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 F
2 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 F
2 and F
3 generations and that of F
4 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 F
4 generation under both drought-stress and optimum-irrigated environments was mostly better than three cycles started from the F
2 generation. Therefore, delaying selection for grain yield to the F
5 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 F
3 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 (F
2–F
5) 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 (F
6), Cycle 1 (F
7), and Cycle 2 (F
8)—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.
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 F
5 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 F
6 generation. The GCV and PCV in the F
6 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 (h
2) 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 h
2 means the trait is less affected by the environment, and vice versa. In the early-generation selection from F
2 to F
5, on the same population, after recording three cycles of the selection index [
28], the h
2 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 h
2 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/m
2). In the F
4 generation, Ref. [
5] noted an h
2 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 F
6 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 F
6 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.