User-friendly SAS application for performing Tai’s Stability Analysis (1971)

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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

1. Tai GCC, 1971. Genotypic stability analysis and its application to potato regional trials. Crop Sci 11:184–190.
2. 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
3. Semantic Scholar (2021) https://www.semanticscholar.org/paper/SAS-applications-for-Tai%27s-stability-analysis-and-x-Thillain...