Comparison of Desired-Genetic-Gain Selection Indices in Late Generations as an Insight on Superior-Family Formation in Bread Wheat (Triticum aestivum L.)

Abstract

Wheat is one of the most important sources of food worldwide. A selection index helps in making selection decisions and permits the exploitation of information on correlated traits to improve yields. Two cycles of pedigree selection based on the desired-genetic-gain selection index were imposed to identify the best index to isolate promising lines. The base population was composed of 120 families of bread wheat in the F₆ generation. Eight combinations were constructed from six traits, i.e., days to heading (DH), number of spikes/plant (NS/P), grain yield/plant (GY/P), number of grains/spike (NG/S), mean spike weight (MSW) and mean grain weight (GW). The narrow-sense heritability of NS/P, NG/S, MSW and GW increased from cycle 1 to cycle 2, revealing an increase in the observed gain and homogeneity of the selected families for these traits from cycle to cycle. After the second cycle, the observed gain in GY/P ranged from 9.5 to 23.75% of the mid-parent. The best index for improving GY/P was index 2 (composed of GY/P, NS/P, NG/S, MSW and GW). The indices involving DH were inferior for improving GY/P. The desired-genetic-gain index was efficient in simultaneously improving several involved traits and was a good method to preserve genetic variability. Furthermore, six superior promising families were identified.

1. Introduction

Wheat is an important source of food and calories for the global population. The author of [1] stated that more than one billion people suffer from food shortage, and this figure is predicted to double by 2050. The main objective in wheat breeding programs is improving grain yield to meet the demand of the growing population. This is often difficult because of the large number of genes involved and low heritability associated with quantitative traits, including grain yield per se. Pedigree selection is proven to be an efficient method for improving grain yield [2,3], with selection typically starting in the F₂ generation; this includes all genotypes of favorable genes in either the homozygous or heterozygous condition, whose frequency declines in subsequent generations. However, Ref. [4] found a weak correlation between the grain yield of spaced plants in the F₂ and F₃ generations and that of F₄ and successive generations grown at normal seed density. In addition, Ref. [5] indicated that the polygenic nature of grain yield, low heritability, linkage, nonadditive gene actions, and the presence of genotype-by-environment interactions reduce the efficiency of the selection for grain yield per se, mainly in early segregating generations. Ref. [6] found that the observed genetic gain of one cycle of selection from the F₄ generation under both drought-stress and optimum-irrigated environments was mostly better than three cycles started from the F₂ generation. Therefore, delaying selection for grain yield to the F₅ generation is favorable to plant breeders and research centers after the plants have reached acceptable levels of working homozygosity. Many researchers have pointed to the effectiveness of selection for GY per se in bread wheat in early generations [6,7,8,9,10,11,12,13].

Evidently, the selection index proved to be the best breeding method for the genetic improvement of several traits simultaneously in crop plants. The theory of discriminate function in wheat was introduced in Ref. [14], and in Ref. [15] in animals; hence the concept is known as the Smith–Hazel index. Meanwhile, Ref. [16] proposed the base index, and Refs. [17,18] proposed the desired gain index and applied it to wheat. The authors of [15,19] indicated that the selection index is more efficient than single-trait selection, and Ref. [7] proved that the Smith–Hazel index was better for improving grain yield/plant (GY/P) than selection for grain yield (GY) per se. A comparison was conducted by [20] to analyze the difference between the Smith–Hazel, desired-gain and weight-free indices; it concluded that the Smith-Hazel index was superior to the other methods in identifying high yielding lines, but with reduced protein content. However, the weight-free and desired-gains indices were effective for improving protein content but were less efficient for selecting top-yielding lines in the F₃ generation. It was found, by the authors of Ref. [21], that the index based on “desired gains” showed the highest genetic gains in the three situations. While Ref. [22] noted that index selection (discriminate functions using eight characters based on plant height, grains per spike and grain yield per plant) might be more effective and efficient for identifying high-yielding wheat genotypes. The use of the selection index was better than direct selection for grain yield in two environments, as denoted by the author of Ref. [23]. A study was conducted by the authors of Ref. [24] for 63 models of selection index based on the discriminant function technique using six traits. The expected genetic advance increased as the number of traits involved in an index increased. The index, based on grain yield per plant, 100-grain weight, days to maturity, harvest index and number of effective tillers per plant, had the highest genetic advance. When Ref. [25] compared the Pesek–Baker (PBI) with the Smith–Hazel (SHI) indices to identify superior genotypes in wheat, this revealed that PBI was more efficient than SHI for two years under irrigation and drought-stress conditions. Furthermore Ref. [5] found that the selection-based index gave the highest genetic gain in grain yield, followed by the Smith–Hazel index, and single-trait selection was not appropriate in either direct or correlated gains. The presence of genotype–environment interactions reduce the genetic gain of the selection-based index but can avoid the limits of single-trait selection [26].

Selection indices were proven in Ref. [27] to be the best breeding method in advanced generations of wheat, since they simultaneously improved several traits of interest. Direct selection for grain yield and desired genetic gain index was applied by [28] to improve GY/P in early generations (F₂–F₅) under drought-stress and optimum-irrigation environments. The results proved that the selection index was better for improving GY than single-trait selection for selections practiced and evaluated either under drought-stress or optimum-irrigation environments. Furthermore, antagonistic selection for GY (upward selection in bad environments) in these materials was better than synergistic selection (upward selection in good environments) for improving GY/P either for selections evaluated either under drought stress or under normal irrigation. The best index for improving GY/P involved GY/P, grain weight and number of grains per spike. The objective of this study was to measure and compare the observed genetic gains in GY/P and their correlated traits after two cycles of selection, starting in the late generations—Cycle 0 (F₆), Cycle 1 (F₇), and Cycle 2 (F₈)—of a bread wheat cross (Giza 164 × Sids 4); this was based on eight models of a weight-free desired-gain selection index model from six traits under optimum irrigation environments.

2. Results

The analysis of variance (

Table 1. Mean squares, genotypic (GCV%) and phenotypic (PCV%) coefficients of variation, heritability in broad sense (H%), maximum, minimum, means with their standard error, and expected genetic gain (GA) of the traits in the base population (F₆ generation).

Item	DH	PH, cm	SL, cm	NS/P	GY/P	NG/S	MSW	GW
Fam	97.15 **	231.24 **	14.06 **	13.76 **	17.46 **	593.52 **	1.47 **	1.42 **
Reps	9.72	782.39	11.57	67.05	160.90	524.10	23.95	11.31
Error	1.64	15.88	0.98	0.54	2.82	0.95	0.01	0.01
GCV%	7.27	8.80	14.96	30.21	20.40	27.79	27.23	14.26
PCV%	7.33	9.12	15.52	30.82	22.28	27.81	27.34	14.30
H%	98.31	93.13	93.00	96.07	83.83	99.84	99.18	99.50
Mean	77.65 ± 0.74	96.26 ± 2.30	13.95 ± 0.57	6.95 ± 0.42	10.83 ± 0.97	50.57 ± 0.56	2.56 ± 0.06	4.82 ± 0.05
MAX	93.00	120.33	19.83	14.83	17.87	91.33	5.15	6.19
MIN	66.33	75.00	9.00	2.00	5.97	28.07	1.47	2.84
(P1) Sids 4	68.00	85.00	16.00	6.33	8.90	56.33	2.30	5.60
(P2) G164	83.00	100.00	10.00	8.00	11.67	41.33	1.60	4.60
GA	6.61	9.66	2.38	2.43	2.39	16.59	0.82	0.81
GA/mean%	8.51	10.03	17.05	34.98	22.06	32.81	32.04	16.80

** Significant at 0.01 level of probability. GA = expected genetic gain from selection superior 20 families, DH = days to heading, SL= spike length, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = mean spike weight, GW = 100-grain weight, GY/P = grain yield/plant.

) shows significant (p ≤ 0.01) differences among the 120 families in the F₆ generation cycle 0 for all the studied traits. The genotypic coefficient of variation (GCV) ranged from medium, for days to heading (DH) (7.27%) and plant height (PH) (8.8%), to high for the other traits. Furthermore, the minimum and maximum of the families for all traits were located outside the two parents, reflecting the wide variability and feasibility of selection in these materials. Heritability, in the broad-sense, was very high and unreliable, and ranged from 93.13% for PH to 99.50% for grain weight. The expected genetic gain from selecting the 20 superior families, as a percentage of the mean, ranged from 8.51% for DH to 34.98% for the number of spikes/plant (NS/P); this was related to the phenotypic variance rather than heritability estimates.

2.1. Genotypic Correlation

Days to heading (DH) (

Table 2. Genotypic correlation among traits in the base population (F6 generation).

Trait	DH	PH	SL	NS/P	GY/P	NG/S	MSW	GW
DH		0.14	−0.49 **	0.34 **	0.07	−0.24 *	−0.30 **	−0.19
PH			0.03	0.11	0.33 **	−0.005	−0.02	0.06
SL				−0.37 **	0.09	0.40 **	0.52 **	0.13
NS/P					0.32 **	−0.31 **	−0.52 **	−0.20 *
GY/P						−0.04	0.20 *	0.19
NG/S							0.52 **	−0.31 *
MSW								−0.03

DH = days to heading, SL = spike length, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = mean spike weight, GW = 100-grain weight, GY/P = grain yield/plant. * = significant (at 0.05 of probability), ** = highly significant (at 0.01 probability).

) showed moderate negative correlations with spike length (SL), mean spike weight (MSW) and number of grains/spike (NG/S); a weak correlation with 100-grain weight (GW); and a positive correlation with NS/P (0.34). A positive correlation was obtained between PH and GY/P (0.33). Spike length had a negative correlation with NS/P (−0.37) and positive correlations with NG/S (0.40) and MSW (0.52). The number of spikes/plant showed a positive correlation with GY/P and negative correlations with NG/S and MSW. The number of grains/spike had a positive correlation with MSW (0.52) and a negative one with GW (−0.31). The correlations of all traits with GW were weak, except with NG/S.

2.2. Genotypic and Phenotypic Coefficients of Variability

The selection for different indices (

Table 3. Genotypic (GCV%) and phenotypic (PCV%) coefficients of variability in the two cycles of selection.

Index No.		DH	PH	SL	NS/P	GY/P	NG/S	MSW	GW
Index 1 C1	GCV%	7.71	6.55	10.39	21.82	29.85	18.81	13.32	12.70
	PCV%	7.73	6.68	10.47	22.06	31.02	18.90	13.62	12.73
C2	GCV%	5.43	4.30	10.16	22.27	17.86	21.66	14.66	7.81
	PCV%	5.55	5.03	10.64	22.69	18.11	22.29	16.14	9.01
Index 2 C1	GCV%	9.05	8.78	14.03	21.68	27.82	14.73	15.54	15.39
	PCV%	9.06	8.80	14.11	22.08	28.61	15.01	15.89	15.41
C2	GCV%	5.02	6.73	13.69	15.85	21.46	25.37	16.19	7.91
	PCV%	5.21	7.03	14.00	16.50	21.89	26.38	18.53	8.36
Index 3 C1	GCV%	7.36	9.56	11.03	18.10	20.47	19.05	20.36	10.92
	PCV%	7.37	9.59	11.15	18.22	21.96	19.13	20.42	10.95
C2	GCV%	5.02	6.73	13.69	15.85	21.46	25.37	16.19	7.91
	PCV%	5.21	7.03	14.00	16.50	21.89	26.38	18.53	8.36
Index 4 C1	GCV%	0.75	9.58	12.81	22.68	26.84	22.66	28.03	13.28
	PCV%	0.76	9.60	12.91	22.92	27.94	22.73	28.11	13.31
C2	GCV%	6.26	8.25	11.45	41.16	38.79	11.65	13.89	8.21
	PCV%	6.44	8.75	11.83	41.31	38.87	13.12	14.50	8.96
Index 5 C1	GCV%	7.35	10.16	10.61	15.32	18.95	24.14	21.85	10.71
	PCV%	7.36	10.18	10.72	15.52	19.76	24.24	21.91	10.73
C2	GCV%	4.63	2.04	11.10	19.55	20.26	20.72	15.35	8.23
	PCV%	4.78	4.07	11.44	20.51	20.72	21.10	16.13	8.54
Index 6 C1	GCV%	7.94	9.14	13.51	21.75	33.26	21.40	25.74	13.28
	PCV%	7.96	9.16	13.60	21.86	33.71	21.49	25.82	13.31
C2	GCV%	7.57	6.43	12.78	23.36	21.61	13.50	11.82	8.68
	PCV%	8.05	7.14	13.06	24.42	22.13	13.84	12.89	9.27
Index 7 C1	GCV%	5.88	7.26	10.07	21.28	23.97	21.50	22.78	10.49
	PCV%	5.89	7.32	10.19	21.58	24.82	21.58	22.85	10.52
C2	GCV%	8.17	3.12	13.77	15.66	18.40	18.33	17.38	8.14
	PCV%	8.48	4.15	14.08	16.89	19.27	18.90	17.81	8.77
Index 8 C1	GCV%	9.18	8.92	12.93	22.11	17.69	22.80	27.36	12.39
	PCV%	9.19	8.94	13.03	22.36	18.43	22.87	27.44	12.42
C2	GCV%	5.61	5.61	11.28	15.14	19.38	17.51	18.81	7.70
	PCV%	6.04	6.30	11.66	17.05	19.90	18.20	19.63	8.23

DH = days to heading, SL = spike length, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = mean spike weight, GW = 100-grain weight, GY/P = grain yield/plant.

) illustrates that the GCV% was slightly lower than the PCV% in all cases. This is expected, because the genetic variance is always lower than the phenotypic one, except in cases of an error variance equal to zero. It can be seen that in cycle 2, the families of index 1 and index 2 were the same. Generally, the decrease in GCV% from C0 (F₆) to C1 (F₇) and C2 (F₈) for all indices was slight, except in indices 1, 3 and 5 for DH, in which it was depleted after the second cycle. The variability in the other traits involved in different indices was still high after the second cycle and was sufficient for further cycles of selection. In few cases (indices 4 and 7), the GCV% in GY/P after the second cycle exceeded that in C0. It can be concluded that the desired-genetic-gain index preserves and maintains genetic variability in the population.

2.3. Heritability Estimates

The estimates of heritability in the broad sense (

Table 4. Heritability in the broad (H%) and in narrow sense (h²), as estimated from parent–offspring regression for the traits under selection pressure.

Cycle		DH	NS/P	GY/P	NG/S	MSW	GW
C0	H%	98.31	96.07	83.83	99.84	99.18	99.50
	h2	-	-	-	-	-	-
Index 1 C1	H%	99.52	97.86	92.57	99.06	95.68	99.61
	h2	0.44	0.64	0.55	0.48	0.36	0.43
C2	H%	95.87	96.33	97.23	94.42	82.52	75.28
	h2	0.79	0.90	0.50	0.49	0.47	0.53
Index 2 C1	H%	-	96.41	94.55	96.32	95.61	99.70
	h2	-	0.63	0.62	0.45	0.47	0.59
C2	H%	-	92.31	96.14	92.53	76.29	89.45
	h2	-	0.65	0.60	0.78	0.82	0.80
Index 3 C1	H%	99.65	-	86.90	99.17	99.48	99.48
	h2	0.78	-	0.67	0.48	0.50	0.50
Index 4 C1	H%	-	-	92.32	99.35	99.44	99.60
	h2	-	-	0.70	0.49	0.56	0.49
C2	H%	-		99.58	78.82	91.74	83.97
	h2	-	-	0.74	0.56	0.53	0.82
Index 5 C1	H%	99.65	-	92.00	-	99.42	99.50
	h2	0.77	-	0.71	-	0.60	0.51
C2	H%	93.89	-	95.64	-	90.54	92.82
	h2	0.85	-	0.66	-	0.71	0.62
Index 6 C1	H%	-	-	97.37	-	99.37	99.63
	h2	-	-	0.73	-	0.55	0.49
C2	H%	-	-	95.34	-	84.06	87.68
	h2	-	-	0.72	-	0.56	0.60
Index 7 C1	H%	99.46	-	93.30	99.28	-	99.47
	h2	0.76	-	0.67	0.44	-	0.46
C2	H%	92.92	-	91.08	94.08	-	86.06
	h2	0.82	-	0.76	0.67	-	0.48
Index 8 C1	H%	-	-	92.19	99.35	-	99.56
	h2	-	-	0.63	0.50	-	0.56
C2	H%	-	-	94.80	92.59	-	87.44
	h2	-	-	0.71	0.54	-	0.64

- The trait is not involved in the index.

), either in the F₆ generation or in the two cycles of selection, were high and unreliable because the evaluation took place in one location, for one year, as mentioned before. The narrow-sense heritability was estimated via parent–offspring regression and mostly increased from cycle 1 to cycle 2 except for few cases. The families of cycle 2 in both index 2 and index 3 were the same. Therefore, the results of C2 of index 3 were omitted. The narrow-sense heritability of DH increased from 0.44 to 0.79 for index 1, from 0.77 to 0.85 for index 5 and from 0.76 to 0.82 for index 7 in C1 and C2, respectively. Narrow-sense heritability of NS/P, NG/S, MSW and GW showed the same trend and increased from C1 to C2, while in GY/P, this trend was lost in five out of eight indices.

2.4. Means of the Selected Families

The means of the selected families after the second cycle are listed in

Table 5. Means of the parents and the selected families after the second cycle of selection.

Index 1 “Involved DH, NS/P, GY/P, NG/s, MSW, GW”
Family No.	DH	PH, cm	SL, cm	NS/P	GY/P, g	NG/S	MSW, g	GW, g
6	88.67 **	94.67	14.33 *	8.03 **	20.33 **	60.37 **	2.92 *	6.47 **
22	84.67	93.33	15.00 **	5.25	14.43	45.39	2.76	6.16 *
30	81.67	85.00	13.33	7.93 **	13.70	28.00	1.73	6.22 **
35	82.33	88.33	12.67	4.85	13.27	59.26 **	2.80	5.57
77	75.00 **	85.00	12.33	6.32	17.00 **	54.06 *	2.74	5.56
Average	82.47	89.27	13.53 *	6.48 *	15.75 **	49.41 *	2.59	6.00 **
Index 2 “Involved NS/P, GY/P, NG/s, MSW, GW”
4	88.67 **	94.67	15.33 **	8.03 **	20.33 **	63.67 **	3.10 *	6.47 **
7	85.33	100.00 **	12.33	7.88 **	14.33	30.38	1.82	6.00 *
55	91.67 **	103.33 **	15.33 **	8.18 **	21.50 **	48.28	2.67	5.52
56	92.33 **	98.33 **	15.00 **	7.18 *	20.17 **	65.72 **	2.88	5.52
107	82.33	85.00	11.33	6.32	12.77	36.82	2.02	5.56
Average	88.07 **	96.27 **	13.87 *	7.52 **	17.82 **	48.98	2.50	5.81 **
Index 4 “Involved GY/P, NG/s, MSW, GW”
41	93.33 **	103.33 **	14.67 **	9.40 **	22.17 **	44.27	2.36	5.38
44	82.00	86.67	14.00 *	4.02	10.20	46.01	2.55	5.60
48	81.67	86.00	16.33	3.00	6.98	42.09	2.33	6.40 **
54	91.33 **	103.33 **	13.67	9.28	21.33 **	53.60	3.03 **	5.79 *
57	92.67 **	103.33 **	12.67	10.50	23.82 **	60.73 **	3.29 **	5.00
Average	88.20 **	96.53 *	14.27 **	7.24 **	16.90 **	49.34	2.71 **	5.63 **
Index 5 “Involved DH, GY/P, MSW, GW”
46	77.00 **	94.67	16.00 **	8.03	20.33 **	63.67 **	3.10 **	6.47 **
55	85.67	86.67	14.33 **	5.08	15.45	64.18 **	3.04 **	5.52
60	83.00	91.67	13.00	7.57 *	17.83 **	51.70 *	3.10 **	6.13 **
42	88.00 **	95.00	15.33 **	7.75 **	17.25 **	39.67	2.25	5.62
97	81.67	90.00	13.67	5.77	10.68	35.50	2.14	5.93 **
Average	83.07	91.60	14.47 **	6.84 **	16.31 **	50.54 *	2.72 **	5.93 **
Index 6 “Involved GY/P, MSW, GW”
9	88.67 **	94.67	15.83 **	8.03	20.33 **	52.70 **	2.86 *	6.47 **
37	79.67	85.00	13.67	4.27	12.70	37.09	2.39	6.15 **
40	90.00 **	100.00 *	12.67	6.92	16.98 *	56.30 **	2.73	5.55
41	100.00 **	103.33 **	15.00 **	9.37 **	21.50 **	57.40 **	3.20 **	5.38
70	82.67	90.00	11.67	6.53	13.28	49.76	2.29	6.18 **
Average	88.20 *	94.60 *	13.77 *	7.02 *	16.96 **	50.65 **	2.69 *	5.94 **
Index 7 “Involved DH, GY/P, NG/s, GW”
26	88.67 *	94.67	16.33 **	8.03 **	20.33 **	65.00 **	3.19 **	6.47 **
39	89.00 *	91.67	14.50 *	6.27	16.13	44.55	2.56	5.77 *
55	89.33 *	86.67	15.50 **	6.18	18.17 **	57.74 **	3.10 **	5.52
56	75.00 **	86.67	12.00	5.77	15.80	49.95	2.76 *	5.52
69	73.00 **	89.33	12.33	6.53	11.53	35.59	1.82	5.13
Average	83.00	89.80	14.13 **	6.56 *	16.39 *	50.57 *	2.69 **	5.68 **
Index 8 “Involved GY/P, NG/S, GW”
36	91.67 **	101.67 **	15.83 **	8.03 *	20.33 **	62.93 **	3.20 **	6.47 **
40	90.00 **	100.00 *	12.33	6.92	16.98 **	40.86	2.51	5.55
41	91.67 **	98.33 *	13.67	7.07	18.95 **	58.06 **	3.03 **	5.38
56	79.00	86.67	12.67	7.27	11.93	37.83	1.65	5.79 *
34	84.67	96.67	13.33	5.50	14.25	47.20	2.73	5.55
Average	87.40 *	96.67 *	13.57 *	6.96 *	16.49 **	49.38	2.63	5.75 **
SIDS4 (P1)	80	86.67	14.67	4.70	12.00	46.55	2.56	5.50
G164 (P2)	87	95.00	11.00	7.55	16.80	45.88	2.23	4.90
Mid-parent	83.50	90.83	12.83	6.13	14.40	46.22	2.39	5.20
LSD.05	2.48	6.25	1.15	0.75	1.27	6.95	0.47	0.72
LSD.01	3.49	8.77	1.61	1.05	1.78	9.76	0.65	1.01

*, ** significant from the mid-parent at 0.05 and 0.01 levels of probability, respectively. DH = days to heading, SL = spike length, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = mean spike weight, GW = 100-grain weight, GY/P = grain yield/plant.

. The averages of the families of the eight selection indices showed significant increases (p ≤ 0.01) in GY/P from the mid-parent, ranging from 15.75% for index 1 to 17.82% for index 2. In most indices, the means of the traits involved in the index significantly surpassed the mid-parent. The average of the indices involving DH (index 1, 5 and 7) showed insignificantly more earliness than the mid-parent, accompanied with a significant increase in NG/S. Meanwhile, the average of the other indices (index 2, 4, 6 and 8) showed significant (p ≤ 0.05–p ≤ 0.01) lateness. Furthermore, the indices not involving DH were the best for improving GY/P and NS/P. Index 2 ranked first for improving mean GY/P (17.82 g), followed by index 6 (16.96 g), index 4 (16.90 g), index 8 (16.49 g), index 7 (16.39 g) and index 5 (16.31 g), while index 1 had the lowest mean GY/P (15.75 g).

2.5. Direct and Correlated Genetic Gain

The observed direct and correlated genetic gains in both C1 and C2 as a percentage of the mid-parent are listed in

Table 6. The observed direct and correlated genetic gain in percentage of the mid-parent in cycle 1 (C1) and cycle 2 (C2) of selection.

Index No.	DH	PH	SL	NS/P	GY/P	NG/S	MSW	GW
Index 1 C1	−0.06	−0.30	5.12 **	5.33 *	5.22 *	4.23	7.69 **	8.38 **
C2	−1.24	−1.72	5.45 *	5.74 *	9.35 **	6.92 *	8.14	15.29 **
Index 2 C1	4.09 **	4.80 **	7.62 **	13.25 **	18.97	4.09	2.64	5.55 **
C2	5.47 **	5.98 **	8.05 *	22.78 **	23.75 **	5.97	4.31	11.78 **
Index 3 C1	−0.56	0.35	9.38 **	5.57 **	4.12	5.25 **	5.89 **	10.23 **
C2	5.47 **	5.98 **	8.05 *	22.78 **	23.75 **	5.97	4.31	11.78 **
Index 4 C1	5.41 **	4.37 **	6.45 **	15.96 **	13.52 *	5.61 **	13.15 **	5.34 **
C2	5.63 **	6.28 *	11.17 **	18.20 **	17.36 **	6.77	13.29 **	8.33 **
Index 5 C1	−0.77 *	0.67	12.03 **	9.37 **	11.01 *	5.72 **	12.33 **	13.00 **
C2	−0.52	0.84	12.73 **	11.67 **	13.26 **	9.36 *	13.80 *	14.06 **
Index 6 C1	5.60 **	5.87 **	6.76 **	6.65 **	14.16 **	4.12 **	10.50 **	8.54 **
C2	5.63 *	4.15 *	7.27 *	14.67 *	17.78 **	9.60 **	12.48 *	14.31 **
Index 7 C1	−1.03	−0.44	12.79 **	5.98 *	11.02 *	7.66 **	11.59 **	11.52 **
C2	−0.60	−1.14	10.13 **	7.05 *	13.84 *	9.41 *	12.18 **	9.26 **
Index 8 C1	5.26 **	5.19 **	5.41 **	8.37 **	11.42 *	4.90 **	8.16 **	8.11 **
C2	4.67 *	6.42 *	5.71 *	13.58 *	14.51 **	6.84	9.71	10.51 **

DH = days to heading, SL = spike length, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = mean spike weight, GW = 100-grain weight, GY/P = grain yield/plant. *, ** significant at 0.05 and 0.01 levels of probability, respectively.

. There was a general increase in the direct observed gain for traits involved in the index from C1 to C2, except for MSW in index 3. After the second cycle, the observed gain in GY/P ranged from 9.5% for index 1 to 23.75% for index 2. The best index for improving GY/P as a percentage from the mid-parent was index 2 (23.75%), followed by index 6 (17.78%), index 4 (17.36%), index 8 (14.51%), index 7 (13.84%), index 5 (13.26%) and index 1 (9.35%).

3. Discussion

Many breeders and research stations use direct selection for GY through pedigree selection with some modifications, either in the early generations or in the F₅ generation, after the population has reached an acceptable level of homozygosity. However, single-trait selection was mostly accompanied by adverse effects on other correlated traits [6,7,10,28]. Furthermore, the genetic variability decreased rapidly after two or three cycles of selection. However, the selection index proposed in Refs. [14,15,16,18] proved to be an efficient method for improving multiple traits simultaneously, and preserved genetic variability to a great extent compared to single-trait selection [5,7,23,25,28,29,30,31]. In the present study, two cycles of the desired-genetic-gain selection index were imposed on a bread wheat population of late generations that started in the F₆ generation. The GCV and PCV in the F₆ generation were high for all traits except DH. The GCV% was moderate (7.27%) for DH, while it was high and reached 30.21% for NS/P, 20.40% for GY/P, 27.79% for NG/S and 27.23% for MSW. The family means were located outside the range of the parents. This provides evidence of the presence of sufficient genetic variability and feasibility of selection (Table 1). Meanwhile, the evaluation of the families in one location for one season inflated the genetic variance via the hidden confounding effects of the interactions among families, locations, and years [6,7,28,32]. Therefore, heritability in the broad sense and the expected genetic advance were high and unreliable.

It should be recalled that the population under study originated from a cross between Giza 164 and Sids 4. Giza 164 is taller and is higher in NS/P and GY/P, while Sids 4 is earlier in heading, longer in SL, and higher in NG/S, MSW and GW. The characteristics of the parents were reflected in the genotypic correlations among the traits of the population. Therefore, DH showed negative correlations with SL, NG/S, and MSW, and positive ones with NS/P and PH. In other words, late mature families represent the characteristics of Giza164 (late in maturity, longer in height, high in NS/P and GY/P, and short SL). Then, PH showed positive correlations with GY/P and NS/P; additionally, NS/P showed a positive correlation with GY/P and negative correlations with both NG/S and MSW. Meanwhile, NG/S had a positive correlation with MSW, and both showed a negative correlation with DH (the characteristics of Sids4).

Heritability in the narrow-sense (h²) is the proportion of variation in a progeny that is a result of additive variance, and may be transmitted; moreover, it causes the resemblance between parents and offspring. Heritability in the narrow-sense, as estimated by parent–offspring regression, increased towards homozygosity, as expected, from C1 to C2, except for a few cases. For different indices, it ranged from 0.44 to 0.85 for DH, from 0.63 to 0.90 for NS/P, from 0.50 to 0.74 for GY/P, from 0.44 to 0.67 for NG/S, from 0.36 to 0.82 for MSW and from 0.43 to 0.82 for GW. A high h² means the trait is less affected by the environment, and vice versa. In the early-generation selection from F₂ to F₅, on the same population, after recording three cycles of the selection index [28], the h² ranged from 0.16 to 0.40 for DH, 0.07 to 0.25 for GY/P, 0.19 to 0.22 for GW, 0.17 to 0.22 for NG/S, 0.12 for NS/P and 0.21 for MSW. It is obvious that heritability increased from early to late generations in the same population with increasing homozygosity. Ref. [25], a study of the efficiency of different selection indices on 33 landraces, reported that h² ranged from 0.16–0.755 for DH, 0.241–0.408 for number of spikes, 0.784–0.892 for NG/S, 0.848–0.833 for GW and 0.345–0.448 for GY (g/m²). In the F₄ generation, Ref. [5] noted an h² of 0.17, 0.0, 0.11, 0.62 and 0.32 for DH, NS, GY, NG/S and GW, respectively.

The average indices of the families always hide the individual superior families. Breeders of late generations seek families that produce high yields and possess correlated traits. Family No. 6 (index 1), No. 4 (index 2), No. 9 (index 6), No. 26 (index 7) and No. 36 (index 8) could be considered promising families. They significantly exceeded (p ≤ 0.05–p ≤ 0.01) the mid-parent and, in some cases, the better parent in six to eight traits. However, these five families were later in maturity than the mid-parent. Meanwhile, family No. 46 (index 5) was significantly (p ≤ 0.01) earlier than the mid-parent, and significant surpassed the mid-parent in SL, GY/P, NG/S, MSW and GW. It can be concluded that, except for DH, the indices simultaneously improved all the traits involved.

The observed genetic gain of an index implies that an index has been performed [18]. In this study, the best observed gain in GY/P was 23.75% of the mid-parent recorded for index 2 (involving NS/P, GY/P, NG/S, MSW and GW). However, Index 1, which involved the same traits plus DH, had the lowest observed gain (9.35%) for GY/P. Involving DH in an index resulted in insignificant favorable observed gain towards earliness after the second cycle and lowered the observed gain in GY/P. Except for index 3, pairs of indices differed only in DH (indices 1 and 2; indices 5 and 6; indices 7 and 8); it can be noted that the index involving DH had less observed genetic gain in PH, NS/P and GY/P; meanwhile, NG/S, MSW and GW tended to increase. This could be due to the negative correlations of DH with SL, NG/S, MSW and GW in the base population in the F₆ generation. In fact, the use of the selection index lessened the effects of negative correlations among the traits involved. It is expected that the selection index alters the variance and covariance among traits [18]. In these materials, there was a wide difference in the DH of the two parents (Sids4, headed at 68 days, and Giza 164, headed after 83 days in the F₆ generation). Ref. [33] indicates that when a component trait showed negative correlations with the other traits in an index, this reduced the genetic gain. In the three cycles of the selection index in the early generations of the same materials, the best selection index gave an observed gain of 34.40% of the better parent. The large observed gain in early generations could be due to high levels of heterozygosity. Ref. [25] noted an expected genetic gain of 2.75 and 1.79 for grain yield in two years.

4. Materials and Methods

4.1. Plant Materials and Field Trials

The plant genetic materials were composed of 120 families in the F₆ generation of bread wheat (Triticum aestivum L.), originating from a cross of ‘Giza 164’ and ‘Sids4’ bread wheats. The pedigree of Giza 164 is KVZ/Buha’’S’’//K al/Bb, and that of Sids4 is Maya’’S’’ Man (S)//CMH74.AS92/3/Giza157-2.

The experiments were conducted at the Faculty of Agriculture Experimental Farm, Assiut University, Egypt (longitude: 31.125° E, latitude: 27.25° N, elevation: 45 m/148 ft). The planting dates were 25 November in 2017/2018, and 28 November in both the 2019/2020 and 2020/2021 seasons. During land preparation, super phosphate (${\mathrm{P}}_2{\mathrm{O}}_5$, 15.5%) was added at a rate of 357.14 kg/ha. Nitrogen fertilization in the form of ammonium nitrate (33.5% N) was added at a rate of 190.5 kg/ha in two equal doses, before the first and second irrigations. The experiments received the first irrigation at planting and another four irrigations throughout the growing seasons.

In the 2017/2018 season, the 120 families in the F₆ generation, along with the two parents, were sown in a randomized complete block design with three replications in rows that were 30 cm apart. The experimental unit was a single row three meters in length. After full emergence, seedlings were adjusted to ten per meter. The recorded data in the three seasons were days to heading (DH), plant height (PH, cm), spike length (SL, cm), number of spikes/plant (NS/P), grain yield/plant (GY/P, g), number of grains/spike (NG/S), main spike weight (MSW, g) and 100-grain weight (GW, g). At the end of the season, 20 plants from each family were harvested. The families were ranked for eight models of desired-genetic-gain index according to [18,34]. The characters incorporated in each index are shown

Table 7. The traits involved in the eight indices.

INDEX	The Traits of Each Index
INDEX 1	DH	NS/P	GY/P	NG/S	MSW	GW
INDEX 2		NS/P	GY/P	NG/S	MSW	GW
INDEX 3	DH		GY/P	NG/S	MSW	GW
INDEX 4			GY/P	NG/S	MSW	GW
INDEX 5	DH		GY/P		MSW	GW
INDEX 6			GY/P		MSW	GW
INDEX 7	DH		GY/P	NG/S		GW
INDEX 8			GY/P	NG/S		GW

DH = days to heading, NS/P = number of spikes/plant, NG/S = number of grains/spike, MSW = main spike weight, GW = 100-grain weight, GY/P = grain yield/plant.

.

The 20 highest-scoring families for each index were identified, and the best plant in GY from each was saved for the second season. In the 2019/2020 season, the 20 selected plants in the F₇ generation for each selection index, along with the two parents, were sown as in the previous season. At the end of the season, the families of each index were ranked according to the Ref. [18] selection index, and the five families with the highest index scores were selected for evaluation in the 2020/2021 season (the F₈ generation).

4.2. Statistical Analysis

The analysis of variance, covariance, phenotypic (σ²p) and genotypic variance (σ²g) and significance tests were performed as in [34] on a plot-mean basis. The statistical model of the randomized complete block design is

Y_ij = μ + ηi + Σ_j + e_ij

where i = 1,2,3, ⋯, t and j = 1,2, ⋯, b, with t treatments and b blocks; μ is the overall mean based on all observations; ηi is the effect of the ith treatment response; Σ_j is the effect of jth block; and e_ij is the corresponding error term, which is assumed to be independent and normally distributed with a mean of zero and constant variance.

In the random model of the RCBD, the genotypic variance (σ²g) = (MSg − MSe)/r, phenotypic variance (σ²p) = σ²g + MSe/r, MSg = genotypes mean square, MSe = error mean square, and r = number of replications.

The genotypic (GCV) coefficients of variation and the genotypic correlations among pairs of traits were estimated as outlined by [35], as follows:

The covariance components were used to compute the genotypic correlation on a line-mean basis between the various characters as follows:

$$\mathrm{rg}=\frac{\mathsf{\sigma }\mathrm{g}1.2}{\sqrt{\left({\mathsf{\sigma }}^2\mathrm{g}1\right)\left({\mathsf{\sigma }}^2\mathrm{g}2\right)}}$$

where $\mathsf{\sigma }\mathrm{g}1.2$ is the genetic covariance between trait 1 and trait 2, and σ²g is the genetic variance.

GCV% = (σg/mean) × 100, PCV% = (σp/mean) × 100

where, σg and σp = genotypic and phenotypic standard deviations, respectively.

Heritability in the broad sense (H) and the genetic advance were computed using the formula adopted by [36,37] as follows:

Heritability in the broad sense (H%) = (σ²g/σ²p) × 100 and the expected genetic gain in the F₂ = k × σp × H

where, the environmental variance σ²_E = (σ²_P1 + σ²_P2)/2, σ²p = F₂ variance, σ²g = σ²p − σ²_E, σ²_P1 = variance of the first parent, σ²_P2 = phenotypic variance of the second parent, and k is the selection intensity from selecting 10% of the superior plants.

Heritability in the narrow sense (h²) was estimated via parent–offspring regression, as outlined in [38].

The observed genetic gain was calculated as a percentage from the mid-parent. The significance of the direct and correlated observed genetic gain was calculated using least significant difference (LSD).

LSD for mid-parent observed gain = t_α((MSE/(r × f) + MSE/(r × 2))^0.5,

where t_α = tabulated t at 0.05 or 0.01 level of probability, r = number of replications, MSE = error mean squares, and f = number of families.

The selection index coefficients were calculated as outlined in Ref. [39] according to the following matrix formulation:

b = G⁻¹h. p/z

where b is the vector of index coefficients, G⁻¹ is the inverse of the genotypic variance-covariance matrix, h is the vector of desired genetic gains, and p/z is the reciprocal of the selection differential in standard units.

Since p/z is constant for any experiment, an equivalent solution can be obtained from:

b = G⁻¹h

The desired genetic gain (h) was adopted as the increase of 10% of the mean for different traits, and the decrease of 10% of days to heading.

The selection index of a line was in the form

I_k = b₁x_1k + b₂x_2k + b₃x_3k + …

where I_k is the index value of the kth line, and x_1k, x_2k, x_3k, … is the mean values of the traits for that particular line.

5. Conclusions

It can be concluded that the desired-genetic-gain selection index in the late generations of these materials was effective in identifying superior promising families. All the indices simultaneously improved all the traits involved. Except for DH, the indices preserved the genetic variability after two cycles of selection.