User-friendly SAS application for AMMI analysis of Genotype x Environment interaction (GEI)

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Several multivariate procedures proposed to explore GEI include principal component analysis (PCA), additive main effects and multiplicative interactions (AMMI) and genotype plus GEI biplot analysis. AMMI extracts genotype and environment main effects and uses interaction principal components (PCA) to explain patterns in the GE interaction or residual matrix, which provides a multiplicative model. The AMMI biplot analysis is an effective tool to diagnose the GEI patterns graphically. The AMMI model combines ANOVA for main effects of the genotype and environment with principal components analysis of GEI and uses PCA for visualizing the GEI in what is known as a biplot diagram (Zobel et al., 1988; Gabriel 1971). 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 genotypes to be screened and selected in a plant breeding program.

A user-friendly SAS macro application AMMI, using Microsoft Windowing Environment to perform stability analysis of GEI was published by Thillainathan and Fernandez (2001). Several agronomists and horticulturists used this user-friendly SAS macro application to assess genotypic stability estimates (47 citations; Semantic Scholar 2021). However, this originally published macro application is not compatible with SAS Enterprise Guide or in SAS studio environment. Therefore, an enhanced user-friendly SAS macro application that is compatible in SAS Display manager, SAS Enterprise Guide, SAS Studio is developed and presented here.

AMMI User-friendly SAS macro application:

First download and unzip the AMMI.Zip specified in this post.  SAS version 9.4 for was used to develop SAS MACRO programs and the relevant MACRO-CALL file for AMMI analysis. The requirements for using this SAS macro 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/IML should be installed to get complete results.

The steps for performing the user-friendly SAS macros are:

Step1: Create a temporary SAS data file like the example data file included with the zip file. This data should contain the following variables:

• Variable Genotype (GEN), which is a categorical variable.
• Variable Environment (ENV), which is also a categorical variable.
• Optional: Variable Blocks or replications (BLK); Replication will be treated as fixed blocks.
• Response variable (s) Y (e.g., yield), which is a continues variable.

Step2:  Open the AMMI macro-call file in your preferred SAS environment. 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 file, following options are given to:

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 file. Also, the users can select one of the following ODS output file format when saving the output

produced by the SAS macro TAIGEI:

Display: Files are not saved but displayed in the SAS results Window.

PDF: PDF files suitable for PDF format

WORD: RTF files suitable for including in Microsoft products.

WEB: HTML files suitable for including in HTML-based Web documents.

Step 4. Submit the SAS macro call file.

After inputting all required fields (Figure 1), Run the macro-call file. The MACRO-CALL file automatically accesses the SAS AMMI macro from the specified location. After a successful run, this macro will generate following stability biplots.

 

Figure 1 Sample macro-call input for the AMMI macro Figure 2 Genotypic response mean and the first three PCA genotypic component scores from AMMI analysis

The AMMI model is a hybrid analysis that incorporates both the additive and multiplicative components of the two-way data structure. The AMMI biplot analysis is 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 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 genotypes to be grouped based on the similarity of performance across diverse environments.

In the first biplot (Figure 3), the first and second principal component (PCA1 and PCA2) scores for the genotypes and environments are displayed. In the second biplot (Figure 4), the first PCA scores and the mean yields for genotype and the environments are displayed. Purchase (1997) suggested an equation for AMMI analysis called AMMI stability value (ASV). PCA1 has a stronger effect than PCA2 in the sum of square G × E; therefore, a factor was added to PCA1 for the symmetrical discrepancy with PCA2, in such a way that, the role of PCA1 and PCA2 fit in the sum of square G × E. In this equation, the most stable genotype and test environment have minimum ASV (Movahedi et al., 2020).

Figure 3 Biplot of genotype and environment scores using first two PC scores from AMMI analysis Figure 4 Scatter plot of PCA1 by genotype and environment means from AMMI analysis

References

1. Gabriel, K.R. 1971. The biplot graphic display of matrices with application to principal component analysis. Biometrika 58:453–467.
2. Kempton, R.A. 1984. The use of biplots in interpreting variety by environment interactions. J. Agric. Sci. 103:123–135
3. Gauch, H.G. 2006. Statistical analysis of yield trials by AMMI and GGE. Crop Sci. 46:1488–1500.
4. Zobel et al., 1988 R.W. Zobel, M.J. Wright, H.G. Gauch 1988 Statistical analysis of a yield trial. Agron J, 80 (3) pp. 388-393
5. Thillinathan, M and G.C.J. Fernandez. 2001 SAS applications for Tai’s Stability analysis and AMMI model in Genotype x Environment Interactions (GEI) effects. J. Heridity. 93(4):367-371
6. Semantic Scholar (2021) https://www.semanticscholar.org/paper/SAS-applications-for-Tai%27s-stability-analysis-and-x-Thillain...
7. Purchase JL. Parametric analysis to describe genotype × environment interaction and yield stability in winter wheat [PhD thesis]. Bloemfontein: University of the Orange Free State; 1997. [Google Scholar].
8. Movahedi H, Mostafavi K, Shams M & Golparvar A R (2020) AMMI analysis of genotype × environment interaction on grain yield of sesame (Sesamum indicum L.) genotypes in Iran, Biotechnology & Biotechnological Equipment, 34:1, 1013-1018