biplot analysis of met data iita

7/31/2019 Biplot Analysis of MET Data IITA

1/68

Contact: [email protected]

Weikai YanMay 2006


2/68

Weikai Yan 2006

Multi-Environment Trials (MET)

MET are essential MET are expensive

MET data are valuable MET data are not fully used


3/68

Weikai Yan 2006

Why biplot analysis?

Biplot analysis can help understand METdata Graphically, Effectively, Conveniently


4/68

Weikai Yan 2006

Outline

Multi-environment trial (MET) data Basics of biplot analysis Biplot analysis of G-by-E data Biplot analysis of G-by-T data Better understanding of MET data Conclusions


5/68



6/68

Weikai Yan 2006

MET data isa genotype-environment-trait

(G-E-T) 3-way table Multiple Genotypes

Multiple Environments Multiple Traits


7/68 Weikai Yan 2006

A G-E-T 3-way table containsmany 2-way tables

G by E: for each trait G by T (trait): in each environment;

across environments E by T: for each genotype; across

genotypes

G-E-T data >> G-E data



A G-E-T 3-way table isan extended 2-way table

G by V: each E-T combination as a variable (V)

P by T: each G-E combination as a phenotype

(P)



A G-E-T 3-way table impliesinformative 2-way tables

Association by environment 2-waytables

Associations: among traits between traits and genetic markers



Goals of MET data analysis

Short-term goals: Variety evaluation

Response to the environment (G x E)

Trait profiles (G x T) Long-term goals:

To understand the target environment (G x E) the test environments (G x E) the crop (G x T) the genotype x environment interaction (A x T)


11/68Contact: [email protected]

Most two-way tables can be

visually studied using biplots



Origin of biplot

Gabriel (1971)One of the mostimportant advances indata analysis in recentdecadesCurrently

> 50,000 web pagesNumerous academicpublicationsIncluded in moststatistical analysispackages

Still a very newtechnique to mostscientists

Prof. Ruben Gabriel, The founder of biplot Courtesy of Prof. Purificacin Galindo

University of Salamanca, Spain



What is a biplot?

Biplot = bi + plot plot

scatter plot of two rows OR of two columns, or scatter plot summarizing the rows OR the columns

bi BOTH rows AND columns

1 biplot >> 2 plots



Mathematical definition of a BiplotGraphical display of matrix multiplication

Inner product property P ij =OA i *OBj *cos ij Implies the product matrix

A(4, 2) B(2, 3) P(4, 3)

121284

96103

151262

69201

321

214

332

321

044

313

332

341

a

a

a

a

bbb

y

x

bbb

a

a

a

a

y x

Matrix multiplication

-4

-3

-2

-1

0

1

2

3

4

5

-4 -3 -2 -1 0 1 2 3 4 5

X

Y

O

A1A2

A3

A4

B1

B2

B3

5.0

cos =0.8944

4.472

P11 = 5*4.472*0.8944 = 20



Practical definition of a biplotAny two -way table can be analyzed using a 2D-biplot as soon as it can be

sufficiently approximated by a rank- 2 matrix. (Gabriel, 1971)

214

332

321

044

313

332

341

121284

96103

151262

69201

321

y

x

eee

g

g

g

g

y x

g

g

g

g

eee

G-by-E table

Matrix decomposition

-4

-3

-2

-1

0

1

2

3

4

5

-4 -3 -2 -1 0 1 2 3 4 5

X

Y

O

G1G2

G3

G4

E1

E2

E3

P(4, 3) G(3, 2) E(2, 3)

(Now 3D- biplots are also possible)



Singular Value Decomposition (SVD) &Singular Value Partitioning (SVP)

r

k kj

f

k

f

k ik

SVP

r

k kjk ik

SVDij

ba

baY

1

1

1

))((

(0 f 1)

Singular values Matrixcharacterising the rows

Matrixcharacterising the columns

SVD = PCA?

SVD:

SVP:

The rank of Y, i.e.,the minimum numberof PC required tofully represent Y

Rows scores Column scores

BiplotPlot Plot



Biplot interpretations

Inner-product propertyInterpretations based on biplots with f = 1

approximates YY T, the distance matrix Similarity/dissimilarity among row (genotype) factors

Interpretations based on biplots with f = 0approximates Y TY, the variance matrix

Similarity/dissimilarity among column (environment)factors

Combined use of f = 0 and f = 1

(Gabriel, 2002 Biometrika; Yan, 2002, Agron J; Built in the GGEbiplot software)

))((1

1

r

k kj f k f k ik ij baY



Biplot analysis is

to use biplots to display a two-way data per se (Y), its distance matrix (YYT), and its variance matrix (YTY)

so that relationships among rows,

relationships among columns, and interactions between rows and columns

can be graphically visualized.



Data centering prior to biplot analysis

The general linear model for a G-by-Edata set (P) P = M + G + E + GE

Possible two- way tables (Y): Y = P = M + G + E + GE original data: QQE biplot Y = P M = G + E + GE global-centered (PCA)

Y = P M E = G + GE column-centered: GGE biplot Y = P M G = E + GE row-centered Y = P M G E = GE double-centered: GE biplot

All models are useful, depending on the research objectives (built in GGEbiplot)



Data scaling prior to biplot analysis

Different GGE biplots Yij = ( i + ij )/s j

S j = 1 no scaling S j = (s.d.) j all environments are equally important S j = (s.e.) j heterogeneity among environments is removed

(built in GGEbiplot)



Four questions must be askedbefore trying to interpret a biplot

1. What is the model?How the data were centered and scaled?What are we looking at?

2. What is the goodness of fit?How confident are we about what we see?What if the data is fitted poorly?

3. How singular values are partitioned?What questions can be asked?

4. Are the axes drawn to scale?Are the patterns artifacts?

(All are addressed explicitly in GGEbiplot)


22/68Contact: [email protected]

MEGA-ENVIRONMENT

ANALYSIS

TESTENVIRONMENTEVALUATION

GENOTYPEEVALUATION



Sample G-by-E data(Yield data of 18 genotypes in 9 environments, 1993, Ontario, Canada)


24/68

Weikai Yan 2006

Before trying to interpret a biplot

1. Model selection?Centering = 2 (G+GE) Scaling =0

2. Goodness of fit?

78%.3. Singular value

partitioning?SVP = 2 (environment-

metric )

4. Draw to scale?Yes.


25/68

Weikai Yan 2006

G By E data analysis

MEGA-ENVIRONMENT

ANALYSIS

TEST

ENVIRONMENTEVALUATION

GENOTYPEEVALUATION

Mega-environment is a group of geographical locations that share the same (set of)

best genotypes consistently across years.


26/68

Weikai Yan 2006

Relationships among environments The Environment - vector view

Angle vs.correlation

The anglesamong testenvironments

Environment

grouping


27/68

Weikai Yan 2006

Which -won- where

( Crossover GE is GE that caused genotype rank changes and different winners in

different test environments)

G12

G7G18

G8G13


28/68

Weikai Yan 2006

Are there meaningful crossover GE? The which -won- where view

( Crossover GE is GE that caused genotype rank changes and different winners in

different test environments)


29/68

Weikai Yan 2006

Are the crossover patterns*repeatable?

If YES The target environment can be divided into multiple

mega-environments GE can be exploited by selecting for each mega-

environment

GE G If NO

The target environment CANNOT be divided intomultiple mega-environments

GE CANNOT be exploited GE must be avoided by testing across locations and

years

*Not the environment-grouping patterns Mega-environment is a group of geographical locations that share the same (set of) bestgenotypes consistently across years.

Multi-year data are needed


30/68

Weikai Yan 2006

Classify your target environment intoone of three categories

With Crossover GE No CrossoverGE

Repeatable (2) Multiple MEsSelect for specifically adaptedgenotypes for each ME

(1) Singlesimple MEA single test location,single year suffices toselect a single bestvariety

Not repeatable (3) Single

complex MESelect for generally adaptedgenotypes across the wholeregions across multiple years

ME: mega-environment


31/68

Weikai Yan 2006


MEGA-ENVIRONMENT

ANALYSIS

TEST


GENOTYPEEVALUATION


32/68

Weikai Yan 2006

Discriminating ability and representativeness

Vector length: discriminating ability Angle to the AE: representativeness

Average-environment axis

Average environment


33/68

Weikai Yan 2006

Ideal test environments:discriminating and representative

Ideal test

environment


34/68

Weikai Yan 2006

Classify each test environment intoone of three categories

For each good or useful test environment: is it essential?

Discriminative Notdiscriminative

Representative (2) Good forselecting (moreimportant)

(1) Useless

Notrepresentative

(3) Useful forculling (less important)


35/68

Weikai Yan 2006

Vector length = discrimination= GE = GE1 + GE2

Contribution toProportionateGE

Contribution toNon-proportionateGE


36/68

Weikai Yan 2006


MEGA-ENVIRONMENT

ANALYSIS

TEST


GENOTYPEEVALUATION


37/68

Weikai Yan 2006

Vector length = GGE = G + GE

Contribution To GE(instability)

Contribution To G(mean performance)


38/68

Weikai Yan 2006

Mean vs. Stability


39/68

Weikai Yan 2006

Genotype ranking on both MEAN and STABILITY

The ideal genotype


40/68

Weikai Yan 2006

Genotype classification

MeanStability

High meanperformance

Low meanperformance

High stability Generally adapted(VERY GOOD)

Bad everywhere(VERY BAD)

Low stability Specifically Adapted(GOOD)

Bad somewhere(BAD)

Are there stability genes?!


41/68

Weikai Yan 2006

G x E data analysis summary

1) Mega-environment analysis 2) Test environment evaluation 3) Genotype evaluation

Important comments: (2) and (3) are meaningful only for a single mega-environment Any stability analysis is meaningful only for a single mega-

environment Any stability index can be used only as a modifier to the ranking

based on mean performance


42/68



43/68

Weikai Yan 2006

Inner-product property


44/68

Weikai Yan 2006

Ranking on a single environment


45/68

Weikai Yan 2006

Ranking on two environments


46/68

Weikai Yan 2006

Relative adaptation of a genotype


47/68

Weikai Yan 2006

Compare any two genotypes


48/68



49/68

Weikai Yan 2006

Objectives of G By T data analysis

Genotype evaluation based on traitprofiles

Relationship among breeding objectives


50/68

Weikai Yan 2006

Data of 4 traits for 19 covered oat varieties (Ontario 2004)

(Background info: High yield, high groat, high protein, and low oil are desirable for milling oats)


51/68

Weikai Yan 2006

Relationships among traits


52/68

Weikai Yan 2006

Trait profile of each genotype


53/68

Weikai Yan 2006

Trait profile of a genotype

T i fil i b


54/68

Weikai Yan 2006

Trait profile comparison betweentwo genotypes


55/68

Weikai Yan 2006

Genotype ranking based on a trait


56/68

Weikai Yan 2006

Parent selection based on trait profiles


57/68

Weikai Yan 2006

Independent culling


58/68


MET data are more informativethan you thought

A G E T 3 d t t t i


59/68

Weikai Yan 2006

A G-E-T 3-way dataset contains various 2-way tables

G by E data G by T data E by T data:

for each genotype; all genotypes G by V data:

each E-T as a variable (V) P by T data:

each G-E as a phenotype (P) Genetic association by environment data Trait association by environment data

G i i b i bi l


60/68

Weikai Yan 2006

Genetic-covariate by environment biplot(QTL by environment biplot)

Barley GenomicsData


61/68

Weikai Yan 2006

Trait-association by environment biplot

OatMETData


62/68

Weikai Yan 2006

Four-way data analysis

Year


63/68



64/68

Weikai Yan 2006

Conclusion (1)

GGE biplot analysis is an effective toolfor G by E data analysis to achieveunderstandings about.

1. the target environment,2. the test environments, and3. the genotypes

4. stability analysis is useful only to a singlemega-environment


65/68

Weikai Yan 2006

Conclusion (2)

GGE biplot analysis is an effective toolfor G by T data analysis to achieveunderstandings about.

1. the interconnected plant system,2. positively correlated traits3. negatively correlated traits

4. the strength and weakness of thegenotypes


66/68

Weikai Yan 2006

Conclusion (3)

Biplot analysis is an effective tool for other two-way table analysis

Marker by environment QTL by environment Gene by treatment Diallel cross


67/68

Weikai Yan 2006

Conclusion (4)

Biplot analysis can be VERY EASY From reading data to displaying the biplot: 2 seconds Displaying any of the perspectives of a biplot and

changing from one to another: 1 second Displaying the biplot for any subset: 1 second Learning how to use the software and interpret

biplots: 30 minutes

Everything can be just one mouse-click away


68/68

Contact: Weikai Yan: [email protected] web: www.ggebiplot.com
mailto:[email protected]://www.ggebiplot.com/http://www.ggebiplot.com/mailto:[email protected]

biplot analysis of met data iita

Documents