Non-parametric Measures for Yield Stability in Faba Bean (Vicia faba L.) Advanced Line in Gangetic Plains of India

Faba bean (Vicia faba L.) is among the oldest crops in the world. Globally, it is fourth most important pulse crops of the world after dry beans, drypea and chickpea. Currently, 58 countries produce this bean on large scale. The major faba bean growing countries are China, Egypt, United Kingdom and Syria. About 70% of total global production is contributed by China alone. Probably faba beans are one of the best performing crops under global warming and climate change scenario because of its unique ability to excel under all most all type of climatic conditions coupled with its wide adoptability to range of soil environment. Faba bean being incredible and crop complete food, unfortunately some part of world including India, it is still underutilized crops and not fully exploited so far, though it is seen as an agronomically viable alternative crop to cereal, with a potential of fixing free nitrogen upto 300 kg N ha^-1.  It is a good source of lysine rich protein and good source of levadopa (L-dopa), a precursor of dopamine, can be potentially used as medicine for the treatment of Parkinson’s disease. The quick varietal improvement is being used as one of the important criteria in increasing the yield potential of this crop. In this context there is a need to evaluate and identify the stable genotype that could give standard performance when tested under diverse environment. The status of this crop could be changed as a Potential Crops instead of the underutilized by adopting improved, stable and high in nutritive value of genotypes in cultivation.
       
The major goal of crop improvement program is to increase stability and stabilize crop yield over average of environments. An important step in multi-environmental Trials (MLTs) is to assess the performance of improved genotypes for identifying promising varieties for large-scale propagation. The farmer would like variety which show high performance for yield and desired traits over as a wide range of environmental conditions. Hardly any work has been taken up on genetic improvement of this species so far in India. At a global level information on genetic improvement, adaptability and genotype environment interaction of faba bean is restricted to few publications. The aims of present study were: (i) to identify genotype that has high seed yield as well as most stable performance across different environment; (ii) to investigate the nature of relationship among non-parametric stability measures. To increase and stabilize the production and productivity, identification of suitable variety with high yielding potential are of the paramount  importance stability analysis helps in understanding the varietal adaptation under variable environments. Thus the use of highly adaptable variety is important in stabilizing productivity of over a seasons and region.

Plant materials
 
The material for the study consisted of set of 11 genotype of faba bean subjected to multi-locational seed yield trials for three years (2015-2018) at four locations viz., Faizabad, Hisar, Ludhiana and Ranchi. In each environment, eleven genotypes were tested in advance varietal trial promoted from initial varietal trial of Crop Improvement Programme of AICRN on Potential Crops. These genotypes (Table 1) were developed by various breeders at different research centre of AICRN on Potential Crops in India.


 
Experimental detail
 
At each environment a randomized complete block design was used with three replications. The experimental plot consisted of three row with 4 m. Row to row and plant to plant distances was kept at 30 cm and 10 cm, respectively at all environments. Seed yield was estimated by plot basis and converted into q/ha for each genotype at each tested location.
 
Statistical analysis
 
Test of significance of genotype environment interaction
When Bartlett’s test shows that the experiments have different error structure, the combined analysis requires a weighted analysis of variance taking_. The different steps involved in this case are:
(i) Using the G x E data on mean yields form the column totals  and determine W_jP_j  values.
(ii) Form the row totals 
(iii) Form crude sum of squares of entries in each column, S_{j .}
 (iv) Obtain the correction factor 
 
(v) Computation the different sum of squares as follows:
 


 

The interaction sum of squares I (I=T-G-E) has to be obtained.
       
Following Cochran (1937),  I may be approximated as x² value with the significant point of Chi-square corresponding to  degrees of freedom, n being the error degrees of freedom in different trials. If the experiments differ in size, as a rough approximation the average number of degrees of freedom per experiment is used in place of n. A comparison of the computed x² value with the significant point of Chi-squre corresponding to (n-4) (s-1) (t-1)/(n+t-3) degrees of freedom will provide the necessary test for GE interaction.
 
Non parametric stability analysis
 
The statistical procedures adopted for the stability analysis of the genotypes were those proposed by Huehn (1979), Nassar and Huehn (1987) and Thennarasu (1995). Huehn (1979) proposed the two measures: These are based on ranks of phenotypes in each environment. The phenotypic values of k genotypes are ranked within each environment (j = 1,2……N), giving the lowest value of rank (r_ij) and the highest value of rank k. Then under the biological concept a variety i is considered stable over a set of  environments if its ranks are similar over these environments.
Nassar and Huehn (1987) proposed the two measures: The genotypic stability, which is measured independently of genotypic effects. The actual ranks (r_ij) have to be based on the corrected y_ij = Y_ij - Y_i values. Rank rij and ri have been determined from these corrected (y_ij) values only. Nassar and Huhn (1987) proposed two other stability measures. Here the denominators are based on uncorrected ranks while the numerators on corrected ones. The statistics based on yield ranks of genotypes in each environment are expressed as follows:
Thennarasu’s (1995) non-parametric stability measures

These measures were improved by considering the rank median instead of rank mean in mean deviation formula, because mean deviation is minimum taken from the median. Here the denominators are based on uncorrected ranks while the numerators on corrected ones. The statistics based on yield ranks of genotypes in each environment are expressed as follows:
   
 In the above formulas, r_ij* is the rank of  y_ij and Md_i* are the mean and median ranks for adjusted values, while ri and Mdi are the same parameters computed from the original (unadjusted) values.
 
Combined stability index of genotype
 
A new approach based on yield stability performance calculated  based on the ranking of  the used stability measures of all the genotypes is recommended. t Genotypes having performance of stability measure K are ranked.  CSI(i) of ith genotype is the sum of rank of mean yield of ith genotype (RYi), rank of  mean rank of stability measures of ith genotype and  rank of  standard deviation (RSd(i)) of stability measures. The low value of combined stability index are considered for most stable and high yielding potential genotypes.
 
 
 

 
Correlation analysis
 
The stability parameters were compared using rank correlation in order to understand better the relationship among stability measures.
 
Statistical packages
 
All statistical analysis was done using MS-excel (2007), R, SPSS and SAS packages. All statistical analysis was done using MS-excel (2007), R, SPSS and SAS packages.

The test for significance of genotype x environment interaction
 
In our study, error mean square of the four experiments were heteroscedastic. This was confirmed by Bartlett’s test, which gave a highly significant value for the Chi-square.  Accordingly, the weighted analysis Cochran (1937), x² value with the significant point for test for GE interaction had been calculated. Thus the parametric analysis (x², df19 = 266.75*) shows the presence of GE interaction. If the interaction is so large as to cause rank changes among genotypes, then one can speak of rank interaction, which is also termed qualitative or cross-over interaction. In this type of interaction the true treatment differences vary not only in magnitude but also in direction.  In contrast, in quantitative or non-crossover interaction the treatment differences vary only in magnitude. Following this concept, we now try to assess the intensity of the interaction and draw suitable conclusions from a strictly non-parametric approach.
 
Stability analysis
       
The non-parametric measures are based on the rank of the cultivars across the environment / locations. They give equal weight to each location environments. The variety with less change in ranks are expected to be more stable. For simultaneous selection of most suitable genotypes (high yielding and stable), the calculated value of each non-parametric measures were plotted against mean seed yield performance separately (Table 2).
       


Each generated plot can be divided into four distinct sections; sections IV had low stability and low yield, section III low stability high seed yield and section II high stability and low seed yield and section I high stability and high seed yield. Therefore, the genotype falling in section I are the most favorable genotype (stable and high yielding). Accordingly genotypes from the section I are to be selected. The advanced lines HB 11-15, NDFB 16, HB 11-32, HB 12-8, HB 12-34 had the lowest value and ranked 3^rd, 10^th, 7^th, 2^nd and 1^st for seed yield. The highest Si(1) for genotype HB 12-42, NDFB 16-2, HB 11-12, HFB-1 (C) and Vikrant (C) indicated them to be highly unstable genotypes. The Fig 1-8 represent the plots portrayed by mean seed yield (q/ha) and divided in to four sections.
















       
The genotypes HB 12-34, HB 12-8, HB 11-15, having a high seed yield and small Si⁽¹⁾ values can be considered as a stable and well adapted in all environments. Si⁽²⁾ estimates are simply the variance of the ranks for each genotype across the locations. For the variance of the rank Si⁽²⁾  estimates may show relative stability. The genotype NDFB 16, HB 11-15, HB 11-32, HB 12-8, HB 12-37 are considered stable due to less value of  Si(2). HB 12-8 and HB 11-15, are ranked 2^nd and 3^rd for mean seed yield. The HB 12-8 and HB 11-15 had highest seed yield with less value of Si⁽²⁾. Thus HB 12-8 and  HB 11-15 are considered most stable as well as high yielding genotype.
       
The Si⁽³⁾ and Si⁽⁶⁾ non-parametric measures  were estimated by using the ranks which are given to genotypes on the basis of original mean data within the environment. The results of Si⁽³⁾  and Si⁽⁶⁾ indicated that genotype NDFB 16,  HB 11-32 and  HFB-1(C) rank 1^st, 2^nd and 3^rd respectively. They occupied 10^th, 7^th, 9^th and 5^th positions in mean seed yield as well.
       
Therefore, the HB-12-37 genotype was found to be stable and adapted to all environments. Based on estimates of Si⁽³⁾ and Si(⁶⁾ the genotype NDFB-16-2 and  HB-12-42 were found to be the most unstable genotypes. The plot of Si⁽³⁾ and Si⁽⁶⁾ for mean seed yield for Faba bean genotypes over locations were portrayed and divided in four sections. The genotype HB-12-37 having the high seed yield the small value of Si⁽³⁾ and Si⁽⁶⁾ can be considered as a stable genotype and well adapted to all environments. Section IV exhibits that the genotype are low yielding and small value of Si⁽³⁾ and Si⁽⁶⁾ indicate resistance to environmental fluctuations and therefore indicated specificity of adaptability to low yield environment.
       
Thennarasu’s (1995) non-parametric stability measures for seed yield 11 advance lines are presented in Table 3. According to these stability measures (NPi⁽¹⁾, NPi⁽²⁾, NPi⁽³⁾, NPi⁽⁴⁾ with minimum values were considered more stable. Based on NPi⁽¹⁾, the genotype HB-11-32, HB-12-37, HB-11-15, HB-12-34 with lower values were identified as stable in comparison to other genotype.


       
According to the values of NPi⁽²⁾, the genotype HB-11-32, HB-12-37 and Vikrant had the lowest values, while genotypes HB-12-34, NDFB-16-2 had the highest  values and were considered as relatively unstable in comparison to other genotypes. The genotype HB-11-32, HB-12-37, NDFB-16, Vikrant and HFB-1 had the lowest value of NPi⁽³⁾ and therefore, were the most stable genotypes. However, the genotypes HB-12- 34 and NDFB-16-2 with maximum values were identified as the unstable genotypes. Also, according to NPi⁽⁴⁾, genotype HB-11-32, HB-12-37 had the lowest value and therefore, were the most stable, but genotype HB-12-34, HB-12-8 had highest value of NPi⁽⁴⁾, were unstable genotype.
 
Combined stability index of genotype
 
A new approach known as a genotypic selection index was calculated by ranking the mean seed yield of the genotype across the environment and standard deviation of the rank of eight stability measures. (Sdi), the rank of standard deviation of the rank of eight stability measure were calculated. Genotypic Selection Index is measured in terms of sum of the rank yield, mean rank and the rank of standard deviation of rank stability measure. Low values of this parameter are considered for selection of the stable genotype and high yielding (Table 3). The advanced genotypes HB-12-37 (CSI(i) = 10),  HB-11-15 (CSI(i) = 11); HB-11-32 (CSI(i) = 14) were identified as the  most stable and high potential yielding genotype on the basis of index. Table 3 shows ranking frequencies for the stability measures and mean yield. The genotypes are divided in three layers (Top, Mid, Low) in each environment. The genotype in the top five ranks from each environment were categorized as the stable and adaptive. The stable genotype based on ranking frequency were  HB-12-37 (5), HB-11-15 (7) and HB-11-32.
 
Relationship between mean seed yield and stability measures
 
The relationship of different statistical measures with mean seed yields are presented in Table 4. The mean seed yield was significantly and positively correlated with Si⁽¹⁾,Si⁽²⁾ and NPi⁽¹⁾ (Category I), non-significantly and negative correlated with Si⁽³⁾, Si⁽⁶⁾, (Category II) and significant negatively correlated with NPi(2), NPi(3) and NPi(4) Category III). As the parameters under category I are most suitable to find out the best genotype, either of these three, (Si⁽¹⁾, Si⁽²⁾ and NPi⁽¹⁾ can suitably be used to find out best stable genotypes. As per these parameters, the best stable genotype  in the present case is HB-11-32 followed by HB-12-37 and HB-11-15).



 

This method of analysis is very useful for the selection of the high potential yielding genotypes for crop improvement programme. The eight stability measures used in this study quantified stability of varieties with respect to yield and stability. Simultaneous selection of genotypes for high yield and stability is useful for selection in refined manner. G x E interaction were highly significant (p<0.05), suggesting different response of genotypes to the test location/year. Based on low value of non-parametric measures and combined stability index, HB 12-37 was identified most stable and highest potential yielding genotype (Table 4).

The trials were carried out at different centre in plain region of India. The help extended by the director NBPGR, Network coordinator and breeders at each centre of AICRN on Potential Crops in providing the recorded data for compilation is acknowledged.