AMMI analysis for salt tolerance in bread wheat genotypes

Dharmendra Singh1, 2, S. K. Singh2 and K. N. Singh1
1 Central Soil Salinity Research Institute, Karnal-132001, India
2 Directorate of Wheat Research, Karnal-132001, India

Corresponding author: Dharmendra Singh

E-mail: dsingh4678@rediffmail.com

Abstract

Grain yield data of 15 bread wheat genotypes evaluated under four salt stress conditions for two consecutive years was subjected to the ordinary analysis of variance (ANOVA) and the additive main-effect and multiplicative interaction (AMMI) analysis. The ANOVA indicated that the variance due to genotypes (52.26%) was maximum followed by the variance due to environment (36.05%) and genotype x environments interaction (13.88%) was considered as residual. Thus, the ordinary ANOVA model accounted only for 88.31 per cent of the trial sum of squares that concentrated only on the genotype effects and environment effects. The bioplot from AMMI1 parameters provided the comprehensive understanding of the pattern of the data and indicated that the specifically adapted genotypes would away from the line with IPCA1=0 and next to grand mean level. Thus, 6 genotypes viz., KRL 3-4, Kharchia 65, KRL 99, KRL 19, Amery, BT- Schomburgk and PBW 343  showed general adaptability to all location as these were scattered at the right-hand side of the grand mean level and close to IPCA1 score =0 line. However, environments E1, E3, E4, E5, E6, and E7 had smallest (near to zero) IPCA scores and therefore, relative ranking (not absolute yields) of genotype would be fairly stable in these environments. In addition to the smallest interaction effects, the sites E1, E3, E5 and E7 were high yielding (environment mean yield > grand mean) and thus, deemed to be fit for growing wheat crop in general.

Key Words: Wheat grain yield, G x E interaction, AMMI analysis, Adaptability.                         

              

Introduction         

Excess amount of salt in the soil adversely affects plant growth and development. Nearly 20% of the world’s cultivated area and nearly half of the world’s irrigated lands are affected by salinity (Ashraf 1994, Bray et al. 2000). Increased salt tolerance in crops is widely recognized as an effective way to overcome the limitations of crop production in a salinized area (Munns and James 2003). For improving the salt stress tolerance of crop varieties by plant breeding, it is necessary to identify donor genotypes that have proven tolerance to salt stress during all the growth stages. Genotype x environments (G x E) interaction plays a major role in evaluation of genotypes under different environment (salinity stress) to identify genotypes suitable to different stresses (Munns and James 2003). With an aim to make recommendations about the suitable genotype to be released as varieties, yield trials are conducted with a set of genotypes at different salinity stress environments which is always affected by G x E interactions (Zobel 1990). A significant G x E interaction for a quantitative traits, such as yield can seriously limits efforts in selecting superior genotypes for both new crop production and improved cultivars development (Kang 1990) and would reduce the usefulness of subsequent analysis of means and inferences that would otherwise be valid.

The analysis of variance (ANOVA) is useful for identifying the sources of variability but it provides no insight into the particular pattern of the underlying interaction. On the other hand, the AMMI analysis model is additive and effectively describes the main (additive) effects, while the interaction (residual from the additive model) is non additive and requires other techniques, such as principal component analysis (PCA) to identify interaction patterns. Thus, ANOVA and PCA models combine to constitute the additive Main-effect and Multiplicative Interaction (AMMI) model (Gauche and Zobel 1988, Zobel et al. 1988). The AMMI model is, therefore, a hybrid statistical model incorporating both ANOVA (for additive component) and PCA (for multiplicative component) for analyzing two-way (genotype-by-environment) data structure. The model has, in recent past, been recommended for statistical analysis of yield trials, and was preferred over other customary statistical analyses, such as ordinary ANOVA, principal component analysis and linear regression analysis (Gauch 1988, Zobel 1988). An experiment was conducted to evaluate the performance of the genotypes under different salt stress environments with the following objective (i) to determine the nature and magnitude of G x E interaction effect on grain yield in diverse environment, (ii) to determine environment where wheat genotypes would be adapted and produce economically competitive yields.                                           

 

Materials and methods

Fifteen genotypes (KRL 99, Schomburg, KRL 105, HD 4530, Perenjori, HD 2009, PBW 343, BT-Schomburg, Amery, KRL 3-4, Ducula 4, Cunderdin, KRL 19, Camm, and Kharchia 65) were evaluated in a randomised block design with three replicates at Central Soil Salinity Research Institute, Karnal  in micro plot under four salt stress environments namely Normal (pH2 :8.2), Saline (5.9ds/m), Sodic Low (pH2 :9.2) and Sodic High (pH2 :9.4) for two consecutive years 2004-05 and 2005-06. The yield was recorded and the data was subjected to ordinary ANOVA and AMMI model for analysis. The basic liner model (the ANOVA model) used in the analysis of yield trial is of the from:

γij = μ+gi+ej+δij

Where γij  is the observed response value (e.g., yield) of genotype (cultivar) i in environment j; μ is the grand mean; gi is the effect for genotype i (deviation of g from μ), i=1,…k; ej is the effect for environment j (deviation of e from μ), j =1,…n; and δij is the interaction (=γij- γi- γj + γ..). It is possible to partition the interaction component δij into the sum of multiplicative functions of i and j (Mandel 1971).

γij = μ+gi+ej + Σλk γikαjk +εij

Which yields the AMMI of model λk is the eigen value of interaction principal components axis (IPCA) k, γik and αjk are correspondingly the genotype and environment eigenvectors (i.e., IPCA scores) for the axis k, N is the number of axes retained in the model, and εij is the residual.

Beginning with the ordinary ANOVA procedure (Snedecor and Cocharan 1980) for two way analysis of variance, the AMMI analysis first separates additive variance (μ, gi and ej) from the multiplicative variance (interaction), and then applies PCA to the interaction, i.e., to the residual portion of the ANOVA model to extract a new set of coordinate axes which account more effectively for the interaction patterns (Gauch 1988, Gauch and Zobel 1988, Nachit 1992). Direct estimation of G x E interaction is obtained by the product of IPCA score (s) (λk0.5γik) times the environment IPCA score(s) (λk0.5γjk). The eigen values in PCA are equivalent to sum of squares, and the degrees of of freedom for IPCA axes were calculated as Gollob (1968): df= G+E-1-2k for axis k.

AMMI generates a family of models with different values of N. The simplest model with AMMI0 with N equal to zero considers only the additive effects,namely genotypes and environments means to explain the data matrix. The second model AMMI1 considers main effect and one interaction principal component axis to interpret residual matrix. Similarly, AMMI2 involves main effects and two interaction principal component axes for non additive (interaction) variation, and so on. When one interaction PCA axis account for most G x E, a feature of AMMI model is the biplot procedure in which genotypes and environment-taking mean values on abscissa and IPCA1 scores on ordinate are plotted on the same diagram, facilitating inference about specific interactions as indicated by the sign and magnitude of IPCA1 values of individual genotypes and environments. The statistical analyses were carried out by the software (Gauch 1986).  

 

Results and discussion

Partitioning of variance

Since AMMI model uses additive ANOVA for partitioning of variance due to genotype and environments and analyses its residual (i.e., G x E interaction), analysis for AMMI (Table 1) can also be used for a study of the results of ANOVA. It can be seen from this table that the mean squares for genotypes, environments and G x G interaction were found to be highly significant. This suggested that broad range of diversity existed among genotypes and among environment and that the performance of genotype was differential over environments. Of the total treatment variation (trails SS), the proportion of variation of variance due to difference in genotypes was largest (52.26 per cent) followed by the variance due to G x E interactions (13.88 %: considered as residual in case of ANOVA), and variance due to environment (36.05 %) Thus, ordinary Anova model accounted only for 88.31 per cent of the trail SS concentrating only on the genotype effects and environment effects. Therefore, it could tell use (through statistical test ) whether genotypes, environments and genotype x environment interaction exerted a significant effect, but it did not tell us which genotypes environments and genotype x environment combinations were responsible, nor did it tell us how their responses differ. Conclusively, ANOVA provided no insight into the particular patterns of genotypes or environments that gave rise to interactions, but described only the main effects effectively. These results were also confirmed to the observations made by Snedecor and Cochran 1980. Thus, in the present investigation, ANOVA model was not found to be adequate for analyzing the bread wheat yield data, as G x E interactions were highly significant. Therefore, ANOVA model was combined with PCA model to further analyze the residuals of the ANOVA model, which infact contains G x E interaction. Gauch (1988) suggested further analysis of the effects of G x E interactions even if they are indicated to be non -significant by an F-test in ANOVA. The residual SS which accounted for 33.04 % of the G x E SS with 13.88 % of G x E df was also found to be highly significant. This situation seems to arise due to the presence of highly levels uncontrolled variation but not due to the real G x E interaction. Above analysis, however, seems to suggest the presence of a complex, multidimensional variation in the genotype-by-environment data as the first seven IPCA axes were demonstrated to be highly significant by an F-test (P>0.001). The AMMI models with many IPCA axes are expected to involve rather more noise than the highly complex interactions among genotypes and environment. Further, if the AMMI model incluses more than one IPCA axes, assessment and presentation of genetic stability are not as that from the AMMI model (Gauch 1982, Gauch 1988, Gauch and Zobel 1988, Gauch and Zobel 1994, Nachit et al. 1992). The second and higher IPCA axes, despite significant in the present study, were polled in to residual. Thus, AMMI model (AMMI model with first IPCA axis) was accepted for further study.

 

AMMI1 Biplot: Interpretting specific pattern

The results of AMMI1 analysis can also be easily comprehended with help AMMI1 biplot as presented in Fig. 1. The mean performance and IPCA1 scores for both the genotypes and environment used to construct the biplot (Fig. 1) are presented in Table 2 and Table 3. The biplot --- a graphical representation --- from AMMI1 analysis is a used tool in under standing more comprehensively the specific pattern of main effect and G x E interactions of both the genotypes and environments simultaneously (Crossa et al 1991, Kempton1984, Zobel et al. 1988). The bioplot of parameters accounted for 88.31 per cent of the trail SS. It is clear from the biplot that the points for environment were more scattered than the point for genotypes; this indicated that variability due to environments was higher than that due to genotypes difference. This is also evident from the ANOVA. In Fig. 1, displacement along the abscissa (horizontal axix) reflects difference in main effects whereas displacement along the ordinate (vertical axix) exhibits differences in the interaction effects. When a genotype and an environment fall in the upper or lower portion from the line indicating IPCA1=0 in the biplot, their interactions is positive. However, the genotypes and environments of opposite portions from the IPCA1=0 line show negative interaction. In other words the genotypes and environments with similar signs (either positive or negative) of IPCA1 scores exhibit negative positive and vice versa. Thus, with the help of biplot, the results of present investigation can be interpreted as follow:

1. Identifying high yielding stable genotypes

According to the AMMI model, the genotypes which are characterized by means greater than grand mean and the IPCA score nearly zero are considered as generally adaptable to all environment. However, the genotype with high mean performance and with large value of IPCA score are consider as having specific adaptability to the environments. AMMI Analysis was also conducted and the stability of genotypes was predicted on the basis of mean performance and the magnitude of IPCA1 scores in soybean (Zobel et al. 1988), maize and wheat (Crossa et al. 1990, 1991), sorghum (Zavala-Garcia et al. 1992) and barley (Ramagossa et al. 1993). On the bioplot, the points for the generally adapted genotypes would be at right hand side of grand mean levels (this suggests high mean performance) and close to the line showing IPCA=0 and (this suggests negligible or no G x E Interaction). However, the points for the specifically adapted genotypes would be away from the line with IPCA1=0 and next to grand mean level. Thus  it was from Fig 1 that 6 genotypes, viz., KRL 3-4, Kharchia 65, KRL 99, KRL 19, Amery,BT- Schomburgk and PBW 343  which were scattered at the right-hand side of the grand mean level and close to IPCA1 score =0 line, were declared by the AMMI1 model as having general adaptability to all location. However KRL 105 was equipped with high mean and large IPCA score, hence specifically suited to the favourable environment. Favourable environment for these genotypes can be characterized as with high mean and large IPCA score with same sign as of genotype IPCA1 score. Similar sign of IPCA1 scores implies positive interaction and thus will suggest higher yield of genotypes.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 

2. Identifying favorable environments for wheat genotypes

Environment that appears almost in a perpendicular line have similar means and those that fall almost in a horizontal line have similar interaction pattern. AMMI bioplot (Fig.1) thus exhibited that environment differed in maim effects but they exhibited nearly similar interactions. The environment E1 and E5 had similar main effect but differed in interaction with genotypes. The environment E2, E3, E4, E6 and E8 differed in both main effect and interactions; the ranking in such environment are likely to be quite variable, thus making it complex to produce variety recommendations. Further the environment E1, E3, E5 and E7 were highest yielding and highly interacting, hence are most suitable only for the specifically adapted genotypes. However, environment E1, E3, E4, E5, E6, E7, and all had smallest (near to zero) IPCA scores; relative ranking (not absolute yields) of genotype would be fairly stable in this environment. In addition to the smallest interaction effects, the sites E1, E3, E5 and E7 were high yielding (environment mean yield > grand mean) and therefore, deemed to be suitable for growing wheat crop in general. Selection of environment and requirement of environment for wheat crop may, therefore, be recommended on the basis of the main features of the respective environments. The results confirmed that analysis with its biplot is a very useful tool in analyzing yield trial data. It explains comprehensively both the effects due to genotypes and environments and also their interaction patterns. ANOVA could explain only the genotypes and environments but not interaction which is a significant feature yield trial.        

 

References

Ashraf M (1994) Breeding for salinity tolerance in plants. Crit Rev Plant Sci 13: 17-42.

Bray EA, Bailey-Serres J and Weretilnyk E (2000) Responses to abiotic stresses. In: Biochemistry and Molecular Biology of Plants. Gruissem W, Buchnnan B and Jones R eds. American Society of Plant Physiologists, Rockviile, MD, 1158-1249.

Crossa J, Gauch HG and Zobe RW (1990) Additive main effect and multiplicative interaction analysis of two international maize cultivar trails. Crop Science 30: 493-500.

Crosa J, Fox PN, Pfeiffer WH, Rajaram S and Guch HG (1991) AMMI adjustment for statistical analysis of an international yield trial. Theor Appl Genet 81 :27-37.

Gauch HG (1982) Noise reduction by eigenvector ordination. Ecology  63: 1643- 1649.

Gauch HG (1986) MATMODEL:A FORTRAN-77 programe for AMMI, ANOVA and Finaly Wilkinson regression models for two–way data matrices with or without replication. Microcomputer Power, Ithaca, New York.

Gauch HG (1988) Model selection and validation for yield trials with interaction. Biometrics 34: 705-715.

Gauch HG and Zobel RW (1988). Predictive and postdicctive success of statistical analyses of yield trial. Theor Appl Genet 76:1-10.

Gauch HG and Zobel RW (1994) AMMI analysis of yield trials. Contribution from Soil, Crop and Atmospheric Science and USDA-ARSNAA, Bradfield Hall, Cornell University, Ithaca,NY14853-1901.

Gollob HF (1968) A ststistical model which combines feature of factor analysis and analysis of  variance techniques. Psychometrika 33: 73-175.

Kang MS (1990) Genotype by Environment Interaction in Plant Breeding. Department of Agronomy, Louisiana State University, Baton Rouge, Louisiana.

Kempton RA (1984) The use of biplots in interpreting variety by environment interactions. J Agric Sci 103: 123-135.

Mandel  J (1971) A new analysis of variance model for nonadditive data. Technometrics 13: 1-18.

Munns R and James RA (2003) Screening method for salinity tolerance: a case study with tetraploid wheat. Plant and Soil  253: 201-208.

Nachit MM, Nachit G, Ketata H, Gauch HG and Zobel RW (1992) Use of AMMI and liner regression models to analyze genotype environment interaction in Durum wheat. Theor Appl Genet 83: 597-601.

Romagossa I and  Molina Cano JL (1993) Intergration of statistical and physiological analyses of adaptation of near isogenic barley lines. Appl Genet 86: 822-826.

Snedecor GW and Cochran WG (1980) Statistical Methods.7th Edn. Iowa State University Press Ames 1A. pp264-265.

Zaval-Garcia F, Barmal-Cox PJ and Estian JD (1992) Potential grain from selection for yield stability for grain sorghum populations. Appl Genet 85: 112-119.

Zobel RW, Wright MG and Gauch HG (1988) Statistical analysis of yield trial. Agron J 80: 388-393. 

Zobel RW (1990) A powerful statistical model for understanding genotype by environment interaction. In: ‘Genotype by Environment Interaction in Plant Breeding’ (Ed., M.S.Kang, 1990), pp 126-140. Department of Agronomy, Louisiana State University, Baton Rouge, Louisiana.