GEA-R

Genotype x Environmental Analysis with R forWindows

Biometrics and Statistics UnitAngela Pacheco

CIMMYT,Int.

23-24 Junio 2015

GEA-R

About GEI

In agricultural experimentation, a large number ofgenotypes are normally tested over a wide range ofenvironments.Advanced breeding materials must be evaluated in multiplelocations for more than one year.The occurrence of the GEI effect further complicates theselection of superior genotypes for a target population ofenvironments.

GEA-R

About GEI

The presence of the GEI confirms particular genotypesbeing superior in particular environments.Several statistical methods were developed for resolvedthat kind of problems, for example, AMMI, SREG, PLS,Stability analysis and Factorial regression.

GEA-R

What is?

GEA-R description

http://hdl.handle.net/11529/10203

GEA-R is a set of R programs that performs statisticalanalyses to calculate AMMI, SREG, PLS, StabilityAnalysis, Factorial Regression, in order to make boxplotsand histograms. GEA-R contains a graphical JAVAinterface that helps the user to easily choose input files,which analyses to implement, and which variables toanalyze.

GEA-R

How does it works?

GEA-R requirements and installation

Windows operating system.For install, you only need to follow the instructions.When you install GEA-R, you will can start the programdirectly of the programs window

GEA-R

How does it works?

GEA-R requirements and installation

Or you will search the folder in C:\GEA-R, the foldercontains the following files:

When using GEA-R for the first time, you must load (justonce) the R-version that GEA-R will use to perform theanalysis, or in case that you don’t have installed R, GEA-Rinstalled automatically.

GEA-R

How does it works?

GEA-R requirements and installation

The R-version is loaded by clicking on ‘Load R’. GEA-R willdisplay a list of the R-versions detected as installed,usually in the Program Files folder. To look for installedR-versions located in another folder, click on the ‘Browse’button.

GEA-R

How does it works?

GEA-R requirements and installation

Once the R-version is loaded, GEA-R will verify if allpackages exist and will automatically try to install them ifthey do not.When the R-version is loaded and the packages are ready,the next step is to open the input file to be analyzed.

GEA-R

How does it works?

GEA-R Help

Whenever you need help,you can click in ”Help” button,andGEA-R show you two options: ”Manual”, in it you find stepby step an explanation for do the analyses; and ”About...”,in it you find the citation and license for GEA-R.

GEA-R

How does it works?

Preparing for the analysis

GEA-R

How does it works?

Preparing for the analysis

GEA-R

Types of Analyses

Additive main effect and multiplicative interactionanalysis (AMMI)

GEA-R

Types of Analyses

AMMI

Method for analyzing GEI to identify patterns of interactionand reduce background noise.Combines conventional ANOVA with principal componentanalysis.May provide more reliable estimates of genotypeperformance than the mean across sites.

GEA-R

Types of Analyses

AMMI

Biplots help to visualize relationships among genotypesand environments; show both main and interaction effects.Enables you to identify target breeding environments andto choose representative testing sites in thoseenvironments.Enables you to select varieties with good adaptation totarget breeding environments.

GEA-R

Types of Analyses

AMMI Model

Yijk = µ + Gi + Ej +∑

λkαikγjk + dij + eijk

µ the grand mean.Gi the genotype deviations from the grand mean.Ej the environment deviations from the grand mean.λk kth eigenvalue.αik principal component score for the i th genotype for the k th principal component axis.γjk principal component score for the j th environment for the k th principal component axis.dij residual GEI not explained by model.eijk residual model.

GEA-R

Types of Analyses

AMMI: General Interpretation

Usually need only the first 2 PC axes to adequately explainthe data.Genotypes that occur close to particular environments onthe biplot show specific adaptation to those environments.A genotype that falls near the center of the biplot (smallPC1 and PC2 values) may have broader adaptation.

GEA-R

Types of Analyses

AMMI: General Interpretation

Acute angles indicate positive correlation, with vectors inexactly the same directions representing a correlation of 1.Obtuse angles represent negative correlations, withopposite directions indicating a correlation of -1.Perpendicularity of directions indicates a correlation of 0.

GEA-R

Types of Analyses

Sites Regression Model (SREG)

GEA-R

Types of Analyses

SREG

This model is recommended when the environments arethe main source of variation in relation to the contributionsof the genotypes and the GEI with respect to the totalvariability.The biplot graphics is used to visualize patterns andinteractions without environmental effects.

GEA-R

Types of Analyses

SREG

In addition, as a difference with AMMI model, thistechnique allows the detection of GEI in terms of thecrossover effect resulting from great changes in theranking of the genotypes across the environments.

GEA-R

Types of Analyses

SREG Model

Yijk = µ + Ej +∑

λkαikγjk + dij + eijk

µ the grand mean.Ej the environment deviations from the grand mean.λk kth eigenvalue.αik principal component score for the i th genotype for the k th principal component axis.γjk principal component score for the j th environment for the k th principal component axis.dij residual GEI not explained by model.eijk residual model.

GEA-R

Types of Analyses

SREG: General Interpretation

Usually the first principal component represents responsesof the genotypes that are proportional to the environments,which are associated with the GEI without change of therange.The second principal component provides informationabout cultivation locations that are not proportional to theenvironments, indicating that those are responsible of theGEI crossover interaction.

GEA-R

Types of Analyses

SREG: General Interpretation

This technique allows the determination ofmega-environments, which mean parts of the cultivationarea of a species that show homogeneous environmentalconditions, where the performance of certain genotypes issimilar through the years.

GEA-R

Types of Analyses

Partial Least Square (PLS)

GEA-R

Types of Analyses

PLS

Is a model for to incorporate external variables(environmental or genotypic).Is convenient if you have more variables than observationsand there is high collinearity among variables.Can be used for to determinate which of these externalvariables influence in the GEI.

GEA-R

Types of Analyses

Factorial Regression (FR)

GEA-R

Types of Analyses

FR

Also helps us to incorporate environmental and genotypiccovariates and allow us to choose which covariate providesgreater proportion of the variability in the GEI.FR is easier to interpret than PLS, but may give misleadingresults when there are correlations among the explanatoryvariables in the model.

GEA-R

Types of Analyses

FR

Similar to stepwise multiple regression, where additionalvariables are added to the model in sequence untilsufficient variability due to GEI can be explained.

GEA-R

Types of Analyses

FR Model

Yij = µ + Gi + Ej +Gc∑g=1

xigξig + eij

µ the grand mean.Gi and Ej the genotype and environment deviations from the grand mean.xig genotipic covariatesξig the environmental factoreij residual model.Gc number of genotipic covariates (Gc<genotypes)

GEA-R

Types of Analyses

Stability Analysis

GEA-R

Types of Analyses

Stability parameters

Stability parameter Symbol Increased stability if:Variation coefficient CV small valuesShuckla’s variance σ2 small valuesPerkins and Jinks B values close to 1Perkins and Jinks D small values

Eberhart and Russell (regression coefficient) b values close to 1Eberhart and Russell (mean square deviation) S2

d small valuesDetermination coefficient R2 big values

Wricke’s ecovalence W small valuesSuperiority measure P small values

Average absolute rank difference of genotype on the environment S(1) small valuesVariance ranges of environments S(2) small values

GEA-R

Types of Analyses

GGEBiplot

The GGEBiplotGUI package provides a graphical user interfacefor the construction of, interaction with, and manipulation ofGGE biplots in R. Some of the functions of the package are:

Ranking the cultivars based on their performance in anygiven environment.Ranking the environments based on the relativeperformance of any given cultivar.

GEA-R

Types of Analyses

GGEBiplot

Comparing the performance of any pair of cultivars indiferent environments.Identifying the best cultivar in each environment.Grouping the environments based on the best cultivars.

GEA-R

Types of Analyses

GGEBiplot

Evaluating the cultivars based on both average yield andstability.Evaluating the environments based on both discriminatingability and representativeness.

GEA-R

Messages

It’s ready?

GEA-R

Messages

It’s ready?

If you have problems with your data set.

GEA-R

Summary

Summary Results

AMMI SREG PLS Stability Analysis Factorial RegressionFinal Score Final Scores Biplot PLS Stability Coefficients ANOVA for general modelGollobs Test Gollobs Test Final Scores Plot CV ANOVA for Best model

Biplot PC1 vs PC2 Biplot PC1 vs PC2 Plot Eberhart&Russel Coefficient Summary of steps for factorial regressionBiplot PC1 vs PC3 Biplot PC1 vs PC3Biplot PC2 vs PC3 Biplot PC2 vs PC3Biplot PC1 vs Yield Biplot PC1 vs Yield

Biplot 3D Biplot 3DAll Biplots with polygon All Biplots with polygon

GEA-R

THANK YOU!!