​Best Linear Unbiased Prediction with Additive Main and Multiplicative Interaction for Stability Analysis of Barley Genotypes Evaluated in Coordinated Program

G×E interaction has been assessed by the differential expression of genotypes over the environments (Ajay et al., 2020). AMMI model explains more information as comprises of additive main effects of genotype and environment and the multiplicative effect of G´E interaction (Gauch, 2013). Research studies observed the better performance of AMMI model than linear regression models and other multivariate procedures (Bocianowski et al., 2019). Several of AMMI based stability measures are available in literature (Zali et al., 2012; Agahi et al., 2020). Researchers have introduced different selection criteria for simultaneous selection of yield and stability (Rao and Prabhakaran 2005; Farshadfar, 2008; Farshadfar et al., 2011). BLUP and AMMI, two distinct approaches, utilized to distinguish the pattern from the random error components in G×E interactions (Piepho et al., 2008). The benefits of two important techniques AMMI and BLUP nested into a Superiority Index measure for stability and adaptability of genotypes (Olivoto et al., 2019).

Sixteen advanced genotypes at seven locations and eighteen genotypes at five locations were evaluated under research field trials during 2018-19 and 2019-20 cropping seasons respectively. Field trials were conducted at research centers in randomized complete block designs with four replications. Recommended agronomic practices were followed to harvest good yield. Details of genotype parentage along with environmental conditions were reflected in Table 1 and 2 for ready reference.
 

 

       
Stability measure weighted average of absolute scores has been calculated as
 
Where:
WAASB_i= Weighted average of absolute scores of the i^th genotype (or environment).
IPCA^ik= Score of the i^th genotype (or environment) in the k^th. 
IPCA and EP_k= Amount of the variance explained by the k^th IPCA.

Superiority index allowed weighting between yield and stability measures (WAASB) to select genotypes that combined high performance and stability as:
   
Where,
rG_i and rW_i = Rescaled values for yield and WAASB, respectively, for the ith genotype.
Gi and Wi = Yield and the WAASB values for i^th genotype.
SI= Superiority index for the i^th genotype that weights between yield and stability.
q_Y and q_S= Weights for yield and stability assumed to be of order 65 and 35 respectively in this study.
 
AMMI analysis was performed using AMMISOFT version 1.0, available at https://scs.cals.cornell.edu/people/hugh-gauch/ and SAS software version 9.3.

AMMI analysis of barley genotypes
 
First year of study 2018-19
 
Highly significant effects of environment (E), G×E interaction and genotypes (G) had been observed by AMMI analysis. Environment explained about 31.8% of the total sum of squares due to treatments significantly indicated diverse environments caused most of the variations in genotypes yield (Table 3). Significant proportion of G×E interaction deserved the stability estimation of genotypes over environments (Ajay et al., 2020). Genotypes explained only 9.3% of total sum of squares, whereas G´E interaction accounted for 38.4% of treatment variations in yield. More of G×E interaction sum of squares as compared to genotypes indicated the presence of genotypic differences across environments and complex G×E interaction for wheat yield. Partitioning of G´E interaction revealed that the first five multiplicative terms (IPCA1, IPCA2, IPCA3, IPCA4 and IPCA5) of AMMI were significant and explained 35.4%, 29.6%, 25.7%, 5.7% and 2.8% of interaction sum of squares, respectively. Total of significant components were 99.2% and remaining 0.8% was the residual or noise that discarded (Oyekunle et al., 2017).
 

 
Second year of study 2019-20
 
Highly significant effects of environment (E), G×E interaction and genotypes (G) had been observed by AMMI analysis. Environment explained about significantly 42.5% of the total sum of squares due to treatments indicating that diverse environments caused most of the variations in genotypes yield (Table 4). G×E interaction accounted for 30.3% whereas Genotypes contributed only 8.4% of total treatment variations in yield. Further analysis of G×E interaction observed three multiplicative terms (IPCA1, IPCA2 and IPCA3) explained 49.2%, 24.3% and 19.7% of interaction sum of squares, respectively. Total of these components were to the tune of 93.2% and remaining was noise that was discarded.
 

 
Ranking of barley genotypes as per AMMI based stability measures
 
First year of study 2018-19
 
Least value of absolute IPCA1 expressed by HUB268, DWRB201, RD2999 and higher value achieved by RD3002 (Table 5). Low values of (EV) associated with stable behaviour, the genotypes HUB267 followed by RD2999, NDB1173 expressed lower values and maximum value by KB1754 genotype. Measure SIPC identified HUB267 followed by RD2999, DWRB201 as of stable nature, whereas KB1754 would be of least stable type. Za measure considered absolute value of the relative contribution of IPCs to the interaction revealed DWRB201, HUB267 and RD2999 as genotypes with descending order of stability, whereas KB1754 genotype with the least stability. ASTAB measure observed genotypes HUB267 and DWRB201 as stable and KB1754 was least stable in this study (Rao and Prabhakaran 2005). All significant IPCAs had been considered by MASV and MASV1 measures. Values of MASV1 showed that the genotypes, RD2552, DWRB201 and RD2999 were most stable and DWRB201, HUB267 and RD2999 would be stable by MASV measure respectively (Ajay et al., 2020).  Measure W1 favoured RD3002 RD2552, RD3002 while as per W2, genotypes identified were RD3000, RD2552, RD3002 while W3 favoured RD3000, KB1754, RD3002 whereas W4 settled for KB1754, RD3000, NDB1445. Finally lower values of WAASB associated with stable nature of KB1754, RD3000, NDB1445 genotypes as for considered locations of the zone at the same time maximum deviation from the average performance across environments obtained by DWRB201.
 

 
Second year of study 2019-20
 
Least absolute values of IPCA1 expressed by RD2907, HUB274, KB1845 and higher value achieved by KB1815 (Table 6). Minimum values of EV associated with stable behaviour of RD3015, NDB1173, RD2907 genotypes and maximum value had by RD3016 genotype. SIPC measure identified RD2907, NDB1173 followed by RD3015 for the lower value, whereas RD3016 would be of least stable behaviour. Za measure revealed RD2907, NDB1173 and RD3015 genotypes in descending order of stability, whereas RD3016 genotype with the least stability. ASTAB measure observed genotypes NDB1173, RD2907 and RD3015 as most stable and genotype RD3016 was least stable in this study (Rao and Prabhakaran 2005). RD2907, NDB1173, RD3015 genotypes were of choice by of MASV1 and MASV measure observed RD2907, NDB1173, RD3015 as the stable genotypes while KB1815  would be unstable (Ajay et al., 2019). W1 measure selected KB1815, BH1032, RD2794 while measure W2 favoured KB1815, RD3016, HUB273 barley genotypes. Lower value of WAASB measure had observed for RD3016, KB1815, HUB273 and large value by RD2907.
 

 
Superiority indexes as per AMMI and BLUP: Barley genotypes
 
First year of study 2018-19
 
Stability alone is not a desirable selection criterion as stable genotypes may not be a high yielder, simultaneous use of yield and stability in a single measure is essential (Kang 1993; Farshadar et al., 2008). Simultaneous Selection Index also referred to as genotype stability index (GSI) or yield stability index (YSI) (Farshadar et al., 2011) was computed by adding the ranks of stability measure and mean yield of genotypes. Least ranks for IPCA1 measure exhibited by DWRB201, NDB1445 and HUB268 were considered as stable with high yield, whereas high values suggested as least stable yield for RD3002 genotype (Table 7). EV measure identified RD2552, NDB1173 andHUB267 whereas SPIC favoured DWRB201, RD2552 and HUB267genotypes. Genotypes DWRB201, RD2552 and DWRB207 possessed lower value of Za measure. ASTAB measure achieved the desirable lower values for DWRB201, DWRB207, HUB268. Composite measure MASV1 found RD2552, DWRB201, KB1762 and as per MASV ranks DWRB201, RD2552, KB1762 genotypes would be of choice for these locations of the zone.
 

       
Average yield of genotypes favoured NDB1445, RD2552, DWRB201 where Geometric adaptability index selected NDB1445, RD2552, DWRB201 while Harmonic mean of yield values pointed for NDB1445, DWRB201, RD2552 as suitable genotypes as far as considered locations are concerned. Superiority index while weighting 0.65 and 0.35 for average yield and stability found DWRB201, NDB1445 and RD2552 as of stable performance with high yield. Least magnitude of SIgm ranked DWRB201, NDB1445, DWRB207 as desirable genotypes while SIhm measure favoured DWRB201, DWRB207, NDB1445 barley genotypes.
 
Second year of study 2019-20
 
Ranks for IPCA1 measure favoured HUB274, RD2907, RD3017 as per the least values, whereas large values of KB1815 suggested unstable high yield (Table 8). EV measure settled for RD3017, NDB1173 and HUB274 genotypes. Minimum ranks of SPIC favoured RD3017, RD2907 andHUB274 genotypes. Lower value of Za measure possessed by RD3017, HUB274 andRD2907 genotypes for stable higher yield as compared to others genotypes. Barley genotypes RD3017, NDB1173, RD2907 were selected as per values of ASTAB measure accounted AMMI analysis with BLUP of genotypes yield values. Composite measure MASV1 selected RD3017, RD2907, NDB1173 while RD3017, RD2907, NDB1173 identified by MASV as genotypes of choice for these locations of the zone. Superiority index while weighting 0.65 and 0.35 for GAI and stability found RD3017, RD2907 and HUB274 as of stable performance with high yield. While considering Harmonic mean and stability identified RD2907, RD3017, NDB1173 barley genotypes.
 

       
Maximum yield expressed by RD3016 followed by KB1822 and RD3017 as good variation had been observed from 32.4 to 22.2 q/ha among genotypes. Genotypic adaptability index expressed the higher values by RD3016 KB1822, RD3017 whereas Harmonic mean of genotypic values ranked RD3016, KB1822, RD3017 barley genotypes. Superiority index had observed lower value expressed by RD3017, RD2907, HUB274 and large value by KB1815.
 
Biplot clustering pattern
 
First year of study 2018-19
 
Loadings of studied measures as per first two significant principal components were reflected in table 9. Biplot graphical analysis considered two PCAs accounted as 60.7% of variation of the stability measures accounted by both (Bocianowski et al., 2019). Studied measures grouped into three major clusters. MASV1 clubbed with ASTAB, EV, SIPC, Za, W3, WAASB and MASV measures (Fig 1). Yield based measures clubbed with corresponding SI measures. Measure IPCA1 and W2 maintained distance from measures and observed as outliers in different quadrant.
 

 

 
Second year of study 2019-20
 
Biplot graphical analysis based on first two significant principal component analysis (PCA) of the measures to explore the association if any among them (Fig 2). However, the loadings of the measures as per first two PCs were reflected in Table 10. Nearly 71.8% of variation of the stability measures accounted by two PCAs. Two major groups of measures depicted in Fig 2. Large number of AMMI based measures clubbed together and separate cluster of SI was also observed. Superiority indexes depicted very strong association ship irrespective of average, geometric or harmonic values of genotypes. AMMI based measures and stability measures as per absolute values of scores tend to be of strong correlated pattern.
 

 

Simultaneous use of stability and yield would be more appropriate to recommend high-yielding stable genotypes. Advantages of AMMI and BLUP had been combined in Superiority Indexes to increase the reliability of multi-locations trials analysis. The researchers may prioritize the productivity of a genotype rather than its stability (and vice-versa) as per the goal of crop breeding trials.

The barley genotypes were evaluated at research fields at coordinated centers of AICW & BIP across the country. First author sincerely acknowledges the hard work of all the staff for field evaluation and data recording of genotypes.