Use of Graphical and Numerical Approaches for Diallel Analysis of Grain Yield and Its Attributes in Bread Wheat (Triticum aestivum L.) under Varying Environmental Conditions

Abstract

Improving yield is the main aim of plant breeders. In the case of bread wheat (Triticum aestivum), a major challenge in this regard is genotype–environment interactions, and a knowledge of these is required to successfully select high-yielding genotypes. In this study, graphical and numerical approaches of diallel analysis have been used to reveal such interactions. Ten different wheat genotypes were crossed using a half-diallel approach. The parents, hybrids, and standard checks were evaluated at the Regional Research Station, Anand Agricultural University, Gujarat, Anand, India under both standard and late-sown conditions in two separate years (E₁ and E₂ (normal-18 November 2018 and late sown-10 December 2018, respectively, Rabi 2018–2019), E₃ and E₄ (normal-18 November 2019 and late sown-10 December 2019, respectively, Rabi 2019–2020)). For each sowing, ‘t²’ values were calculated for eleven phenotypic characteristics: days to 50% heading, days to maturity, plant height, number of effective tillers per plant, length of main stem, number of spikelets per main spike, number of grains per main spike, grain yield per main spike, grain yield per plant, 1000-grain weight, and harvest index. Components of the gene effect revealed that the number of spikelets per main spike in E₂ and E₄, and the number of grains per main spike in E₂ were governed by both additive and dominance gene action across the environments. Other characteristics were the greater influence of the dominance gene effect, except for days to 50% heading in E₁, E₂, E₃, and E₄; days to maturity in E₂, E₃, and E₄; grain yield per main spike in E₄. Many characteristics exhibited overdominance, an asymmetrical distribution of positive–negative, dominance–recessive genes, and narrow-sense heritability in all environments. In graphical analysis, regression value ‘b’ was unity for days to 50% heading (E₁ and E₄) and 1000-grain weight (E₃ and E₄), which revealed an absence of digenic interactions for these characteristics in the respective environments. Therefore, a given population may be improved to isolate superior recombinants for the development of desired parents in future breeding programs.

1. Introduction

Wheat (Triticum aestivum L.) is the world’s most consumed cereal, serving as the main source of food for approximately one third of the world’s population [1]. The growing population has necessitated the enhancement of cereal crop production worldwide. It is essential to enhance the production of cereal crops accordingly. The yield and attributes have been improved and fully exploited using breeding-based methods in various cereal crops including bread wheat [2]. An estimate of gene action is crucial in a successful breeding program. For plant breeders, parent selection is exceedingly important during the breeding of high-yielding varieties of crop plants. Information on the genetic architecture of yield and its attributes is essential for the removal of undesirable crosses based on the performance of the early generations and the improvement of crosses effectively [3]. Studies have suggested that diallel analysis is a viable method for understanding the genetic background of quantitative characteristics and to determine the parent potential [4,5]. A plant breeder has to perform effective selection in the segregating populations using diallel analysis, in order to understand the genetic basis of the characteristics.

There are various approaches available for the analysis of diallel crosses such as Griffing’s and Hayman’s approaches [6,7]. These two are often used in the data interpretation in breeding programs, such as in crop improvement, to elucidate the inheritance of characteristics and the nature of gene action [8].

The gene interaction and their effects can be determined using a numerical and graphical approach (Wr-Vr graph). The Wr-Vr approach estimates the ratio of the number of dominant genes to that of recessive genes existing in the common arrays of the parents, and is calculated from diallel tables. This is subsequently subjected to graphical representation and interpretation. The area under the regression line in the graph indicates the degree of dominance. Additionally, we can create parabola limits in this graph. This method is simple and facilitates easy data analysis and interpretation if the main assumptions of the diallel analysis are fulfilled [8]. He [9] noted that diallel analysis delivers more conformation than other methods, but has more crucial assumptions [10]. Diallel analysis facilitates the detection of an epistasis or linkage [10]; however, Griffing’s diallel approach does not [6]. When using Griffing’s analysis to estimate variance components, it has been suggested that simple tests, such as the Wr-Vr evaluation found in Hayman’s model [7], may be used to confirm the presence of an epistasis and/or linkage disequilibrium [11,12]. The validity of the hypothesis of the additive-dominance model can be verified by a unit slope of the regressions of Wr and Vr and non-significance of t², as prescribed by [7].

Constraints reduce the production potential due to climate changes that occur throughout the growth season. One of the main factors affecting the yield and productivity of the wheat crop is heat stress. For wheat crop enhancement, it is necessary to comprehend how genes interact with their environment. In light of the aforementioned information, in this work, we employed the diallel analysis described in [10,13] to clarify the genetic makeup of the parents with regard to various characteristics and to estimate the gene action for various quantitative characteristics in bread wheat. Our findings can be used in particular breeding programs to produce the desired outcomes.

2. Materials and Methods

2.1. Plant Material and Field Performance Evaluation

The experimental material comprised 10 parents, their 45 hybrids, and 2 check varieties. Here, Figure 1 represents the plant stature of parents and checks.

The genotypes represented cultivated (commercial varieties and checks) in

Table 1. List of varieties and their pedigree information.

Sr. No.	Released Varieties	Pedigree	Source
1	GW 451	GW324/4/CROC_1/AE.SQUARROSA (205)/JUP/JY/3/SKAUZ/4/KAUZ/5/GW 339	Centre of Excellence for Research on Wheat, SDAU, Vijapur, Gujarat
2	GW 496	HD 2285/CPAN 1861
3	LOK 1	S 308/S 311
4	GW 322	PBW 173/GW 196
5	GW 366	DL 802-3/GW 232
6	HI 1544	HIND162/BOBWHITE/CPAN 2099
7	GW 173	TW 275 -7-6-10/LOK1
8	GW 11	LOK 1/HW 1042//LOK 1
9	HD 2864	DL509-2/DL377-8
10	UAS 385	GW344/UAS239/DWR162
Standard check varieties
1	MASC 6222–TS	HD 2189*2//MASC 2496
2	HD 2932–LS	KAUZ/STAR//HD 2643

and this material was obtained from the Centre of Excellence for Research on Wheat, Sardarkrushinagar Dantiwada Agricultural University (SDAU), Vijapur, Gujarat. All the experiments were performed in accordance with the relevant guidelines and regulations. All plant materials were available within the institute and are available in the public domain, eliminating the need to obtain permissions. The details of the parental genotypes, Checks, and Hybrid crosses are given in Table 1 and Supplementary Table S1. The characteristics of the selected parental lines are given Figure 2. The crosses were made during Rabi (winter) 2017–2018 and 2018–2019 as per 10 × 10 diallel mating, excluding reciprocals.).

The numerical analysis was performed as per procedures outlined by [7,13,14,15,16,17] described in detail by [18,19] and the graphical approach as per [7,10]. The analysis was based on the following assumptions of diallel analysis: 1. diploid segregation; 2. no differences in reciprocal crosses, i.e., absence of maternal effect; 3. independent action of non-allelic genes in the diallel cross, i.e., absence of epistasis; 4. homozygous parents; 5. genes independently distributed between the parents, i.e., absence of linkages; 6. absence of multiple allelism. These assumptions were verified using the ‘t2’ test [13]. The ‘t2’ test evaluates the adequacy of the basic assumption of the additive dominance model. The material used in this experiment was examined in terms of the treaty with assumptions basic to Hayman diallel analysis. The parents used in this study were homozygous and diverse in their origin, while the maternal effects were presumed to be absent in the studied material. Two general tests, namely, the t2 test and regression of Wr on Vr, were used to test other assumptions. Therefore, a non-significant ‘t2’value would indicate the uniformity of the Wr-Vr, and confirm the validity of the postulated hypothesis, particularly the adequacy of the additive dominance model [20].

The parents, hybrids, and standard checks were evaluated in a complete randomized block design with three replications at the Regional Research Station, Anand Agricultural University, Anand, Gujarat, India (22°35′ N, 72°55′ E) during normal and late-sown conditions in four environments: E₁ and E₂ (normal and late sown, respectively, Rabi 2018–2019), and E₃ and E₄ (normal and late sown, respectively, Rabi 2019–2020). Each treatment consisted of 3 m long female lines with 20 × 10 cm (normal) and 18 × 10 cm (late) inter- and intra-row spacings, respectively. Two different spacings were used as the recommended agronomic practices. Likewise, the recommended nutrient management was deployed to grow a healthy plant stand and raise the crop (Supplementary Table S2). Immediately after sowing, need-based supplementary surface irrigation was provided (Supplementary Table S2). Observations for different quantitative characteristics under study excluding phenological traits, viz., days to 50% heading and days to maturity, were recorded on five randomly selected competitive plants in each experimental unit; however, border plants were excluded while selecting and tagging the plants for recording observations. The phenological characteristics were recorded on a population of an experimental unit.

The recorded observations included yield and its component traits: number of effective tillers per plant, length of main spike, number of spikelets per main spike, number of grains per main spike, 1000-grain weight, grain yield per main spike, grain yield per plant, and harvest index, and morphological traits: days to 50% flowering, days to maturity, and plant height. The replicated mean data were analyzed using Statistical Package for Agricultural Research data analysis (SPAR version 2.0). The Information on statistical tools is used in this study [14].

However, ‘t²’ also tests the adequacy of the basic assumption of the additive dominance model.

The ‘t²’ test for the uniformity test of W_r − V_r is

$${\mathrm{t}}^2=\frac{\mathrm{n}-2}{4}\left[\frac{{\left[\mathrm{V}\mathrm{a}\mathrm{r}.\mathrm{V}\mathrm{r}-\mathrm{V}\mathrm{a}\mathrm{r}.\mathrm{W}\mathrm{r}\right]}^2}{\left\{\left(\mathrm{V}\mathrm{a}\mathrm{r}.\mathrm{V}\mathrm{r}\right)\right.\left(\mathrm{V}\mathrm{a}\mathrm{r}.\mathrm{W}\mathrm{r}.\right)\left.\right\}-\mathrm{C}\mathrm{o}{\mathrm{v}}^2(\mathrm{V}\mathrm{r}.\mathrm{W}\mathrm{r})}\right]$$

It would be compared with table value of ‘t’ at 4 and n − 2 degrees of freedom.

2.2. Estimation of Genetic Parameters

Subsequently, the components of genetic variation, viz., additive effects (D), dominance components (H₁ and H₂), environmental variance (E), covariance of additive and dominance effects (F), and dominance effects of all loci in the heterozygous phase (h²), were estimated. Component analysis was performed only for the data that fit the additive dominance model. These genetic components of variation were calculated from the diallel table as per [9].

The model used to estimate the genetic parameters with consideration of the above equations different genetic parameters were estimated as:

$$\begin{array}{l}\stackrel{\wedge }{\mathrm{D}}= {\mathrm{V}}_{\mathrm{P}}-\mathrm{E}\\ {\stackrel{\wedge }{H}}_1=4\overline{V}r+Vp-4\overline{W}r-(3P-2)E/p\\ {\stackrel{\wedge }{H}}_2=4\overline{V}r-4V\overline{r}-2E\\ \stackrel{\wedge }{h^2}=4{(M{L}_i-M{L}_0)}^2-4(P-1)\stackrel{\wedge }{E}/p^2\\ \stackrel{\wedge }{F}=2V_0{L}_0-4W_0{L}_{0i}-2(P-2)\stackrel{\wedge }{E}/P \mathrm{i}.\mathrm{e}., 2 \mathrm{Vp}-4 \overline{\mathrm{W}}\mathrm{r}-2 (\mathrm{P}-2)\stackrel{\wedge }{\mathrm{E}}/\mathrm{p} \\ \widehat{E}=\frac{\mathrm{V}\mathrm{E}}{\mathrm{r}}={\mathrm{M}}^1\mathrm{e}\end{array}$$

For pooled analysis, E-pooled was used instead of E.

where:

P = Number of parents.

$\stackrel{\wedge }{D}$ = Component of genetic variation due to additive gene effect.

${\stackrel{\wedge }{H}}_1$ = Component of genetic variation attributable to dominant effects of genes.

${\stackrel{\wedge }{H}}_2$ = Component of genetic variation due to dominant effect corrected for genes distribution.

$\stackrel{\wedge }{F}$ = Relative frequency of dominance to recessive alleles in the parental population and variation in the dominance level over loci.

$\stackrel{\wedge }{h^2}$ = Net dominance variable effect expressed as the algebraic sum over all the loci in heterozygous condition in all the crosses.

$\stackrel{\wedge }{E}$ = Component of variation due to environmental effect.

3. Results

3.1. Numerical Approach

We estimated the ‘t²’ values for different characteristics in each environment, presented in

Table 2. ‘t²’ value and regression coefficient for different metric characteristics of Wr on Vr.

SN	Characteristics	t2 Test				b (Regression)
		E1	E2	E3	E4	E1	E2	E3	E4
1	Days to 50% heading	1.96	0.20	0.60	0.04	0.18 ++	0.87 $$	0.15 +	0.69 $
2	Days to maturity	11.63 **	2.58	0.09	0.07	0.29 $++	0.27 ++	0.51	0.44
3	Plant height	6.21 **	9.56 **	10.18 **	19.17 **	0.19 ++	0.20 ++	0.06 ++	0.17 ++
4	No. effective tillers per plant	1.34	13.53 **	0.45	18.10 **	0.20 ++	−0.13 ++	0.36+	−0.11 ++
5	Length of main spike	3.96 **	1.31	0.93	21.47 **	0.13 ++	0.16 ++	0.37 +	0.22 $++
6	Number of spikelets/main spike	7.07 **	0.20	3.28	2.04	0.24 ++	0.60	0.31 ++	0.59
7	Number of grains per main spike	3.01	0.208	6.68 **	0.24	−0.07 ++	0.57	0.04 ++	0.65
8	Grain yield per main spike	34.90 **	0.004	21.91 **	0.04	0.10 ++	0.14 +	0.08 ++	0.20
9	Grain yield per plant	29.21 **	7.32 **	43.61 **	7.99 **	0.22 $++	0.01 ++	0.21 $++	0.13 ++
10	1000-grain weight	1.81	0.04	0.97	0.006	0.67 $$+	0.46 $$++	0.71 $$	0.66 $
11	Biological yield per plant	476.05 **	7.14 **	88.27 **	8.41 **	−0.04 ++	0.04 ++	−0.06 ++	0.20 ++
12	Harvest index	0.97	11.22 **	3.94 *	9.71 **	−0.20 ++	0.55 $$++	−0.29 ++	0.35 $++

*, ** Significant at 5% and 1% levels, respectively; $, $$ Significant at 5% and 1% levels, respectively, when Ho: b = 0; +, ++ Significant at 5% and 1% levels, respectively, when Ho: b = 1; E₁: Normal Sowing, E₂: Late Sowing (Rabi 2018–2019); E₃: Normal Sowing, E₄: Late Sowing (Rabi 2019–2020).

. Among the twelve characteristics studied, the estimated ‘t²’ values were found to be significant for the three characteristics: plant height, grain yield per plant, and biological yield per plant in all the environments; however, the t² for days to 50% heading was non-significant in all the environments. The ‘t²’ value of the remaining characteristics was significant in either E₁, E₂, E₃, E₄, or a combination of the environments. The significance of ‘t²’ suggested the failure of certain assumptions (diploid segregation, no differences in reciprocal crosses, independent action of non-allelic genes in the diallel cross, i.e., absence of epistasis, homozygous parents, genes independently distributed between the parents, i.e., no linkages and no multiple allelism) of diallel analysis. Therefore, estimates of the uniformity of the Wr-Vr value are shown in

Table 3. Non-significant genetic components for days to 50% heading, days to maturity, no. of effective tillers per plant, and length of main spike.

Days to 50% Heading					Days to Maturity $			No. of Effective Tillers Per Plant &		Length of Main Spike &
Genetic Components	E1	E2	E3	E4	E2	E3	E4	E1	E3	E2	E3
$\hat{\mathrm{E}}$	0.44	0.60 *	0.64	0.54	0.91	0.54	0.82	0.28	0.30	0.14 **	0.13 **
$\hat{\mathrm{D}}$	17.32 **	7.37 **	19.04 **	7.09 **	5.11 **	10.15 **	2.93 **	0.87	0.74	0.13	0.13
$\hat{\mathrm{F}}$	−2.16	5.22 **	1.58	5.73 **	2.04	1.19	0.82 **	−0.08	−1.04	−0.19	0.13
$\hat{\mathrm{H}}$1	49.19 **	10.69 **	42.75 **	10.74 **	19.88 **	24.31 **	10.56 **	11.18 **	9.58 **	1.82 **	2.11 **
$\hat{\mathrm{H}}$2	41.79 **	9.36 **	36.90 **	8.75 **	13.80 **	17.58 **	8.21 **	8.25 **	7.89 **	1.45 **	1.55 **
$\hat{\mathrm{h}}$2	10.64	0.01	11.33	0.23	3.41	4.76	4.25	0.08	0.04	0.88 **	1.22 **
($\hat{\mathrm{H}}$1/$\hat{\mathrm{D}}$)0.5	1.69	1.20	1.50	1.23	1.97	1.55	1.90	3.59	3.59	3.79	4.01
$\hat{\mathrm{H}}$2/4$\hat{\mathrm{H}}$1	0.21	0.22	0.22	0.20	0.17	0.18	0.19	0.18	0.21	0.20	0.18
KD/KR	0.93	1.83	1.06	1.98	1.23	1.08	1.16	0.97	0.67	0.67	1.28
$\hat{\mathrm{h}}$2/$\hat{\mathrm{H}}$2	0.25	0.00	0.31	0.03	0.25	0.27	0.52	0.01	0.01	0.61	0.79
% Heritability (narrow sense)	24.58	48.33	30.33	49.69	19.21	28.64	18.35	6.53	5.91	4.69	5.01

^$: only three environments sowing; ^&: only two environments sowing. KD/KR = {(4$\hat{\mathrm{D}}\hat{\mathrm{H}}$₁)^0.5 + $\hat{\mathrm{F}}$}/{(4$\hat{\mathrm{D}}\hat{\mathrm{H}}$₁)^0.5 − $\hat{\mathrm{F}}$}; *, ** Significant at 5 and 1 percent levels, respectively; E₁: Normal Sowing, E₂: Late Sowing (Rabi 2018–2019); E₃: Normal Sowing, E₄: Late Sowing (Rabi 2019–2020).

and

Table 4. Non-significant genetic components for no. of spikelets per main spike, no. of grains per main spike, grain yield per main spike, 1000-grain weight, and harvest index.

No. of Spikelets per Main Spike $				No. of Grains per Main Spike $			Grain Yield per Main Spike &		1000-Grain Weight				Harvest Index #
Genetic Components	E2	E3	E4	E1	E2	E4	E2	E4	E1	E2	E3	E4	E1
$\hat{\mathrm{E}}$	0.49 **	0.39 **	0.36 **	1.53	6.85 **	3.14	0.02	0.01	0.63	0.64	1.01	0.79	9.34
$\hat{\mathrm{D}}$	2.01 **	0.82	2.19 **	17.21	23.12 **	21.02 **	0.09 **	0.10 **	12.46 **	30.12 **	13.82 **	30.78 **	66.93
$\hat{\mathrm{F}}$	−0.31	−0.28	0.53	12.26	2.40	4.56	0.19	0.23 **	−4.71	12.56	−0.54	14.22	115.29
$\hat{\mathrm{H}}$1	5.26 **	5.04 **	4.47 **	98.85 **	109.88 **	121.19 **	0.49 **	0.45 **	41.62 **	68.97 **	37.71 **	62.35 **	357.26 **
$\hat{\mathrm{H}}$2	4.81 **	3.87 **	3.86 **	79.04 **	78.17 **	85.93 **	0.35 **	0.29 **	32.99 **	52.25 **	30.82 **	47.28 **	290.10 **
$\hat{\mathrm{h}}$2	11.25 **	−0.13	5.63 **	13.29	33.53 **	35.67 **	0.15 **	0.07	77.41 **	85.02 **	76.95 **	90.71 **	59.62
($\hat{\mathrm{H}}$1/$\hat{\mathrm{D}}$)0.5	1.62	2.48	1.43	2.40	2.18	2.40	2.38	2.07	1.83	1.51	1.65	1.42	2.31
$\hat{\mathrm{H}}$2/4$\hat{\mathrm{H}}$1	0.23	0.19	0.22	0.20	0.18	0.18	0.18	0.16	0.20	0.19	0.20	0.19	0.20
KD/KR	0.91	0.87	1.19	1.35	1.05	1.09	2.65	3.37	0.81	1.32	0.98	1.39	2.19
$\hat{\mathrm{h}}$2/$\hat{\mathrm{H}}$2	2.34	−0.03	1.46	0.17	0.43	0.42	0.43	0.24	2.35	1.63	2.50	1.92	0.21
% Heritability (narrow sense)	21.06	10.58	28.99	15.65	14.62	13.99	18.27	29.12	20.31	33.80	24.63	37.49	19.32

^$: only three environments sowing; ^&: only two environments sowing; ^#: only one environments sowing. KD/KR = {(4$\hat{\mathrm{D}}\hat{\mathrm{H}}$₁)^0.5 + $\hat{\mathrm{F}}$}/{(4$\hat{\mathrm{D}}\hat{\mathrm{H}}$₁)^0.5 − $\hat{\mathrm{F}}$}; ** Significant at 5 and 1 percent levels, respectively. E₁: Normal Sowing, E₂: Late Sowing (Rabi 2018–2019); E₃: Normal Sowing, E₄: Late Sowing (Rabi 2019–2020).

.

3.1.1. Days to 50% Heading

The ‘t²’ value was non-significant in all environments. The significance of additive (D) and dominance (H₁ and H₂) components of the gene effect revealed that the characteristic was governed by both additive as well as dominant gene actions in all the environments. The estimates of the average degree of dominance suggested the presence of overdominance in all environments (E₁:1.69%, E₂:1.20%, E₃:1.50%, and E₄:1.23%). An asymmetrical distribution of positive and negative alleles among the parents was observed in all environments as the H₂/4H₁ was <0.25. The positive values of F and KD/KR > 1 indicated an excess of dominant genes in all environments, except E₁. At least one dominant gene or group of genes appeared to govern the characteristic as the h²/H₂ was <1 across all environments. The dominant gene or group of genes was not computed, as h² values were positive or non-significant. The estimates of narrow-sense heritability were low to medium in all analyses (E₁: 24.58%, E₂: 48.33%, E₃: 30.33%, and E₄: 49.69%) (Table 3).

3.1.2. Days to Maturity

The ‘t²’ value was found to be significant in E₁, whereas it was non-significant in the other environments. The significance of additive (D) and dominance (H₁ and H₂) components of the gene effect revealed that the characteristic was governed by both additive as well as dominance gene effects in all environments; however, preponderance gene effects were noticed through the magnitude of the component of gene effects.

The estimates of the average degree of dominance suggested the existence of overdominance gene action in all environments (E₂:1.97%, E₃:1.55%, and E₄:1.90%). An asymmetrical distribution of positive and negative alleles among the parents was observed in all environments as the value of the H₂/4H₁ ratio was less than 0.25. Positive values of F and KD/KR > 1 in all the analyses indicated an excess of dominant genes among the parents. At least one dominant gene or group of genes appeared to govern the character as the h²/H₂ was <1 across the environments. The dominant gene or group of genes was not computed, as the h² values were positive or non-significant. The estimates of narrow-sense heritability were low in all the environments (E₁: 19.21%, E₂: 28.64%, and E₃: 18.35%), which also confirmed that the characteristic was under the control of dominance gene effects (Table 3).

3.1.3. Number of Effective Tillers per Plant

The ‘t²’ value was significant in E₂ and E₄, which suggested a non-adherence to failure of certain assumptions of diallel analysis. The significance of both dominance components (H₁ and H₂) of the gene effect in E₁ and E₃ indicated that the characteristic was mainly governed by dominance gene effect. The estimate of the average degree of dominance (3.59) suggested the presence of overdominance. The asymmetrical distribution of positive and negative alleles among the parents was observed as the H₂/4H₁ was less than the expected value (0.25). The negative value of F and KD/KR < 1 indicated that the characteristic was controlled by several recessive genes. h²/H₂ < 1 suggested that at least one dominant group of genes governed this trait. The dominant gene or group of genes was not computed, as the h² values were positive or non-significant. The estimate of narrow-sense heritability was extremely low in E₁ (6.53%) and E₂ (5.91%), which also confirmed that this characteristic was under control of the dominance gene effect (Table 3).

3.1.4. Length of Main Spike

The ‘t²’ value was significant in E₁ and E₄, which suggested failure of certain assumptions of diallel analysis. The significance of only dominance components (H₁ and H₂) of the gene effect in E₂ and E₃ revealed that the characteristic was solely governed by dominance gene action. The estimates of the average degree of dominance ((H1/D)^0.5) suggested the presence of overdominance. H₂/4H₁ < 0.25 indicated the asymmetrical distribution of positive and negative alleles among the parental genotypes. The negative F value and KD/KR < 1 observed in E₂ indicated that the characteristic was controlled by several recessive genes; however, in E₃, the characteristic was mainly governed by several dominant genes as the values of F were positive and KD/KR was <1. The estimates of h²/H₂ ratio indicated that at least one dominant group of genes appeared to govern this trait in E₂ and E₃. Significant and positive estimates of h² in both environments indicated a net dominance gene effect sum over loci. The estimates of narrow-sense heritability were low in both E₂ (4.69%) and E₃ (5.01%) (Table 3).

3.1.5. Number of Spikelets per Main Spike

The ‘t²’ value was significant in E₁, whereas it was non-significant in the rest of the environments. However, additive components of the gene effect had a greater influence in E₂ and E₄, and dominance components (H₁ and H₂) of the gene effect were significant in E₂ and E₄ with the prevalence of the dominant gene effect, whereas only the dominance gene effect governed the characteristic in E₃. The values of the average degree of dominance indicated the presence of over-dominance in all the three environments. H₂/4H₁ < 0.25 indicated an asymmetrical distribution of positive and negative alleles among the parental genotypes. The negative F value and KD/KR < 1 indicated that the characteristic was mainly controlled by several predominant recessive genes in E₂ and E₃. The positive value of F and KD/KR > 1 indicated that the characteristic was controlled by several dominant genes in E₄. The estimate of h²/H₂ ratio was >2 in E₂ and >1 in E₄ and one dominant group of genes appeared to govern this characteristic. The estimate of narrow-sense heritability was low in E₂ (21.06%), E₃ (10.58%), and E₄ (28.99%), which also confirmed that this characteristic was mainly under the control of the dominance gene effect (Table 4).

3.1.6. Number of Grains per Main Spike

The ‘t₂’ value was significant in E₃, whereas it was non-significant in the rest of the environments. Additive (D) and dominance components (H₁ and H₂) of the gene effect were significant with the preponderance of the dominant gene effect in E₂ and E₄, whereas only the dominance gene effect was involved in E₁. The values of the average degree of dominance indicated the presence of overdominance. H₂/4H₁ < 0.25 indicated the asymmetrical distribution of positive and negative alleles among the parental lines in E₁, E₂, and E₄. The positive values of F and KD/KR > 1 indicated a symmetrical distribution of dominant and recessive genes among the parental genotypes, and the action of several dominant genes across the environments. h²/H₂ < 1 suggested that at least one dominant group of genes governed this trait. Significant and positive estimates of h² in E₂ and E₄ indicated the net dominance gene effect sum over loci. The estimates of narrow-sense heritability were low in E₁ (15.65%), E₂ (14.62%), and E₃ (13.99%) (Table 4).

3.1.7. Grain Yield per Main Spike

The ‘t²’ value was significant in E₁ and E₃, which suggested failure of certain assumptions of diallel analysis. The significance of additive (D) and dominance components (H₁ and H₂) of the gene effect in E₂ and E₄ revealed that the characteristic was governed by both additive and dominance gene action. The estimate of the average degree of dominance (E₂: 2.38 and E₄: 2.07) suggested the presence of overdominance. An asymmetrical distribution of positive and negative alleles among the parents was observed as the value of H₂/4H₁ was less than the expected value (0.25). The positive value of F and KD/KR > 1 indicated that the characteristic was controlled by several dominant genes. h²/H₂ < 1 suggested that at least one dominant group of genes governed this trait. A significant and positive estimate of h² observed in E₂ indicated the net dominance gene effect sum over loci. The estimate of narrow-sense heritability was low in E₂ (18.27%) and E₄ (29.12%), which also confirmed that this characteristic was under control of the dominance gene effect (Table 4).

3.1.8. 1000-Grain Weight

The ‘t²’ value was non-significant in all the analyses. The significance of additive (D) and dominance components (H₁ and H₂) of the gene effect revealed that the characteristic was governed by both additive and dominance gene actions in all environments. The estimates of the average degree of dominance suggested the presence of overdominance in all the environments. H₂/4H₁ < 0.25 indicated an asymmetrical distribution of positive and negative alleles among the parental genotypes in all the environments. The positive value of F and KD/KR > 1 in E₂ and E₄ indicated that the characteristic was controlled by several dominant genes, while a negative value of F and KD/KR < 1 in E₁ and E₃ indicated that the characteristic was controlled by several recessive genes. h²/H₂ > 1 indicated that more than two to three dominant groups of genes appeared to govern this characteristic. Significant and positive estimates of h² in all the environments indicated the net dominance gene effect sum over loci. The estimates of narrow-sense heritability were low or medium in all the analysis (E₁: 20.31%, E₂: 33.80%, E₃: 24.63%, and E₄: 37.49%) (Table 4).

3.1.9. Harvest Index

The ‘t²’ value test was significant in E₂, E₃, and E₄, which suggested failure of certain assumptions of diallel analysis. The significance of only dominance components (H₁ and H₂) of the gene effect in E₁ revealed that the characteristic was solely governed by dominance gene action. The estimate of the average degree of dominance (2.31) suggested the existence of overdominance. An asymmetrical distribution of positive and negative alleles among the parents was observed as the value of H₂/4H₁ was less than the expected value (0.25). The positive value of F and KD/KR > 1 indicated that the characteristic was controlled by several dominant genes. h²/H₂ < 1 suggested that at least one dominant group of genes governed this trait. The estimate of narrow-sense heritability was low (19.32%), which also confirmed that this characteristic was mainly controlled by the dominance gene effect (Table 4).

3.2. Graphical Analysis

To test the validity of the basic assumptions postulated for diallel analysis [5], the Wr-Vr homogeneity ‘t²’ test was performed. The ‘t²’ value was significant for most of the characteristics either in E₁, E₂, E₃, and E₄, or in their different combinations, indicating failure of any of the basic assumptions of diallel analysis. However, further verification of the validity of the assumption in respect of the presence or absence of epistatic gene effects could be made more precisely from the Wr-Vr graph. The array points on the Wr-Vr graph are expected to fall on the line of unity (45^°) and, therefore, the value of regression ‘b’ should significantly deviate from zero, but not from one, suggesting the absence of an epistatic gene effect. b was statically at par one for days to 50% heading (E₁ and E₄) and 1000-grain weight (E₃ and E₄), which revealed an absence of digenic interactions for these characteristics in the respective environments (Table 2).

The graphical analyses are presented in Figure 3, Figure 4, Figure 5 and Figure 6 and are described as follows.

3.2.1. Days to 50% Heading

In E₂, the regression line (Y = 0.8771x − 0.6627) was intercepted by the Wr axis below the origin, indicating the presence of overdominance (Figure 3). Among the parents, HD 2864 had a higher frequency of dominant genes, as these parents occupied the nearest position to the origin of the regression line. Accordingly, the parents GW 366, HI 1544, and UAS 385 had a higher frequency of recessive genes, as they occupied the farthest position from the origin, whereas LOK 1, GW 322, GW 173, and GW 11 had an equal proportion of dominant and recessive genes as they occupied an intermediate position on the regression line. The parents GW 451 and GW 496 may carry the genes, causing inter-allelic interaction as they occupied the positions outside the truncated area of the graph. The slope of the regression line of the Wr-Vr graph was statistically equal to unity in E₄ (Y = 0.6967x − 0.1504), indicating the absence of digenic interactions (Figure 4). Similarly, the regression line intercepted by the Wr axis passed through the origin, indicating the presence of complete dominance.

Among the parents, HD 2864 and GW 496 had a higher frequency of dominant genes as they occupied the nearest position to the origin of the regression line, whereas GW 366 and HI 1544 had a higher frequency of recessive genes as they occupied the farthest position from the origin; GW 451, LOK 1, GW 322, GW 11, GW 173, and UAS 385 had an equal proportion of dominant and recessive genes as they occupied an intermediate position on the regression line.

3.2.2. 1000-Grain Weight

The regression line (Y = 0.711x – 2.5028) was intercepted by the Wr axis below the origin, indicating overdominance for the characteristic in E₃ (Figure 5). The array point of parent GW 451 was closest to the origin, thereby indicating its contribution to the several dominant genes, whereas the parent HD 2864 occupied a position at the tail of the regression line, indicating it as a carrier of the several recessive genes. Moreover, the rest of the parents, GW 451, GW 496, GW 322, HI 1544, GW 173, GW 11, and UAS 385, occupied intermediate positions on the regression line, indicating an equal distribution of dominant and recessive genes within them. The parents LOK 1 and GW 366 could be carriers of genes causing inter-allelic interaction as they occupied positions outside the truncated area of the graph.

In E₄, the slope of the regression line of the Wr-Vr graph was linear and probably at par to one. The regression line (Y = 0.6615x – 1.4252) intercepted the Wr axis below the origin, indicating the presence of overdominance. The scattered array points of the parents on and around the regression line revealed the existence of sufficient variability among the parents. The array point of LOK 1 occupied a position closer to origin, indicating that it would likely contribute dominant genes in high frequency; whereas the parents, GW 173, GW 11, and UAS 385, occupied positions at the tail of the regression line, indicating their contribution to the high frequency of recessive genes. Moreover, the rest of the parents occupied intermediate positions on the regression line within the truncated area, indicating an equal distribution of dominant and recessive genes within them (Figure 6).

4. Discussion

4.1. Numerical Approach

Components of the gene effect revealed that most of the characteristics were governed by both additive and dominance gene action across the environments with a greater influence of the dominance gene effect, except for days to 50% heading in E_1, E_2, E₃, and E₄; days to maturity in E₂, E₃, and E₄; grain yield per main spike in E₄. For the number of effective tillers per plant (E₁ and E₃), length of main spike (E₂ and E₃), number of spikelets per main spike (E₃), number of grains per main spike (E₁), and harvest index (E₁), only the dominant component (H₁ and H₂) of the gene effect was significant. The findings also indicated the involvement of both additive and non-additive gene action in the inheritance of yield and related traits in bottle gourd [19,21,22].

The values of the average degree of dominance varied across the environments. The overdominance behavior of interacting alleles was depicted for days to 50% heading (E₁, E₂, E₃, and E₄), days to maturity (E₂, E₃, and E₄), number of effective tillers per plant (E₁ and E₃), length of main spike (E₂ and E₃), number of spikelets per main spike (E₂, E₃, and E₄), number of grains per main spike (E₁, E₂, and E₄), grain yield per main spike (E₂ and E₄), 1000-grain weight (E₁, E₂, E₃, and E₄), and harvest index (E₁). The higher proportions of dominant genes observed in most of the characteristics are in agreement with the earlier findings of [23]. Thus, both the additive and dominant variances were the predominant components governing the expression of yield and its components in accordance with [24]. He also reported that non-additive gene action plays important roles in controlling grain yield under both drought stress and favorable growing environments [25].

An asymmetrical distribution of positive–negative and dominance–recessive genes was depicted for most of the characteristics. However, days to 50% heading (E₂, E₃, and E₄), days to maturity (E₂, E₃, and E₄), length of main spike (E₃), number of spikelets per main spike (E₄), number of grains per main spike (E₁, E₂, and E₄), grain yield per main spike (E₂ and E₄), 1000-grain weight (E₂ and E₄), and harvest index (E₁) exhibited a lack of dominant genes; whereas days to 50% heading (E₁), number of effective tillers per plant (E₁ and E₃), length of main spike (E₂), number of spikelets per main spike (E₂ and E₃), and 1000-grain weight (E₁ and E₃) exhibited an excess of recessive genes. H₂/4H₁ indicated a symmetrical distribution of positive and negative dominant genes in parents in all the studied characteristics and the result is in agreement with [26].

The estimates of narrow-sense heritability were low for days to 50% heading (E₁ and E₃), days to maturity (E₁ and E₃), number of effective tillers per plant (E₁ and E₃), length of main spike (E₂ and E₃), number of spikelets per main spike (E₂, E₃, and E₄), number of grains per main spike (E₁, E₂, and E₄), grain yield per main spike (E₂ and E₄), 1000-grain weight (E₁, E₂, E₃, and E₄), and harvest index (E₁), which indicated that these characteristics were under greater influence of the dominant gene effect. The narrow-sense heritability was moderate for days to 50% heading (E₂ and E₄), which confirmed that this characteristic was under the control of both additive and dominant genes. Narrow-sense heritability was generally small and ranged from 0.86 to 66.67%.

4.2. Graphical Approach

In graphical analysis, b was unity for days to 50% heading (E₁ and E₄) and 1000-grain weight (E₃ and E₄), which revealed an absence of digenic interactions for these characteristics in the respective environments. Based on the interception of the regression line on the Wr axis, the degree of dominance was depicted as overdominance for days to 50% heading (E₂) and 1000-grain weight (E₃ and E₄), whereas it was complete dominance for days to 50% heading (E₄). The dispersion of parents around the regression line revealed that parents LOK 1, GW 451, and GW 496 were close to the origin of the coordinate, and accordingly had >75% of dominant genes; parents GW 322 and HI 1544 had 50% dominant genes; while parent GW 366 was far from the origin and, therefore, mostly had recessive genes [26].

Environmental influence is an important factor affecting yield potential, especially temperature and precipitation. Understanding the interactions between environment and genotype, and environmental conditions and nutrition are a prerequisite for the improvement of the wheat crop [27,28,29].

5. Conclusions

Components of the gene effect revealed that the number of spikelets per main spike in E₂ and E₄, and the number of grains per main spike in E₂ were governed by both additive and dominance gene action across the environments with a greater influence of the dominance gene effect, except for days to 50% heading in E₁, E₂, E₃, and E₄; days to maturity in E₂, E₃, and E₄; grain yield per main spike in E₄. Grain yield per plant was influenced by the overdominance gene effect. Selection may be delayed by the time, dominance will be diluted, and transgressive segregants could be identified.

In graphical analysis, b was unity for days to 50% heading (E₁ and E₄) and 1000-grain weight (E₃ and E₄), which revealed an absence of digenic interactions for these characteristics in the respective environments. The remaining characteristics exhibited a non-random distribution of genes at different loci among the parents or the presence of inter-allelic interaction at different loci. The contradiction between the approaches of the genetic component of variation and Wr-Vr graph analysis could be ascribed to the presence of correlated gene distribution.