad et al. (2015) reported over dominance gene action for most of the investigated traits a 5 x 5 complete diallel. Additive type of gene action with partial dominance for plant height was reported by Ojaghi et al. (2010) and for the number of spikes per plant by Kaukab et al. (2014). Significant and positive K _D /K _R ratio values signified the important role of dominant genes for most of the traits.

The findings of Akram et al. (2008) are in accordance with the results of the present study. Non-significant and positive value of h ² indicated un-important role of net dominant effect due to heterozygous loci in the expression of these traits. High to moderate narrow sense heritability estimates were recorded, in this study, for PHT, HD, TKW and BIO indicating large additive proportion in the total genetic variation. High to moderate heritability values were also reported for number of days to 50% flowering, plant height and 1000-kernel weight by Fikre et al. (2015). Low narrow sense heritability estimates were found, in this study, for Chl, SN, SW and GN. Ketata et al. (1976) and Hassan et al. (2013) also reported low heritability due to the presence of dominance effects for yield related traits in wheat. Increased values of HD, PHT, SW and BIO were determined by dominant genetic factors, whereas, Chl and SN traits were governed by recessive genetic factors. Besides, the placement of array points indicated that parental genotypes Ain Abid and Mahon-Demias had the maximum dominant genes, while Acsad₈₉₉, Acsad₁₁₃₅ and Rmada extreme recessive genes for most of the traits by considering both groups of parents. The h ² /H ₂ ratio showed that PHT and SN might be controlled by two and four groups of dominant genes, respectively; while Chl, HD, TKW, GN and BIO might be controlled by one group of genes. In their study, Yao et al. (2011) reported that wheat traits were controlled by one to four groups of dominant factors.