1. Introduction

In the world, great attention is paid to the wide use of geographically distant varietal samples in scientific research aimed at improving parameters of valuable economic traits of common beans. On the hybrids of these varietal samples, large-scale studies are conducted to determine the genetic laws of inheritance, variability, transmission from generation to generation, and correlative dependence of physiological, biochemical and morphobiological traits, in particular, valuable economic traits.

Common bean is a crop grown in many countries and it is an important nutritional legume, that is, its cultivars and specimens are rich in protein, carbohydrates, minerals (iron and zinc) and essential vitamins. The first introduction of common beans from Central America to Western Europe dates back to the 16th century [1].

Genetic studies conducted by scientists on common bean (Phaseolus vulgaris L.) from a practical point of view revealed that the presence or absence of purple stripes on the outer surface of the flower can serve as a morphological trait for the selection of light red and white seeds [2].

Colored lines have been observed in Central American genotypic groups of beans. In contrast, South American (eg, Chile, Nueva Granada, and Peru) genotypes have been found to lack colored lines on the petals [3].

The heritability of some traits (seed coat color, plant height, 100 seed weight) was analyzed in the samples belonging to Phaseolus vulgaris L.species. The color of the seed coat depends on the interaction of at least 2 loci (P and R), and the epistatic effect on R. genotypes, which are recessive for some of the Ñ genes, has been determined. It was noted that the seed coat color has monogenic control, plant length ratio is 3:1, and 100 seed weight has polygenic characteristics [4].

For example, PI 527735 was obtained from the light pink color of the petal in the common bean, together with the gray-white seeds produced by the gri gene, while the interaction of the recessive allele of the pigment (P) locus with other genes was determined [5,6].

In scientific research, samples of common bean that are wild and sensitive to abiotic stresses were crossbred for interspecific hybridization. The resulting hybrids were found to be cold-resistant and adaptable to regions with a short vegetation period. At the same time, the in vitro method was also used during this research, which served to successfully obtain some hybrid combinations [7].

In recent years, studies have been carried out on the parameters of the traits for seed weight and seed size as the main traits that determine the productivity of common bean plant [8].

Other scientific studies have evaluated the genotypic correlation of agrotechnical traits of common bean. It was observed that the genotypic correlation coefficient is superior to the phenotypic correlation. Number of seeds per plant (0.801) and grain weight (0.641) were found to have more positive effects on grain yield, suggesting direct or indirect selection for grain yield in common bean [9].

2. Research Object and Methodology

The research was carried out at the experimental site of the Faculty of Natural Sciences of Chirchik State Pedagogical University.

As research objects, Solnishko, Ravot, Baby Lima, Calipso Krasnaya, Vir, Belaya Fasol cultivars belonging to Phaseolus vulgaris L.species and F₁-F₂ plants were used.

The following methods were used in the conducted research:

One of economic traits – the number of seeds per plant trait was determined by generally accepted methods [10], the degree of dominance of traits in the first generation hybrids was determined according to S. Wright's formula presented in the works of G. E. Beil and R. E. Atkins [11]:

hp – dominance coefficient;

F₁ – the arithmetic mean of the hybrid trait;

МР – the arithmetic mean of trait of both maternal and paternal forms;

Р – the arithmetic mean of the best paternal or maternal form trait.

hp = 0 – no dominance;

0 <hp< ±1,0 – intermediate dominance;

hp = ±1,0 – complete dominance;

hp > ±1,0 – overdominance.

In hybrids of the second generation, the indicator of transmission of the trait from generation to generation (h²) was calculated based on the formula of S.N. Warner [12]:

dispersion of plants;

dispersion of plants;

dispersion of mother plants;

dispersion of plants father plants;

Quantitative results obtained on the basis of all practical experiments were subjected to statistical processing in large and small samples [13].

3. Research Results

The yield of a common bean plant depends on the number of pods produced and the seed weight. Experiments have shown that the number of seeds per plant is one of the variables. A common bean plant has a very high chance of bud formation – flowering – pod formation, but its maintenance depends on the cultivar genotype and cultivation agronomics and environmental stressors. Although seed number per plant is inversely related to pod number, a variable productivity trait such as seed number per pod does not affect the yield as strongly as pod number depending on genotype. The study of the trait for the number of seeds per bush in the original forms selected for the study showed that the high indicator of this trait was determined in Belaya Fasol cultivar with an average of 121.0±1.0 pieces, while in the Vir cultivar the number of seeds per bush was low, on average 67.4± 0.8 pieces (Table 1).

In F₁ plants, similar results were obtained in terms of the trait for the number of seeds per plant, and in the hybrid combinations obtained as a result of crossing positive overdominance, negative overdominance and negative intermediate dominance were noted. For example, in the combination F₁ Ravot x Solnishko, the parameters of the trait for the number of seeds per plant were 88.8 ± 1.2 pieces, the amplitude of variation was 84.0-105.0 pieces, and the coefficient of variation was 6.1%, and the coefficient of dominance (hp=-4.8) was inherited in the case of negative overdominance, and a low indicator of this trait was observed in the combination F₁ Ravot x Calipso Krasnaya (average 74.0±1.1 pieces) and the level of dominance (hp=-1, 6) inherited in a negative overdominant state. In addition, in the F₁ Baby Lima x Vir and F₁ Baby Lima x Calipso Krasnaya combinations, a positive overdominant (hp=2.0, hp=2.3) inheritance was noted for the trait of the number of seeds per plant (Table 1).

Table 1. Inheritance of the traits for seed number and seed weight per plant in the original forms and F1 plants

In the studied F₂ plants, the trait for the number of seeds per plant was analyzed. In the analyzed F₂ plants, a range of variation in terms of the trait for the number of seeds per plant showed 6-7 classes (Table 1). For example, in the F₂ Solnishko x Baby Lima combination, a positive transgressive variability was noted. In this hybrid combination, the highest percentage of plants corresponded to the modal classes (25.0%, respectively) with 101.0-110.0 units per plant for the trait of seeds per plant.

Table 2. Inheritance and variability of the trait for seed number per plant in F2 plants

Furthermore, a wide transgressive variation was noted in F₂ plants, and among the 219 analyzed plants, 52 with 121-130 seeds per plant, 27 with 131-140 seeds, and 3 recombinant forms with 141-150 seeds per plant were isolated in terms of the trait for seed number per plant.

In F₂ plants, the coefficient of transmission of the trait for the number of seeds per plant ranged from h²=80.0 to h²=88.0, which means that 80.0-88.0% of the analyzed trait was found to be inherited under the effect of the genotype of the hybrid form, 12.0-20.0% was inherited under the influence of the external environment. For example, in the F₂ Ravot x Baby Lima combination, the coefficient of transmission of the seed number trait per plant was h²=88.0%, which means that 88.0% of the studied trait for seed number per plant is inherited due to the genotype of the hybrid form, 12.0% is inherited under the influence of the external environment.

It was found that the class for the trait on the number of seeds per plant, which is one of the economic traits of common bean, that is, the range of variation was found to be 6 classes in the F₂ Ravot x Solnishko combination. The largest percentage of studied hybrid plants included modal classes with 101-110 pieces of seeds (31.0%, respectively).

According to the trait for the number of seeds per plant in the F₂ combination a left-sided negative transgressive variation was observed, i.e., a shift of the original forms was noted from the distant classes with the lowest parameters to 2 classes, and a case of separation of plants with more seeds than the original forms was observed. In the combination F₂ Ravot x Solnishko, the coefficient of transmission of the trait for the number of seeds per plant was equal to h²=84.0, which showed that 84.0% of the analyzed trait was inherited due to the genotype of the hybrid form, and 16.0% was inherited by the influence of the external environment.

The analysis of the results for the original forms belonging to the Phaseolus vulgaris L. species selected for the hybridization process according to the trait for the seed weight per plant showed that the parameters on this trait were higher in the Vir cultivar than other cultivars, on average it was 44.4 grams, while the Belaya Fasol cultivar was characterized by lower parameters, an average of 24.5 grams, in terms of the trait for seed weight per plant. Intermediate parameters (average 31.9-40.7 grams) were recorded in other cultivars (Table 1).

In the studied F₁ plants, mainly intermediate, negative intermediate, negative heterosis and positive and negative overdominant inheritance were observed according to the trait for seed weight in one plant. For example, in the combination F₁ Ravot x Solnishko, the average seed weight per plant was 58.9 g, and the amplitude of variation was 50.9-69.5 g, accordingly, we can see that the dominance coefficient was noted to be hp=6.7. In the F₁ Baby Lima x Calipso Krasnaya combination, the seed weight per plant was 33.5 g, the amplitude of variation was 30.9-36.2 grams, and the dominance coefficient was hp=3.6, inheritance was found to be overdominant state, while in the reciprocal F₁ Baby Lima x Calipso Krasnaya combination, an average indicator for this trait was 29.9 g, the amplitude of variation was 26.9-36.2 g, and the dominance coefficient hp=-6.7 was noted to be inherited in a negative overdominant state.

In the original forms, the parameters of the trait for seed weight per plant was 24.5 g in the Belaya Fasol cultivar, while in the Vir cultivar 44.4 g, which was higher than all the selected original sources. In the F₂ plants obtained as a result of hybridization, it was found that the parameters of heterosis in terms of the trait for seed weight per plant were not only maintained, but also increased. In the analyzed F₂ plants, the range of variation in the trait for seed weight per plant covered 3-4-7 classes. For example: We can see that there is a right-sided transgressive variation in the F₂ Ravot x Baby Lima combination. The highest percentage of studied hybrid plants corresponded to modal classes with 47.0-52.9 g parameters (33.0%, respectively).

In addition, wide transgressive variability was observed in F₂ plants, and among the 174 studied plants, 7 forms with a seed weight of 59.0-67.9 g per plant and 8 recombinant forms with 65.0-70.9 g of on this trait were isolated (Table 3).

Table 3. Inheritance and variability of the trait for seed weight per plant in the F2 plants

In F₂ plants, the coefficient of transmission of the trait for seed weight in one plant was from h²=47.0% to h²=97.0%, which means that 47.0-97.0% of the analyzed trait is inherited due to the influence of genotype of the hybrid form, 3.0 -53.0% is inherited due to the influence of the external environment. In particular, in the intraspecific hybrid combination F₂ Baby Lima x Calipso Krasnaya, the coefficient of transmission of the trait for seed weight per plant was h²=97.0%, which means that 97.0% of the studied trait for seed weight per plant is inherited by the influence of the genes, while 3.0 % is inherited due to the influence of the external environment. Furthermore, the F₂ Solnishko x Ravot hybrid combination in the studied F₂ plants had a low gene effect in terms of this trait, that is, the coefficient of transmission from generation to generation was found to be h²=47.0%, which means that 47.0% of the studied trait of seed weight in one plant was inherited due to the genotype of the hybrid form, 53.0% was inherited due to the influence of the external environment.

4. Conclusions

The analysis of the studies showed that the heterosis was mainly observed in the F₁ plants obtained as a result of hybridization in terms of the traits for the number of seeds per plant and seed weight per plant. Recombinant forms (131-150 pieces, 59.0-70.9 grams) were isolated, taking into account the traits for the number of seeds per plant and the seed weight per plant while maintaining the state of heterosis in the studied F₂ plants. It can be concluded that the use of these isolated hybrid forms with high parameters of the traits for seed number per plant and seed weight per plant can be highly effective as a valuable original form for genetic selection studies.