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The Journal of Heredity 2001:92(4)
© 2001 The American Genetic Association 92:367-371

Computer Note

SAS Applications for Tai's Stability Analysis and AMMI Model in Genotype x Environmental Interaction (GEI) Effects

M. Thillainathan, and G. C. J. Fernandez

From the Department of Applied Economics and Statistics 204, University of Nevada, Reno, NV 89557.

Address correspondence to George C. J. Fernandez at the address above.


   Abstract
Top
 Abstract
Introduction
 Methodology
 Results and Discussion
 Conclusion
 References
 
A user-friendly graphical data analysis to perform stability analysis of genotype x environmental interactions, using Tai's stability model and additive main effects and multiplicative interaction (AMMI) biplots, are presented here. This practical approach integrates statistical and graphical analysis tools available in SAS systems and provides user-friendly applications to perform complete stability analyses without writing SAS program statements or using pull-down menu interfaces by running the SAS macros in the background. By using this macro approach, the agronomists and plant breeders can effectively perform stability analysis and spend more time in data exploration, interpretation of graphs, and output, rather than debugging their program errors. The necessary MACRO-CALL files can be downloaded from the author's home page at http://www.ag.unr.edu/gf. The nature and the distinctive features of the graphics produced by these applications are illustrated by using published data.


   Introduction
Top
 Abstract
 Introduction
Methodology
 Results and Discussion
 Conclusion
 References
 
Selection of genotypes for wide adaptability could be severely limited in the presence of genotype x environment interaction (GEI). Therefore, it is necessary to assess the environmental sensitivity of genotypes in terms of higher yields and stability. For the past 40 years the concept of GEI and its stability statistics are being analyzed in different ways. In Tai's (1971) stability analysis, the interaction term is partitioned into two components: the linear response to environmental effects, which is measured by a statistic {alpha}, and the deviation from the linear response, which is measured by another statistic {lambda}. A perfectly stable variety has ({alpha}, {lambda}) = (-1,1) and a variety with average stability is expected to have ({alpha}, {lambda}) = (0,1). Tai's analysis also provides a method of obtaining the prediction interval for {alpha} = 0 and a confidence interval for {lambda} values, so that the genotypes can be distributed graphically in different stability regions of the Tai's plot.

The AMMI model is a hybrid analysis that incorporates both the additive and multiplicative components of the two-way data structure (Shafii et al. 1992; Shafii and Price 1998). The AMMI biplot analysis is considered to be an effective tool to diagnose the GEI patterns graphically. In AMMI, the additive portion is separated from interaction by analysis of variance (ANOVA). Then the principal components analysis (PCA), which provides a multiplicative model (Gabriel 1971; Zobel et al. 1988), is applied to analyze the interaction effect from the additive ANOVA model. The biplot display of PCA scores plotted against each other provides visual inspection and interpretation of the GEI components. Integrating biplot display and genotypic stability statistics enables geno-types to be grouped based on the similarity of performance across diverse environments.

Although many have published program codes for GEI studies in the past, these programs are not very user friendly. SAS program statements for performing Tai's stability analysis were published previously (Fernandez 1991). SAS program statements to perform the AMMI analysis have also been presented (Shafii and Price 1998). However, the SAS program-based approach is considered difficult and not user friendly to agronomists, since a good programming knowledge in SAS is essential to modify these published codes and to perform the GEI analyses. Therefore we have developed user-friendly SAS applications to perform improved Tai's stability analysis and AMMI models to analyze the GEI data.


   Methodology
Top
 Abstract
 Introduction
 Methodology
Results and Discussion
 Conclusion
 References
 
SAS version 6.12 for PC Win/NT was used to develop SAS MACRO programs and the relevant MACRO-CALL windows for Tai and AMMI analyses. The requirements for using these SAS macros are (1) a valid license to run the SAS software on your PC, and (2) SAS modules such as SAS/BASE, SAS/STAT, SAS/GRAPH, and SAS/QC should be installed in your computer to get the complete results.

The procedures for performing the user-friendly SAS macros are the following:

Tai's Stability Analysis
Step 1. Create a GEI SAS dataset or download the sample dataset (Shafii and Price 1998) from the home page at http://www.ag.unr.edu/gf. This data should contain the following variables:

  • Genotype variable (GEN), which is a categorical variable.
  • Environment variable (ENV), which is a categorical variable.
  • Blocks or replications (BLK); replication will be treated as blocks.
  • Response variable Y (e.g., yield), which is a continues numeric variable.

Step 2. Visit the home page (Fernandez 2000) at http://www.ag.unr.edu/gf, click the running dog, and follow the instructions given on the page to go to the download page. Then download Tai's SAS MACRO-CALL window file by clicking he sample demo link, and save this file to a disk and open it in the SAS session. Finally, click the run icon to open the TAIGEI MACRO-CALL window (Figure 1a).



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  		Figure 1.. Screen shots of (a) TAIGEI and (b) AMMI MACRO-CALL windows.

 
Step 3. Input the required values by following the instructions provided in he SAS MACRO-CALL window in TAIGEI (Figure 1a). In addition to inputting the SAS dataset name, environment variable name, response variable name, genotype variable name, and block variable name in the MACRO-CALL window, the users are given the following options:
  1. (1) Options for computing environmental index, which is a quantitative measure of the environmental potential.
  1. mean: The environmental index for a given environment (EIj = the arithmetic mean responses of all genotypes in the jth environment—the grand mean).
  2. median: The environmental index for a given environment (EIj = median response of all genotypes in the jth environment—median responses of all genotypes in all environments). This EI measure is recommenced when a few genotypes perform extremely low or high in some environments.
  3. geometric mean (GM): The environmental index for a given environment (EIj = the geometric mean response of all genotypes in the jth environment—the average of all geometric means). This EI measure is recommended when most genotypes perform extremely low or high in some environments.
  1. (2) Options for saving the SAS output and SAS graphics files. Users can select the folders to save the SAS output and the graphics files by inputting the folder names in the MACRO-CALL window. Also, the users can select one of the following graphic file format when saving the graphics produced by the SAS macro:
  • Display: Files are not saved, but displayed in the SAS graphics Window.
  • WP: CGM files suitable for including in Corel Word Perfect products.
  • WORD: CGM files suitable for including in Microsoft products.
  • GIF: GIF files suitable for including in HTML-based Web documents.

Step 4. Submit the SAS macro. After inputting all required fields, move your cursor to the last macro field, 10 (Figure 1a), and hit the Enter key to run the SAS macro. The MACRO-CALL window file automatically accesses the appropriate SAS macros from the Internet server, College of Agriculture, University of Nevada, and provide the users with the required exploratory graphs, stability estimates, and stability plots.

AMMI Analysis
Step 1. Create a GEI SAS dataset or download the sample dataset from the home page (Fernandez 2000) at http://www.ag.unr.edu/gf. This data should contain the same variables, listed above for running the Tai's stability analysis.

Step 2. Visit the home page (Fernandez 2000) at http://www.ag.unr.edu/gf, click the running dog, and follow the instructions given to go to the download page. Download the AMMI SAS MACRO-CALL window file by clicking the sample demo link, save this file to a disk, and open it in the SAS session. Click the run icon to open the AMMI MACRO-CALL window (Figure 1b).

Step 3. Input the required values by following the instructions provided in the SAS MACRO-CALL window in AMMI (Figure 1b). In addition to inputting the SAS dataset name, environment variable name, response variable name, genotype variable name, and block variable name as in the TAIGEI MACRO-CALL window, include the total number of environments used. Options for saving the SAS output and SAS graphics files are explained under Tai's analysis.

Step 4. Submit the SAS MACRO. Follow the instructions provided in Tai's analysis.


   Results and Discussion
Top
 Abstract
 Introduction
 Methodology
 Results and Discussion
Conclusion
 References
 
By running these SAS macros, the users can obtain the following descriptive graphics illustrating the nature of GEI.

Tai's Analysis
Figure 2 illustrates Tai's stability plot based on {alpha} and {lambda} statistics, which is similar to the published figure (Shafii and Price 1998). It can be argued that the {alpha} and {lambda} statistics derived from the GEI component values are not sufficient to select the higher-yielding and stable genotypes, therefore the mean yield values also must be considered when making the decision. The lack of information about the average response is a shortcoming in Tai's stability plot. To overcome this limitation we have included two additional plots, which include average response value and Tai's stability statistics in the same plot. The relationship between the mean response and {lambda} values for each genotype is illustrated in a scatter plot (Figure 3). The 95percnt; confidence region for the {lambda} statistic is illustrated as two horizontal lines. The diameter of the circle in the scatter plot is proportional to Tai's {alpha} statistic. A three-dimensional plot of response mean versus Tai's stability estimates ({alpha} and {lambda}) is shown in Figure 4. This three-dimensional plot is useful to visually evaluate the yield potential and stability estimates of the genotypes. The different symbols used in the three-dimensional plot separate the genotypes based on the statistical significance of Tai's stability statistics.



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  		Figure 2.. Tai's (1971) stability plot showing different stability regions based on {alpha} and {lambda} statistics. The hyperbola represents a 95percnt; prediction interval for {alpha} = 0; The vertical lines are the limits of a 95percnt; confidence interval for {lambda} = 1.

 


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  		Figure 3.. Relationships between Tai's {alpha} and {lambda} statistics and the genotypic mean response. The magnitude of the {alpha} statistic is proportional to the diameter of the bubbles in the plot.

 


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  		Figure 4.. Three-dimensional plot for Tai's {alpha} and {lambda} statistics versus the genotypic mean response. Different stability regions are denoted by different symbols.

 
AMMI Analysis
Two AMMI analysis biplots shown in Figures 5 and 6 were obtained by running SAS macro for AMMI analysis, and these two biplots are similar to the published figures (Shafii and Price 1998). In the first biplot (Figure 5), the first and second principal component (PCA1 and PCA2) scores for the genotypes and environments are displayed. In the second biplot, the first PCA scores and the mean yields for genotype and the environments are displayed.



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  		Figure 5.. Biplot display of AMMI analysis for PCA component 2 versus PCA component 1 for six genotypes evaluated in 27 environments.

 


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  		Figure 6.. Biplot display of AMMI analysis for PCA component 1 versus mean responses for six genotypes evaluated in 27 environments.

 

   Conclusion
Top
 Abstract
 Introduction
 Methodology
 Results and Discussion
 Conclusion
References
 
The availability of free and user-friendly SAS statistical and graphical applications to analyze GEI, based on Tai's stability analysis and AMMI biplot analysis, are reported here. The steps involved in downloading the necessary MACRO-CALL files from the author's home page (http://www.ag.unr.edu/gf) and the instructions for running the SAS macros are presented in this article. The nature and distinctive features of the graphics produced by these applications are illustrated by using published data (Shafii and Price 1998).


   Footnotes
 
Corresponding Editor: Bruce S. Weir

Received September 7, 2000
Accepted April 30, 2001


   References
Top
 Abstract
 Introduction
 Methodology
 Results and Discussion
 Conclusion
 References
 

    Gabriel KR, 1971. The biplot graphic display of matrices with application to principal component analysis. Biometrika 58:453–467.[Abstract/Free Full Text]

    Fernandez GCJ, 1991. Analysis of genotype x environment interaction by stability estimates. HortScience 26:947–950.[Free Full Text]

    Fernandez GCJ, 2000. Quick results from statistical analysis (visited/last modified August 16, 2000). http://www.ag.unr.edu/gf.

    Shafii B, Mahler KA, Price WJ, and Auld DL, 1992. Genotype by environment interaction effects on winter rapeseed yield and oil content. Crop Sci 32:922–927.[Abstract/Free Full Text]

    Shafii B and Price WJ, 1998. Analysis of genotype-by-environment interaction using the additive main effects and multiplicative interaction model and stability estimates. J Agric Biol Environ Stat 3:335–345. http://www.uidaho.edu/ag/statprog/ammi/.

    Tai GCC, 1971. Genotypic stability analysis and its application to potato regional trials. Crop Sci 11:184–190.[Abstract/Free Full Text]

    Zobel RW, Wright MJ, and Gauch HG, 1988. Statistical analysis of a yield trial. Agron J 80:388–393.[Abstract/Free Full Text]


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