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I proposed a new stress tolerance index (STI) (Fernandez, 1992) that favors high yielding under both unstressed and stressed environments. Inter-relationships among all known selection criteria for identifying superior genotypes were also investigated in this paper. According to Google Scholar (2021) more than 1800 research articles cited this STI and favored this measure to identify both high yielding and stress tolerant genotypes. To facilitate easy and efficient computation of STI and its related measures, I have developed a user-friendly SAS macro application called STI macro. SAS software 9.4 was used to develop this macro application. By using this macro approach, agronomists and plant breeders can effectively perform stress tolerance analysis and spend more time in data exploration, interpretation of graphs, and output, rather than debugging their program errors. STI User-friendly SAS macro application: First download and unzip the STI.zip file specified in this post. 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 should be installed to get complete results.   The steps for performing the user-friendly SAS macros are:   Step1: Create a SAS data or an excel sheet 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. Response means under unstressed (Yp) and stressed environment (Ys) that are continues variables. Treatment variable: Categorical variable identifying different level of stress treatments. Step2:  Open the STI macro-call file in your preferred SAS environment. In addition to inputting the dataset name, response variable name under stressed and unstressed environment, genotype variable name, and treatment variable identifying stress level in the MACRO-CALL file, following options are available to specify in the STI macro.:   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 3. Submit the SAS macro call file. After inputting all required fields (Figure 2), Run the macro-call file. The MACRO-CALL file automatically accesses the SAS STI macro from the specified location. After a successful run, this macro will generate following output.     Following output tables and graphics are generated when you run the STI macro applications:         References Fernandez, G.C.J. (1992) Effective Selection Criteria for Assessing Stress Tolerance. In: Kuo, C.G., Ed., Proceedings of the International Symposium on Adaptation of Vegetables and Other Food Crops in Temperature and Water Stress, AVRDC Publication, Tainan, 257-270.   Google scholar (2021) https://scholar.google.com/citations?user=YJtknlYAAAAJ&hl=en&scioq=stress+tolerance+index++%27gcj+fernandez%27&oi=sra   ... View more

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 Gabriel, K.R. 1971. The biplot graphic display of matrices with application to principal component analysis. Biometrika 58:453–467. Kempton, R.A. 1984. The use of biplots in interpreting variety by environment interactions. J. Agric. Sci. 103:123–135 Gauch, H.G. 2006. Statistical analysis of yield trials by AMMI and GGE. Crop Sci. 46:1488–1500. 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 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 Semantic Scholar (2021) https://www.semanticscholar.org/paper/SAS-applications-for-Tai%27s-stability-analysis-and-x-Thillainathan-Fernandez/12e7be3db72303c8a816446789ace0739fa69804. 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]. 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   ... View more

Tai (1971) proposed partitioning the GEI effect of the i th genotype into stability statistics α i and λ i , based on the principles of structural relationship analysis. The α i measures the linear response of the environmental effect, and λ i measures the deviation from the linear response in terms of the magnitude of the error variance. A genotype having α i = 0 and λ i = 1 was considered of average stability. Approximate procedures for testing the hypotheses α i = 0 and λ i = 1 were given, and a method of obtaining the prediction interval for α i = 0 and a confidence interval for λ i values so that genotypes can be distributed in different stability regions were also suggested (Tai, 1971).   A user-friendly SAS macro application TAIGEI, using Microsoft Windowing Environment to perform stability analysis of genotype X environmental interactions, using Tai’s stability model 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.   TAIGEI User-friendly SAS macro application: First download and unzip the TAIGEI.Zip specified in this post.  SAS version 9.4 for was used to develop SAS MACRO programs and the relevant MACRO-CALL file for Tai’s Stability 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/QC 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. 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 TAIGEI 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: (1) Options for computing environmental index, which is a quantitative measure of the environmental potential. mean: The environmental index for a given environment (EI j = the arithmetic mean responses of all genotypes in the j th environment – the grand mean). median: The environmental index for a given environment (EI j = median response of all genotypes in the j th 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. geometric mean (GM): The environmental index for a given environment (EI j = the geometric mean response of all genotypes in the j th environment- the average of all geometric means). This EI measure is recommended when most genotypes perform extremely low or high in some environments.   (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 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 TAIGEI macro from the specified location. After a successful run, this macro will generate following exploratory graphs, stability estimates, and stability plots. Figure 1 Sample macro-call input for the TAIGEI macro-call     Exploratory graphical analysis of GEI components. Two exploratory graphical plots 1) Box plot (Figure 2)   2) histograms (Figure 3) of GEI component by genotype are automatically generated when you run this macro. Box plots useful to identify any outlying environments and the histograms are useful to rank the genotypes by their GEI component variation.   Figure 2 Boxplot display of GEI component by genotypes. Outlying environments associated with each genotype is also identified.   Figure 3Figure 2 Comparative histogram display of GEI component by genotypes. Total variation associated with each genotype is also identified.   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 α i , and the deviation from the linear response, which is measured by another statistic λ i . The slope coefficients, α i by each genotype are presented in Figure 4. Figure 4 Regression plots of GEI component on Environmental Index by each genotype     Figure 5 Tai's Stability estimates, (α, λi), their significance levels and Lsmeans of response by genotypes   Tai’s stability estimates, their statistical significance and Least square means of each genotypes are presented in Figure 5. A genotype with average stability is expected to have (α, λ i ) = (0,1). Tai’s analysis also provides a method of obtaining the prediction interval for α i ,  = 0 and a confidence interval for λ values, so that the genotypes can be distributed graphically in different stability regions of the Tai’s plot. Figure 6 illustrates Tai’s stability plot based on α and λ statistics. It can be argued that the α and λ 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, I have included one additional plot, which include Lsmean valued and Tai’s stability statistics in the same plot. This three-dimensional plot of response lsmean versus Tai’s stability estimates (α and α) is shown in Figure 7. 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. This 3-d plot of yield by stability estimates is more informative to plant breeders wishing to select higher yielding stable genotypes.   Figure 6 Tai's stability plot showing different stability regions based on (α, λi), stability statistics     Figure 7 Three dimension plot of yield by Tai’s stability estimates       References Tai GCC, 1971. Genotypic stability analysis and its application to potato regional trials. Crop Sci 11:184–190. 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 Semantic Scholar (2021) https://www.semanticscholar.org/paper/SAS-applications-for-Tai%27s-stability-analysis-and-x-Thillainathan-Fernandez/12e7be3db72303c8a816446789ace0739fa69804   ... View more