Generation Mean Analysis, Heterosis, and Genetic Diversity in Five Egyptian Faba Beans and Their Hybrids

Abstract

The faba bean (Vicia faba L.) is a major legume crop; thus, it is important to apply various biometrical techniques to develop the most efficient breeding procedures to face biotic and abiotic stressors. During the four consecutive winter seasons of 2017–2021, five populations of five faba bean hybrids were studied at Sakha agricultural research station in Egypt. Five basic generations, including two parents (P1 and P2) and the first, second, and third generations, were studied. This analysis found significant variations between generations in all attributes studied in all crosses (P1, P2, F1, F2, and F3). Sakha 4 was the earliest parent (138 days) based on the maturity date, whereas Giza 40 had the most significant number of pods and seeds per plant (25.68–78.94), and Giza 716 had the tallest plant height (124.00 cm). Giza 843 and Sakha 4 had the highest seed yield per plant values (62.84 g and 61.77 g). The data demonstrated highly substantial heterosis in the favorable direction over mid and better parents for all features, except for the number of branches in Cross 3 (Giza 40 × Giza 843) over mid and better parents and a maturity date in Cross 1 over mid parents. Contrarily, opposite-direction dominance and dominance × dominance effects increased narrow-sense heredity. Broad-sense heritability values for all examined characteristics were high in all crosses, ranging from 90.24% to 97.67%. In both Crosses 5 (Giza 716 × Qahera 4) and 3, genetic advance through selection ranged from 1.73% at the maturity date to 95.12% for seed yield per plant. Cross 3 (Giza 40 × Giza 843) had the greatest number of branches, pods, and seeds per plant. In conclusion, this study advances our understanding of employing faba beans in breeding programs.

1. Introduction

The faba bean (Vicia faba L.) is a major legume crop in North and East Africa, especially in the Arabian regions. The faba bean has a significant role in Egypt as a cost-effective food with high nutritional value, particularly in terms of protein content, ranging from 22% to 38% [1]. Additionally, faba beans, like other seed legumes, enhance soil fertility, support nitrogen fixation, and play a significant role in crop rotation in several places around the world [2,3]. Faba beans are a staple food grown under many farming systems in Africa and South America. They are grown under low rains in North Africa, heavy rains in Ethiopia, and irrigation in Egypt and Sudan. Breeding for yield potential in faba beans can contribute to sustainability in two ways. The first way is the role that faba beans can play in the resilience of agri-food chains. Egypt, as a developing country, suffers from a shortage of protein supply; therefore, high-yield faba beans can help in the recovery of protein supply, because it has a high protein content. The second way is the important role of faba beans as a legume crop. Legume crops can fix nitrogen and consequently reduce the amount of chemical fertilizers applied, which is considered a primary cause of environmental pollution and the enemy of sustainability. The monoculture of cereals has led to soil degradation and the emergence of pests and diseases because of the use of chemical fertilizers [4]. Therefore, the bean yield has decreased in these countries, with a reduction in the cultivated area to 2.6 million hectares in 2019, while the countries’ imports increased to USD 343 million in 2019 [5]. Therefore, faba bean breeders have used various biometrical techniques to develop the most efficient breeding procedures to face biotic and abiotic stressors in addition to evaluating the genetic effects of genes controlling quantitative traits to maximize yield potentials across a large number of them [6,7,8,9]. In this regard, the knowledge of heterosis and combining ability can assist breeders in selecting acceptable parents. SCA is largely attributable to non-additive (dominance and epistasis) genes, while an analysis of combining ability is often connected with additive gene effects. In addition, the detection of gene activity, including additive, dominant, and epistatic effects, is crucial for any breeding effort. In addition, estimations of heritability and the extent of genetic variability for various attributes are quite valuable in identifying the best descendants. Therefore, breeders should analyze the existing germplasms’ potential for novel re-combinations and their ultimate combining abilities, which have been shown to be of great help in the development of breeding techniques [10,11,12,13].

In faba beans, the higher yield generated by heterozygosity owing to outcrossing has been extensively established. Cross pollination has been linked to higher seed production and quicker growth in faba beans. Depending on the genetic composition of the parents, the heterotic effects of faba beans might vary from highly favorable to significantly negative for certain traits. The magnitude of heterotic effects on important yield-contributing traits, such as number of branches per plant, number of pods per plant, number of seeds per pod, and 100-seed weight, are correlated with the superiority of hybrids over better-parent and standard varieties with respect to grain yield and its attributes [14,15,16,17]. Moreover, the genetic improvement of plant traits depends on genetic diversity [18]. Several molecular markers can be used to reveal the genetic diversity among different Egyptian bean cultivars, which aids in understanding the genetic relationship between elite lines and the selection of distinct parents to cross beans [19,20]. It also assists bean breeders in developing varieties with a diverse genetic background to continue producing beans [21]. Several studies have reported the link between genetic diversity among the parents and the performance of the cross, where heterosis expression is higher in F1 and variation in population segregation [22].

Understanding the mechanism of action of genes and their levels of dominance may aid plant breeders in increasing yield potential [23]. Generation means analysis is a critical method for estimating various genetic effects, including gene action types, heritability, and heterosis [24]. Estimates of heritability help calculate the predicted genetic advance in segregating populations due to selection. A high rate of gene advancement accompanies dependable credible heritability estimations.

Statistical analysis is an efficient tool for estimating various genetic effects, including gene action types, heritability, and heterosis. Generation means analysis is an efficient procedure that utilizes five basic generations: the parents (P1 and P2), and the first, second, and third generations (F1, F2, and F3) [25]. The hybrid superiority in seed yield over mid and better parents is associated with the heterotic effects manifesting in critical yield components such as the number of branches/plant, the number of pods/plant, and the number of seeds/plant; exploiting heterosis may pay off in terms of increasing yield potential and its components. Therefore, this study aims to ascertain the type of gene action and a few genetic factors in five faba bean crosses obtained from six parental faba bean genotypes utilizing five populations from each cross, as well as to select the desirable lines for advanced generation.

2. Materials and Methods

2.1. Experimental Design

The current investigation was conducted at the Experimental Farm of Sakha Agricultural Research Station, Egypt, during four consecutive winter seasons, 2017/2018, 2018/2019, 2019/2020, and 2020/2021. In the first season, 2017/2018, six parental genotypes of faba bean of widely divergent origin were used, i.e., Sakha 1, Sakha 4, Giza 40, Giza 716, Giza 843, and Qahera 4 were crossed under the isolation wire cage in a half-diallel manner to produce 15 F1 crosses in the 2017/2018 season.

F1 hybrids and their parents were grown in the 2018/2019 season using a randomized complete block design with three replications. Additionally, the F1 plants were selfed to produce F2 seeds, and the results of heterosis, coupled with the specific combining ability effects, revealed that the cross combinations Cross 1 (Sakha 1 × Giza 843), Cross 2 (Sakha 4 × Qahera 4), Cross 3 (Giza 40 × Giza 843) Cross 4 (Sakha 4 × Giza 843) and Cross 5 (Giza 716 × Qahera 4) were the best performing, and could be promising crosses.

In the third season, 2019/2020, F1 and F2 seeds from the five crosses were cultivated to obtain F2 and F3 seeds; additionally, the parents of the three crosses were planted and crossed again in the same season to obtain F1 seeds. The seeds collected from the five populations were cultivated as a single cross in a randomized complete block design with three replications during the fourth season, 2020/2021.

Table 1. The names, pedigree, origin, and some features of parental genotypes of faba beans (Vicia faba L.) hybrids.

Parents	Genotypes	Pedigree		Earliness of Maturity	Agronomic Characters
			Origin		Pod Length	Seed Size
P1	Sakha1	Giza 716 × 620/283/85	FCRI *	Very early	Medium	Medium
P2	Sakha 4	Sakha 1 × Giza3	FCRI *	Very early	Long	large
P3	Qahera 4	Individual selection from the breeding program	FACU **	Medium	Medium	Medium
P4	Giza 40	Selected from rebaia 40	FCRI *	Medium	Short	Small
P5	Giza 716	416/842/83 × 503/453/83	FCRI *	Medium	Long	large
P6	Giza 843	561/2076/85 × 461/854/85	FCRI *	Early	Medium	Medium

* FCRI: Field Crop Research Institute ARC, Egypt.; ** FACU Faculty of Agriculture, Cairo University. Cross 1 (Sakha 1 × Giza 843); Cross 2 (Sakha 4 × Qahera 4); Cross 3 (Giza 40 × Giza 843); Cross 4 (Sakha 4 × Giza 843); Cross 5 (Giza 716 × Qahera 4). Very early = day 120; Early = day 145; Medium = day 160.

lists the names, origins, and other agronomic characteristics of these parents.

Each replication contained 66 ridges (2P1, 2P2, 2F1, 10 F2, and 50 F3 families), as well as two border rows on each side. Faba bean seeds were placed on one side of 3-meter-long and 60-centimeter-wide ridges at a 20-centimeter hill spacing, one seed per hill. All recommended cultural practices were implemented in accordance with the suggestion packages. Individual guarded plants from each cross were measured for maturity date (days), plant height (cm), number of branches plant⁻¹, number of pods plant⁻¹, number of seeds plant⁻¹, and seed yield plant⁻¹ (g).

2.2. Statistical and Genetic Procedures

Analysis of components of mean for each cross, the five populations (P1, P2, F1, F2 and F3) were studied and the mean and the variance were calculated. Mather’s Scaling Test was used to test the presence or absence of epistasis. The scaling test was performed following [26,27]. Only two scales (C and D) were used in the present investigation. The two different scales and the formulae for the computation of its standard error are given below:

I. Scales: C = 4F₂ − 2F₁ − P₁ − P₂ and D = 4F₃ − F₂ − P₁ − P₂

Standard error of scales:

S.E. of C = [16V (F₂) + 4V (F₁) + V (P₁) + V (P₂)] ^1/2

and

S.E. of D = [16V (F₃) + 4V (F₁) + V (P₁) + V (P₂)]^1/2

where VP₁, VP₂, VF₁, VF_2, and VF₃ are the variances in the P₁, P₂, F₁, F_2, and F₃ populations, respectively.

The gene effects were estimated using the five-parameters model proposed by [26].

The generation means constitutes different combinations of components of the five populations (P1, P2, F1, F2 and F3).

P₁ = [m] + [d] + [l],

P2 = [m] + [d] + [i],

F1 = [m] + [h] + [l],

F₂ = m + 1/2[h] + 1/4[l],

F3 = m − 1/4[h] + 1/16[l]

where P1 = mean of the large parent; P2 = mean of the small parent; F1 = mean of the first generation; F2 = mean of the second generation; F3 = mean of the third generation; [m] = mean effects; [d] = additive; [h] = dominance; [i] = additive × additive; and [I] = dominance × dominance.

Five parameters are involved in these expressions, and five means are available for their estimation, and the gene effects are estimated as follows:

m = F₂,

d = 1/2P₁ − 1/2P₂,

h = 1/16(4F₁ − 12F₂ − 16F₃),

i = P₁ − F₂ + 1/2(P₁ − P₂ + h) − 1/4l

and

l = 1/3(16F₃ − 24F₂ + 8F₁)

The variances of these estimates are calculated as follows:

Vm = VF₂, Vd = 1/4(VP₁ + VP₂), Vh = 1/36(16VF₁ + 144VF₂ + 256VF₃), Vi = VP₁
+ VP₂ + 1/4(VP₁ + P₂ + Vh) +1/6Vl and Vl = 1/9(256VF₃ + 576VF₂ + 64VF₁)

The standards of these estimates can be determined in the usual way. Thus, for example:

$$\mathrm{V}\left(\mathrm{d}\right)=1/4{\mathrm{VP}}_1+{\mathrm{VP}}_2\mathrm{and}\mathit{S}\left(\mathit{d}\right)=\sqrt[]{\mathit{V}\left(\mathit{d}\right)}$$

The significance of (d) can be tested by calculating t = (d)/S(d).

Heritability was estimated in broad and narrow terms [27]. Additionally, the predicted genetic advance (∆g) due to selection was calculated using a 5% selection intensity, as described in [28], using the genetic gain as a percentage of the F2 mean performance (∆g %) estimations of the potency ratio [29,30].

3. Results and Discussion

Among the factors affecting the Egyptian faba bean breeding are agricultural, environmental, and economic conditions, and the geographical area. It is important to identify novel re-combinations and ultimate combining ability, which have been shown to be of great help in the development of breeding techniques [10,11,12,13]. The use of conventional breeding is necessary in order to promote yield stability and quantity, and to improve resistance against stressors. This is a complicated process due to the partial allogamy of the crop [30].

3.1. Mean Performance

The observed values for all generation variances in the five crosses for all traits examined are listed in

Table 2. Variances (S²) for five populations of five faba bean crosses for all of the studied traits.

Traits	Cross	P1	P2	F1	F2	F3
Maturity date (days)	Cross 1 (Sakha 1 × Giza 843)	1.25	1.33	2.02	21.54	18.25
	Cross 2 (Sakha 4 × Qahera 4)	3.77	2.31	5.62	33.68	24.27
	Cross 3 (Giza 40 × Giza 843)	2.02	2.44	2.39	12.64	9.54
	Cross 4 (Sakha 4 × Giza 843)	2.21	2.55	2.71	6.57	4.89
	Cross 5 (Giza 716 × Qahera 4)	0.72	0.55	0.87	2.33	1.79
Plant height (cm)	Cross 1 (Sakha 1× Giza 843)	8.35	10.54	17.45	88.00	68.74
	Cross 2 (Sakha 4 × Qahera 4)	16.26	18.70	22.92	110.54	87.55
	Cross 3 (Giza 40 × Giza 843)	22.81	24.71	25.61	88.24	66.35
	Cross 4 (Sakha 4 × Giza 843)	16.26	24.71	29.67	78.59	59.98
	Cross 5 (Giza 716 × Qahera 4)	24.59	18.70	26.46	74.67	58.36
No. of branches plant-	Cross 1 (Sakha 1× Giza 843)	0.24	0.26	0.65	2.15	1.65
	Cross 2 (Sakha 4 × Qahera 4)	0.51	0.30	0.51	2.28	1.87
	Cross 3 (Giza 40 × Giza 843)	0.40	0.26	0.25	1.25	0.97
	Cross 4 (Sakha 4 × Giza 843(	0.33	0.26	0.41	1.84	1.49
	Cross 5 (Giza 716 × Qahera 4)	0.42	0.30	0.68	3.22	2.84
No. of podsplant	Cross 1 (Sakha 1× Giza 843)	14.46	18.45	22.74	73.46	54.76
	Cross 2 (Sakha 4 × Qahera 4)	20.23	21.73	27.65	128.90	110.08
	Cross 3 (Giza 40 × Giza 843)	12.54	14.23	19.34	88.67	65.39
	Cross 4 (Sakha 4 × Giza 843)	20.23	21.50	25.67	241.38	179.45
	Cross 5 (Giza 716 × Qahera 4)	19.67	21.73	22.59	54.61	41.67
No. of seedsplant	Cross 1 (Sakha 1× Giza 843)	34.85	47.96	56.38	210.35	181.45
	Cross 2 (Sakha 4 × Qahera 4)	77.59	68.61	84.89	401.98	321.64
	Cross 3 (Giza 40 × Giza 843)	155.67	168.69	182.47	941.67	718.58
	Cross 4 (Sakha 4 × Giza 843)	183.52	47.96	260.60	582.73	478.54
	Cross 5 (Giza 716 × Qahera 4)	118.64	146.64	176.54	430.47	312.64
Seed yield (g)plant Plant-1?	Cross 1 (Sakha 1× Giza 843)	43.88	51.45	55.49	215.34	168.77
	Cross 2 (Sakha 4 × Qahera 4)	102.79	126.66	168.21	512.54	384.64
	Cross 3 (Giza 40 × Giza 843)	121.25	101.44	148.73	411.25	301.25
	Cross 4 (Sakha 4 × Giza 843)	102.79	101.44	239.26	601.41	450.95
	Cross 5 (Giza 716 × Qahera 4)	112.35	126.66	135.99	600.50	439.00

.

The variance in F2 was considerably more significant than the variances in F3, F1, and their parents. Crosses 1 and 4 were superior in terms of plant height, the number of seeds per plant, and seed yield per plant. However, Cross 3 had the maximum number of branches plant⁻¹, pods plant⁻¹, and seeds plant⁻¹, while Cross 1 and 2 had the earliest maturity dates. Cross 4 yielded the highest seed yield plant^-1 in F2 (67.25 g) and in F3 (69.64 g), while Cross 1 placed second in seed yield, with 55.99 g in F2 and 61.48 g in the F3 generation.

The same results were obtained by Lal et al. (2020) and Neda et al. (2021) [31,32], who reported that the faba bean cultivar Giza 843 was the highest in terms of morphological traits such as number of branches per plant and the weight of 100 seeds. The hybridization of different parents isolates useful recombinants in the segregating generations [33]. Furthermore, Okasha (2018b) and Singh et al. (2019) [34,35] stated that F1 excelled in hypothetic and heterosis in these crosses, BGE 029055 × BGE 032012 in plant height, Fb 2481 × BGE 002106 in pod height, BGE 002106 × Fb 2481 in number of pods and seed weight. Regarding the number of seeds per plant, the most successful cross was BGE 032012 × BGE 029055. The inheritance coefficients in all crosses had medium to high values for the trait of seed weight per plant.

3.2. Heterosis, Potency Ratio, and Inbreeding Depression

Heterosis is defined as the variance between the expression of F1 hybrid traits and its homozygous parents means. Heterosis is a mirror for gene actions other than additive ones [36,37].

Table 3. Heterosis, inbreeding depression, and potency ratio in five faba bean crosses for all of the studied traits.

Traits	Cross	Heterosis %		Inbreeding Depression ID %	Potence Ratio
		MP	BP
Maturity date (days)	Cross 1	0.43	4.60 **	−3.40 **	−0.11
	Cross 2	−0.35 *	4.36 **	−7.41 **	0.08
	Cross 3	1.67 **	1.46 **	2.67 **	8.07 **
	Cross 4	1.28 **	2.32 **	−3.46 **	−1.26 **
	Cross 5	−3.10 **	−5.40 **	−0.64 **	−1.28 **
Plant height (cm)	Cross 1	8.62 **	15.12 **	5.10 **	1.53 *
	Cross 2	4.41 **	4.87 **	−8.41 **	10.05 **
	Cross 3	5.91 **	9.28 **	5.73 **	1.91
	Cross 4	4.62 **	5.58 **	−3.75 **	5.10 **
	Cross 5	−3.02 **	−5.44 **	−11.93 **	1.18
No. ofbranches plant-	Cross 1	16.64 **	31.53 **	29.00 **	−1.47
	Cross 2	40.98 **	25.06 **	29.76 **	3.22 **
	Cross 3	−1.36	−0.81	6.34 **	2.43 **
	Cross 4	2.64 **	3.38 **	10.84 **	−3.67
	Cross 5	12.23 **	1.56 **	19.23 **	1.16
No. of podsplant	Cross 1	14.57 **	16.67 *	11.77 **	−8.10
	Cross 2	23.50 **	9.53 **	2.43 **	1.84
	Cross 3	17.73 **	10.79 **	46.22 **	2.83
	Cross 4	−5.77 **	−9.78 **	7.10 **	−1.30
	Cross 5	60.70 **	44.26 **	40.65 **	5.33 **
No. of seedsplant	Cross 1	18.54 **	24.30 **	40.89 **	4.01
	Cross 2	39.63 **	17.94 **	39.40 **	−2.15
	Cross 3	3.47 **	0.67	29.77 **	−1.25
	Cross 4	37.30 **	66.95 **	17.18 **	2.10
	Cross 5	26.26 **	6.33 **	31.72 **	−1.40
Seed yield (g)plant	Cross 1	33.63 **	45.84 **	27.74 **	4.02 **
	Cross 2	40.29 **	21.06 **	18.78 **	−2.54
	Cross 3	8.92 **	9.83 **	23.74 **	10.73 **
	Cross 4	22.29 **	20.03 **	9.30 **	−11.80
	Cross 5	46.23 **	22.39 **	25.90 **	−2.37

Cross 1 (Sakha 1 × Giza 843); Cross 2 (Sakha 4 × Qahera 4); Cross 3 (Giza 40 × Giza 843); Cross 4 (Sakha 4 × Giza 843) and Cross 5 (Giza 716 × Qahera 4). * and ** indicate significance at the 0.05 and 0.01 levels, respectively.

summarizes heterosis data related to mid parents and better parents, potency ratio, and inbreeding depression. The data demonstrate highly substantial heterosis in the favorable direction for mid and better parents for all features, except for the number of branches in Cross 3 for mid and better parents, and maturity date in Cross 1 for mid parents. Due to the partial dominance, the five crosses displayed highly significant levels of heterosis between the mid and better parents, which were negative for maturity date (p = −1.28). Yield and its components had substantial positive heterotic effect values in five crosses for the better parent. However, with respect to seed yield and related features, extremely significant heterotic effects between the mid and better parents were discovered for all variables evaluated in the five crosses, and overdominance was the cause of heterosis in all cases (p > +1) (Table 3).

Previous studies have reported the economic effects of heterosis on yield components, with hybrids having higher heterosis values than the parent for yield components and maturity stage in faba beans [25]. Additionally, Tekalign et al. and Waly et al. [38,39] reported significant heterosis in F1, which increased by 40% compared to the parents. Furthermore, the yield quantity and quality of F1 were higher than the mean values of better and mid parents [40]. At the same time, heterosis in F2 decreased at the mid-point in the F1 hybrid. On the other hand, it was clear of any positive or negative effects of heterosis, with no effect (positive or negative) with respect to plant height or number of branches per plant [41,42]. However, there were considerable positive effects concerning the number of pods per plant and adverse effects in terms of the weight of 100 seeds. Significant positive or negative heterosis might be due to the dominance and overdominance hypothesis and/or epistasis [43]. The considerable positive heterosis of F1 hybrid compared to the mid parent with respect to morphological traits, e.g., plant height, number of branches, numbers of pods and seeds per plant, seed yield, and 100-seed weight, varied based on cross combinations and traits [1].

The inbreeding depression percentage from F1 to F2 was computed, and the results are shown in Table 3. This percentage indicates the extent to which the F2 generation was reduced due to inbreeding. In all crosses except Cross 3, it was significantly and substantially negative in favor of maturity. It was, nevertheless, significant and positive for the most examined treatments in all crosses. As a result, it is logical to assume that heterosis in F1 will be followed by a considerable decrease in F2 performance due to the effect of homozygosity.

Additionally, it is projected that inbreeding depression will decrease the values of non-additive genetic components. Due to the low level of inbreeding depression for the parameters plant height, number of pods and seeds per plant⁻¹, and seed yield per plant, increased vigor in F2 is projected to be primarily due to the accumulation of beneficial additive nutrient genes [44].

Considerable inbreeding depression was noticed in the morphological characteristics of broad bean hybrids (plant height and seed yield), which is considered strong evidence of heterosis effects on these characteristics [45]. However, inbreeding depression in the F2 hybrids was not always related to heterosis in F1 [46]. These findings correspond to those of Checa et al. and Kosev [47,48], who found nonadditive gene interactions and indices of overdominance for the number of pods per plant. According to Gangadhara et al. and Georgieva and Kosev [49,50], inter-pool crosses deliver higher levels of heterosis than intra-pool crosses.

3.3. Estimation of Type of Gene Action

For each attribute in

Table 4. Scaling test and type of gene action estimated by generation mean of the five faba bean crosses for all of the studied traits.

Traits		Scaling Test		Gene Action
	Cross	C	D	m	A	d	aa	dd
Maturity date (days)	Cross 1	21.35 **	−34.81 **	152.57 **	−5.85 **	27.40 **	−74.88 **	15.07 **
	Cross 2	41.89 **	0.55	155.52 **	−6.57 **	6.10 *	−55.12 **	−6.51 **
	Cross 3	−11.53 **	−9.13 **	151.48 **	0.32 *	6.72 *	3.20	4.80 **
	Cross 4	24.69 *	8.93 **	155.99 **	−1.52 **	0.07	−21.01 **	−4.87 **
	Cross 5	−5.73 **	5.82 **	150.39 **	3.75 **	−9.62 **	15.40 **	2.66 **
Plant height (cm)	Cross 1	−5.57 *	26.95 *	116.38 **	−6.37 **	−9.16	43.36 **	−31.64 **
	Cross 2	51.69 **	−39.67 **	133.17 **	−0.52	40.25 **	−121.81 **	34.03 **
	Cross 3	−14.41 *	5.15 **	115.52 **	−3.57 **	1.00	26.08 **	−12.98 **
	Cross 4	29.49 **	1.65	128.31 **	−1.07	9.28	−37.12 **	1.67
	Cross 5	48.80 **	−24.64 **	131.63 **	3.10 **	20.89 **	−97.92 **	30.76 **
No. ofbranches plant-	Cross 1	−3.83 **	0.47	3.11 **	−0.43 **	−0.33	5.73 **	−1.80 **
	Cross 2	−3.07 **	1.13 *	3.54 **	0.46 **	0.20	5.60 **	−0.35
	Cross 3	−1.15 **	0.09 *	3.84 **	−0.02	−0.31	1.65	−0.30
	Cross 4	−1.36 **	0.89 *	3.18 **	−0.02	−0.73	3.00 **	−0.87
	Cross 5	−2.15 **	1.39 *	3.15 **	0.37 **	−0.86	4.72 **	−0.56
No. of podsplant	Cross 1	−5.52 *	10.20 **	22.48 **	−0.40	−4.48	20.96 **	−8.52 *
	Cross 2	6.28 *	14.60 **	21.64 **	2.29 **	−4.47	11.09	−4.11
	Cross 3	−44.03 **	17.03 **	15.30 **	1.52 **	−14.41 **	81.41 **	−15.66 **
	Cross 4	−9.01 *	−0.76	20.59 **	1.05	−2.36	11.00	1.09
	Cross 5	−24.74 **	21.26 **	16.87 **	2.02 **	−7.56	61.33 **	−14.27 **
No. of seedsplant	Cross 1	−117.40 **	15.24 **	52.47 **	−3.47 **	−15.84	176.85 **	−36.66 **
	Cross 2	−88.42 **	15.68 **	53.14 **	11.55 **	−0.30	138.80 **	−2.08
	Cross 3	−89.31 **	38.85 **	55.81 **	2.14	−38.12	170.88 **	−36.52 **
	Cross 4	−11.42 *	37.76 **	65.87 **	−10.29 **	−5.47	65.58 **	−47.65 **
	Cross 5	−68.61 **	29.83 **	54.94 **	11.95 **	−14.59	131.25 **	−7.43
Seed yield (g)plant	Cross 1	−46.98 **	17.96 **	55.99 **	−4.85 **	−0.30	86.59 **	−29.51 **
	Cross 2	−12.28 *	21.94 **	56.41 **	7.87 **	3.27	45.63 *	−0.94
	Cross 3	−53.03 **	6.49 **	51.46 **	−0.52	−7.64	79.36 **	−14.20
	Cross 4	−0.54	22.82 **	67.25 **	1.15	−1.79	31.15	−13.01
	Cross 5	−29.72 **	35.66 **	54.57 **	9.81 **	−5.45	87.17 **	−9.11

Cross 1 (Sakha 1 × Giza 843); Cross 2 (Sakha 4 × Qahera 4); Cross 3 (Giza 40 × Giza 843); Cross 4 (Sakha 4 × Giza 843) and Cross 5 (Giza 716 × Qahera 4). * and ** indicate significance at the 0.05 and 0.01 levels, respectively. C and D = scaling tests; m = mean effects; A = additive; d = dominance; aa = additive × additive; and dd = dominance × dominance.

, five faba bean crosses were investigated to establish the generation mean and the kind of gene action. Scaling tests indicated that non-allelic interactions were present in all crosses, with all characteristics significantly different from zero (Mather, 1949) [27]. Across all crosses, the estimated mean effects (m), which reflect the overall mean as well as locus effects and the interaction of the fixed loci, were extremely significant. Significant additive (a) and dominance (d) genetic variances were observed in Crosses 1, 2, 3, and 5 for maturity date; Crosses 1 and 5 for plant height; Crosses 1 and 5 for number of branches per plant; Crosses 2, 3, and 5 for number of pods per plant; Crosses 1, 4, and 5 and 3 for number of seeds per plant; and Crosses 2 and 5 for seed yield per plant (

Table 5. Heritability percentage in broad (h2b) and narrow (h2n) senses and expected genetic advancement from the selection (GA%) in five faba bean crosses for all of the studied traits.

Traits	Cross	h2b	h2n	GA	GA %
Maturity date (days)	Cross 1	98.22	30.59	5.18	3.40
	Cross 2	97.11	55.88	11.84	7.61
	Cross 3	95.48	49.05	6.37	4.20
	Cross 4	90.53	51.14	4.79	3.07
	Cross 5	92.33	46.63	2.60	1.73
Plant height (cm)	Cross 1	96.56	43.77	14.99	12.88
	Cross 2	95.64	41.60	15.97	11.99
	Cross 3	93.09	49.62	17.02	14.73
	Cross 4	92.51	47.36	15.33	11.95
	Cross 5	92.22	43.69	13.78	10.47
No. of branches/plant	Cross 1	95.53	46.29	2.48	79.63
	Cross 2	95.19	35.96	1.98	56.01
	Cross 3	93.98	44.80	1.83	47.63
	Cross 4	95.48	38.04	1.88	59.25
	Cross 5	96.38	23.60	1.55	49.09
No. of pods/plant	Cross 1	93.69	50.91	15.93	70.87
	Cross 2	95.50	29.20	12.10	55.93
	Cross 3	95.67	52.51	18.05	18.00
	Cross 4	97.67	51.31	29.11	41.35
	Cross 5	90.24	47.39	12.79	75.81
No. of seeds/plant	Cross 1	94.49	27.48	14.55	27.74
	Cross 2	95.21	39.97	29.26	55.07
	Cross 3	95.51	47.38	53.09	95.12
	Cross 4	92.96	35.76	31.52	47.85
	Cross 5	91.45	54.75	41.47	75.49
Seed yield (g)/plant	Cross 1	94.16	43.25	23.17	41.39
	Cross 2	93.53	49.91	41.26	73.14
	Cross 3	92.47	53.50	39.61	76.97
	Cross 4	93.85	50.04	44.80	66.63
	Cross 5	94.80	53.79	48.13	88.19

Cross 1 (Sakha 1 × Giza 843); Cross 2 (Sakha 4 × Qahera 4); Cross 3 (Giza 40 × Giza 843); Cross 4 (Sakha 4 × Giza 843) and Cross 5 (Giza 716 × Qahera 4).

). This may indicate that additive and dominance genetic variances occur in distinct populations. For maturity date in Crosses 2 and 4, plant height in Cross 3, number of branches/plant in Crosses 1 and 2, number of seeds per plant in Crosses 2 and 4, and seed yield/ plant in Crosses 1, 2, and 5, the additive genetic variance (a) was significantly more significant than the corresponding dominance variance (d); this could imply that selection for these traits could be made in early-segregating generations due to additive genes, and the pedigree method would be helpful [51].

In hybrids, unique allelic interactions modify gene expression, which contributes to generating heterotic phenotypes because of gene variation [52,53]. The genes contained in the parental combinations that may contribute directly or indirectly to the traits were examined in numerous cross combinations, indicating variable degrees of F1 superiority in various yield and growth aspects [54]. The manifestations of heterotic effects on yield component characteristics are linked to hybrids’ improved seed yield over their mid parents [55,56,57]. According to Kosev and Georgieva [48], F1 hybrids in most crosses exhibit high heterosis levels for most faba bean traits, as seen by these studies. According to Khazaei et al. [54], the average mid parent heterosis for mature seed weight was 10.6%, and the average mid parent heterosis for juvenile biomass was 14.5%.

On the other hand, dominance effects were more extensive than additive effects for maturity date in Crosses 2, 3, and 4; plant height in Crosses 1, 2, and 5; the number of branches plant⁻¹ in Crosses 4 and 5; the number of pods in Crosses 2, 3, and 5; and the number of seeds/plant in Crosses 1 and 5. This may indicate that dominant gene effects significantly contributed to controlling the genetic variance of these traits in the aforementioned crosses. Intensive selection through later generations using the bulk method was needed to improve these traits. For non-allelic interaction, i.e., additive (aa) and dominance dominance (dd), our data also indicated that the (aa) dominance epistatic effect was more significant and more prominent in magnitude than (dd) in the inheritance of maturity date in Crosses 1, 2, 4 and 5; plant height in all crosses; the number of branches/plant in Crosses 1, 2, 4 and 5 (Table 5). The number of pods plant-1 in Crosses 1, 3 and 5; the number of seeds/plant in all crosses; and the seed yield/plant, on the other hand, would be more successful in the early-segregating generation because the additive gene impact would be greater. However, in Cross 3, (dd) had a bigger magnitude than (aa) in terms of genetic variance for the maturity date. As a result, selecting this trait in the proposed cross would be more effective if dominance and epistatic effects were reduced to a minimum using the bulk method outlined below. The type of variation observed in this study confirmed the type of generation that was previously documented [18,20,58]. Concerning the negative values observed in the majority of cases, either with the main effect, (a) and (d), or with the non-allelic interactions, (aa) and (dd), this could imply that the allelic interaction responsible for low values of these traits.

3.4. Heritability and Genetic Advance from the Selection

Table 5 summarizes heritability in the broad and narrow senses, along with the expected and predicted genetic advancements for the evaluated variables. The estimations of broad-sense heritability (H2) were often more significant than those of narrow-sense heritability (h2), indicating the presence of non-additive gene action. Broad-sense heritability values for all examined characteristics were high in all crosses, ranging from 90.24% to 97.67% for number of pods plant⁻¹ in Crosses 5 and 4. Narrow-sense heritability ranged from medium to high in most cases due to the opposite effects of dominance and dominance × dominance, with values ranging from 23.60% for number of branches/plant in Cross 5 to 55.88% for maturity date in Cross 2. Genetic advancement due to selection varied from 1.73% for maturity date in Cross 5 to 95.12% for the number of seeds/plant in Cross 3. The high probability of genetic advancement would aid the breeder in developing the desired trait through a few election cycles [59].

Backcrossing between elite lines as recurrent parents and external germplasm can promote diversity in the breeding program. Subsequently, the selected lines can be examined for their suitability as components of a synthetic variety. Examining the inheritance of the initial pod height in soybean hybrids identified a distinct form of inheritance from complete dominance to the absence of one [54]. In several reciprocal crosses, additional inheritance was seen, which the authors attribute to the action of cytoplasmic hereditary factors. It was also noted that the coefficient of inheritance for grain yield and its components varied significantly (8.80–70.90%), especially for the number of pods and weight per 100 seeds [60,61,62]. The same authors believed that grain yield might increase successfully by combining these two qualities. According to Bhardwaj and Vikram [63], when dominant gene activities dominate in qualities associated with productivity, breeding in early hybrid generations is unlikely to result in rapid succession.

3.5. Correlation Analysis

Figure 1 reveals that all of the studied traits were normally distributed. SNPP was significantly and positively correlated with SNPP (0.77) and PNPP (0.65). The other characteristics were not significantly correlated with SNPP, meaning that SNPP and PNPP are the essential traits of SYPP. Additionally, there were positive and significant correlations between SNPP and PNPP (0.64) and between SNPP and BNPP (0.58). However, there was no significant correlation between SYPP and BNPP (0.36), which reflects the indirect effect of BNPP on SYPP, via both SNPP and PNPP, with increasing number of branchess per plant, leading to an increase in both number of pods per plant and number of seeds per plant, consequently increasing seed yield per plant. Additionally, neither MD nor PH were important to SYPP, as their correlation with SYPP was not significant [51].

3.6. Cluster Analysis

Cluster analysis was performed using the Euclidian distance dissimilarity measure and Ward’s clustering algorithm [64]. Before computing the distance, the data were standardized due to the different scales of the studied traits. All the studied traits except for BNPP, which had low variance, were used to construct a distance matrix using the Euclidian coefficient. The data from the distance matrix were used to generate the dendrogram showing the similarity among all the varieties and the crosses (Figure 2). The cubic cluster criterion [65] was used to cluster the data, whereas six methods were compared using an agglomerative coefficient to choose the best method for clustering the data. The methods were average, generalized average, single, and weighted, complete, and ward. The agglomerative coefficients for the methods were 0.679, 0.754, 0.524, 0.720, 0.804, and 0.847, respectively. Indicating that the ward method was the best method for clustering the obtained data. The internal validation used for the resources presented here indicates that they can be successfully applied to faba bean breeding programs, with 30 indices being used to determine the appropriate number of clusters in the data [18,66]. The results of the internal validation revealed that two clusters exist in the data (Figure 2). According to our results (Figure 3), it can be observed that all the varieties and crosses are clustered into two clusters with the averages of the studied traits (

Table 6. Average of the studied traits for the 2 clusters.

Clusters	MD	PH	PNPP	SNPP	SYPP
Cluster1	148.53	119.50	20.51	60.35	54.68
Cluster2	151.91	121.60	23.64	77.02	66.83

). Because of the overlap between clusters, principal component clustering was performed to clarify the intervention between the two clusters.

Figure 4 shows the data clusters focusing on SYPP and variance. The color scale is used to distinguish between the different values of SYPP, whereas the size scale is used to distinguish between different values of variance. Cross 1 F1 and Cross 5 F1 had the highest yield (color scale) and the lowest variance (size scale), meaning more stable crosses. Additionally, all the F1 values for all crosses had high yield and low variance. In comparison, all F2 and F3 values for all crosses had low yield and high variance.

Additionally, as a result of cluster analysis, our results (Figure 5) showed the relationship between the studied traits and all the varieties and crosses based on the scaled data using a color scale. All F1 crosses tended to have high SYPP and higher values of SNPP and PNPP and moderate MD. Qahera 4, Cross 3 F2, and Sakha 1 had the lowest SYPP due to the low values of SNPP and PNPP. Neither PH nor MD affect SYPP [67].

The dissimilarity among all varieties and crosses based on the Euclidean distance of the scaled data using a color scale was investigated (Figure 6). Higher values of dissimilarity are associated with darker red color, and lower dissimilarity values are associated with blue color. Sakha 1 had the highest dissimilarity with all of the varieties and crosses except for Sakha 4. Additionally, Qahera 4 has higher dissimilarity with all F1 crosses. The most similar crosses were Cross 4 F1 and Cross 5 F1. The least similar entities were Sakha 1 and Cross 2 F2. Cross 1 was more similar to Giza 843 than Sakha 1, indicating the dominance of Giza 843 on the traits of its crosses. The same was observed for Cross 2, with Cross 2 being more similar to Sakha 4 than to Qahera 4. Cross 3 was more similar to Giza 843 than to Giza 40. Cross 4 was more similar to Giza 843 than to Sakha 4. Cross 5 was more similar to Giza 716 than to Qahera 4. In conclusion, in descending order, the most effective varieties were Giza 843, Giza 716, Sakha 4, Qahera 4, and Sakha 1. Therefore, these varieties should be selected in the breeding program in that order.

4. Conclusions

The F1 mean values were greater than the mid parent value for all attributes evaluated in all crosses. The F2 values were nearly equivalent to the mid parent values and less than the F1 values in all crosses. In contrast, the F3 values were later than the F2 values, and were similar to or lower than the F2 values for all other investigated traits, indicating the occurrence of inbreeding depression. It is worth noting that Cross 1 and Cross 4 performed best in terms of maturity date and seed yield per plant, whereas Cross 3 performed best in terms of the number of branches, pods and seed yield per plant. As a result, the resources presented here can be successfully applied to faba bean breeding programs.