​Construction of Selection Indices by using Different Economic Coefficients in Indian Bean [Lablab purpureus (L.) Sweet]

Indian bean (Lablab purpureus L. Syn. Dolichos lablab L., 2n = 22) is a well-known vegetable crop of India and South-East Asia. It is an important subsistence crop in many countries, especially Sudan (George, 2011). In India, vegetables are important crop in the horticulture sector, occupying 10.32 million hectare of area with average productivity of 18.4 tonnes/hectare for the year 2020-21. Indian bean is one of the perennial vegetable crop in India which is consumed as vegetable, pulse and forage.
       
The variability present in a population can be partitioned into heritable and non-heritable parts with the aid of genetic parameters such as genetic coefficient of variation, heritability and genetic advance (Miller et al., 1958). Yield is a complex character of any crop governed by quantitative traits and its grown environment, thus, selection for grain yield becomes difficult unless the association between the yield contributing characters are known. Genetic variability (Sivasubramanian and Madhavamenon, 1973), heritability along with genetic advance (Johnson et al., 1955) of traits, path analysis (Wright, 1923), allows unfolding coefficients of correlations into direct and indirect effects on yield are essential criteria for crop improvement (Alcantara Neto et al., 2011).
       
The selection indices based on yield attributing characters viz. pods per plant, plant spread and green-pod yield was considered more effective than selection based on green-pod yield alone (Rathnaiah, 1986). Hadavani et al., (2018) and Rukhsar et al., (2021) constructed selection indices in the Indian bean and cowpea respectively on different characters using a discriminant function analysis. Lima et al., (2015) evaluated selection efficiency of plant architecture, plant disease, grain type and yield by means of a selection index in order to obtain superior progenies for traits. Singh and Ramgiry (2018) computed selection indices on the basis of linear combination of 40 soybean germplasm based on nodulation, yield and quality traits. Choudhary et al., (2017) studied Mungbean genotypes to assess the magnitude of genotypic variability, heritability and selection indices among the yield components and their direct and indirect effects on grain yield. The method of selection indices adopted by Nyo et al., (2020) to regularized indices for breeding value prediction using fifty improved rice genotypes. Yang et al., (2021) developed an optimized protocol for selection of sugarcane seedlings that balances the desire to maximize genetic gains but also be cost and labor efficient.
               
The main aim of breeding program is the improvement of the economic value of an individual through selection which is applied to the several traits simultaneously because economic value depends on more than one trait (Lynch and Walsh, 1998; Bernardo, 2002). Appropriate weights will be allocated to each character following their relative economic importance. There is no standard strategy to assign weights to the biometrical characters in the selection indices method. Hence, the current study has been carried out for construction of selection indices by taking different weights.

The study was carried out at College farm, N. M. College of Agriculture, Navsari Agricultural University, Navsari, India during late Kharif, 2018-2019. The experimental material consisted of fifty five F4 progenies and two check varieties (GNIB-21 and GNIB-22) of Indian bean [Lablab purpureus (L.) Sweet]. These F4 progenies were obtained from four crosses viz., GNIB-21 × GP-1 (2 progenies), GNIB-21 × GP-167 (14 progenies), GNIB-21 × GP-189 (22 progenies) and GNIB-21 × GPKH-120 (17 progenies). The field experiment was conducted in RBD with three replications. The observations on seed yield per plant and its component characters were recorded from five randomly selected competitive plants for each treatment in each replication. Average values per plant were computed for different yield contributing characters viz. X₁ = Seed yield per plant (g), X₂ = Plant height (cm), X₃ = Pods per plant, X₄ = Pod width (cm) and X₅ = Days to maturity. Data recorded for yield contributing characters were subjected to analysis of variance (Panse and Sukhatme, 1978).
 
Selection index
 
Selection index (Smith, 1937) based on ‘Discriminant function’ which was given by Fisher (1936). Further Hazel (1943) developed a method of selection index based on the path coefficients. Appropriate weights was assigned to each character according to their relative economic importance. An attempt has been made by assigning different type of economic weights viz. equal weight [W₁], genotypic correlation coefficients [W₂] and genotypic path coefficients (Direct effect) [W₃]. Total 31 selection indices were constructed by taking five single characters as well as all possible combinations of these five characters.
 
Economic coefficients (Weights)
 
In the present study, different economic coefficients were obtained as weights and these weights has been used for the construction of selection indices.
 
Equal weight [W₁]
 
In equal weight method, a value of 1 was assigned to all characters to construct selection indices i.e.  
Genotypic correlation coefficient [W₂]

The genotypic correlation coefficient was calculated between seed yield per plant (X₁) and different yield contributing characters (X₂, X₃, …..X₅) as per the formula given below:

                                                                                                          
Where,
r_g (x_i,x₁) = Genotypic correlation coefficient between X_i and X₁ (i = 2, 3,…,5).
σ_g (x_i,y)    = Covariance between X_i and X₁.
σ²_g (x_i)   = Genotypic variance of the variable X_i.
σ²_g (x₁) = Genotypic variance of the variable X₁.
 
Genotypic path coefficients (Direct effect) [W₃]

Correlation coefficient was computed from variance and covariance components as suggested by Burton, (1952), Wright, (1968) and Singh and Chaudhary, (1985). The correlation coefficient was further partitioned into direct and indirect causes according to Dewey and Lu, (1959). The path coefficients (P_ij) are obtained as follow:

                                                                                                    
Where,
P_ij = Path coefficient.
B^-1 = Inverse of correlation matrix of character X_i and X₁.
A = Correlation matrix between character X_i and X₁.
 
Expected genetic advance/gain                                                                         

Genetic advance explains the degree of gain obtained in a character under a particular selection pressure. High genetic advance coupled with high heritability estimates offers the most suitable condition for selection which indicates the presence of additive genes in the trait and further suggest reliable crop improvement through selection of traits (Ogunniyan and Olakojo, 2014). The expected genetic advance/gain is calculated as (Dabholkar, 1992).
  Where,
Z / P = Selection intensity i.e. 2.06 at 5% level of significance.
G_ij = Genotypic variance and covariance of the different component characters (i=j=1,2,…p characters).
P_ij = Phenotypic variance and covariance of the different characters.
a_i = Weight assigned to ith character.
b_i = Coefficient of ith character.
b_j = Transpose of b_i.
 
Per cent relative efficiency (PRE)
 
The relative efficiency of each index has been calculated using genetic gain of seed yield as standard.
 
Selection score
 
The value of the progeny was measured using selection score (H) which is calculated as under: Where,
X_i  = Value of ith character (i = 1 to 5).
b_i  = Coefficient of ith character.
       
The best five progenies were selected on the basis of highest score from all the methods (W₁, W₂ and W₃).
 
Spearman rank correlation
 
The method-wise ranking was done based on selection score to identify the progenies with their value. The Spearman rank correlation analysis (1904) was employed to find out the degree of association between different weight methods.

Mean performance of progenies
 
The data were recorded on different quantitative traits has been taken for the analysis of variance (Table 1). Significant variation existed in all the selected traits studied except days to maturity. The seed yield per plant was found significantly higher in progeny F₃B144-2 (17.18 g) and statistically at par with F₃D214-6*1 (13.86 g). The maximum plant height was observed in F₃C246-2 (58.95 cm) followed by F₃C246-3*2 (58.79 cm). The progeny F₃D269-10*2 (32.96) had maximum pods per plant followed by F₃D214-6*1 (31.25). The pod width was found maximum in progeny F₃B144-4 (1.64 cm) followed by F₃B144-8a (1.63 cm). The presence of sufficient variability in all the progenies for all selected characters indicates that selection can be made among the progenies for further improvement.
 

 
Genotypic correlation coefficients and path coefficients analysis
 
The genotypic correlation coefficients between seed yield per plant and its different selected traits is presented in Table 2 along with path coefficients which estimated through path analysis at genotypic level. Correlation study revealed that all the traits showing high positive significant genotypic relationship with seed yield per plant. Days to maturity showed highest value of association with seed yield per plant (0.65) followed by pod width (0.55), plant height (0.53) and pods per plant (0.44).
 

       
Path coefficient analysis has been used to determine the nature of relationships between seed yield per plant and its contributing components. It has been seen that yield attributing characters have significant positive direct effect (rg) on seed yield per plant therefore it has been used in crop breeding programs. The days to maturity showed highest direct effect (0.68) followed by pod width (0.65), pods per plant (0.41) and plant height (0.23).
 
Selection indices for individual and all combination of yield contributing character
 
Selection indices has been constructed by taking different weight (W_i)  for all selected individual and all possible combinations of the characters. Among all possible combinations, the top two selection indices with respect to their Percent relative efficiency (PRE) and genetic gain in different methods are presented in Table 3. It has been observed that PRE and genetic gain is higher in equal weight method (W₁) as compared to remaining methods (W₂ and W₃). It has been also found that selection index (I₁₂₄₅) i.e. combinations of four characters viz. seed yield per plant, plant height, pod width and days to maturity, showed high PRE and genetic gain w.r.t. remaining selection index obtained by all combinations of characters.
 

       
The current study also reveals that the selection index which includes more than one characters, gave high genetic advance, which suggest the utility of constructing of selection indices for effective simultaneous improvement in several characters and achieving higher genetic gain in late kharif season. Overall it observed that equal weight method provide more PRE and high genetic gain as compared to other weight methods. It has been also observed that in construction of selection indices the addition of X₃ (Pods per plant) character in I₁₂₄₅ which resulted reduction of PRE from 410.82 to 408.79% in W₁ weight methods. Ranking of Indian bean progenies based on selection scores The selection score has been calculated for each progenies of Indian bean based on best selection index i.e. I₁₂₄₅ for all weight methods. The progenies were ranked based on their selection score and top first 5 rank is presented in Table 4. It has been observed that selection scores obtained through equal weight (W₁) found apparently higher followed by W₂ and W₃ weight methods. It reveals that equal weight method performed better than other two methods. The ranking of progenies moderately similar for all the three weight methods (Fig 1). Further it has been seen that progeny F₃B144-2 possessed 1^st rank under all the weight methods and thus recommended for future breeding programme. It was perceived that Progeny F₃C181-8*1 and F3B144-6 possessed 2^nd rank in W1 and W₂ weight methods respectively while 4th under W₂ and W₃ weight method respectively.
 

 

 
Rank correlation between different weight (W_i) methods
 
Rank correlation has been calculated between assigned ranks to progenies based on selection scores and seed yield per plant (Table 5). The results designated that all correlation coefficients among different weight methods were more than 0.75 and highly significant which indicated the ranking of progenies based on the selection index I₁₂₄₅ with highest PRE under different weights method and comparatively similar for all the progenies. It has been seen that there is highly positive correlation which explained closed association with W₃ method (rs=0.99) followed by W₁ and W₂ weight method.
 

The genetic gain and PRE was observed higher in equal weight method than other two methods, therefore one can use equal weight to achieve higher genetic gain in Indian bean for purpose of breeding improvement programs. The study also determined PRE further increased with the inclusion of two or more characters. The best PRE was obtained with four character combinations (I₁₂₄₅). Looking towards the simplicity of assigning weight and achieving highest genetic gain and PRE, the selection index, combinations of seed yield per plant, plant height, pod width and days to maturity was suggested to select the progenies for Indian bean seed yield improvement with equal weight method.

None.