8 Association Mapping

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Marcos Malosetti & Fred van EeuwijkIntroduction to mixed model QTL mapping using GenStat

13-15th December 2010, ESALQ Piracicaba, So Paulo, Brazil


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QTL mapping

Objective of QTL mapping studies:describe phenotypes in relation to underlying geneticfactors (called QTL)QTL = Quantitative Trait Locus

Finding statistical association betweeninformation at the DNA level (molecular markers)and phenotypic variation

Linkage analysis: common approach, conventional

QTL mappingLD mapping or association mapping : more recently


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Linkage and linkage disequilibrium

Statistical association between markers andphenotypes found when there is linkage(disequilibrium) between markers and QTLs.Linkage disequilibrium (LD): non-random

association of alleles at two locinot necessarily on the same chromosome

Linkage: non-random association of alleles at twoloci due to limited recombination between the loci

Linkage necessarily involves loci on the samechromosome


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Conventional QTL mapping versus LD mapping

Designed crosses Association panel

Both, linkage analysis and LD mapping, rely on linkagedisequilibrium to detect QTLs


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Conventional QTL mapping versus LD mappingDesigned crosses Association panel

LD marker-QTL is only consequence of linkage.

LD marker-QTL can be consequence of linkage but alsoother factors can cause LD.

Population admixture


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Genetic relatedness / population substructure

All genotypes of a segregating population have by

expectation equal relatedness/correlationIn association mapping panels the genotypesshow heterogeneous genetic relatedness:

Unstructured: coefficient of coancestry ij Structured genetic relatedness (populationsubstructure)

Not accounting for relatedness (coancestry orpopulation substructure) will cause spuriousassociationsLD mapping requires more elaborated modelling of thegenetic relatedness in the population


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Association panel: a set of interconnected genotypes

known or unknownpopulation history


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K

Genetic correlation between individuals: unstructured

K = kinship, coeff. of coancestry

pedigree

markers


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Genetic correlation between individuals: structured

Identify sets of more or lesshomogenous genotypes


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Quantifying genetic relatedness / Structuring VCOV(G)

Bayesian clustering STRUCTURE (Pritchard etal. 2000)It can be computationally intensivePopulation assumptions not always compatible with

plant populations (mainly developed to be used inhuman population genetics)Not always obvious how to define the model to use

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A n c e s t r y

Genotype

EMed

Turk

SWMed

NMed2

NMed6


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Quantifying genetic relatedness / Structuring VCOV(G)

Classical multivariate approachesSimple, fastSimilar results with STRUCTUREWhere to define boundaries between groups?

Other criteria (e.g. geographical origin)


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Eigenanalysis


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Eigenanalysis

PCA on genotype x marker scores matrix with aformal test for the number of axes (dimensions)No discrete groups, but set of PCs be used ascovariates in marker trait association analysisWhen PCs are introduced in random part of amixed model, they will approximate the fullgenetic relationship matrix

Straightforward, simple, and is easy to program ina conventional statistical package


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Mixed models and LD mapping in GenStat

LD mapping models should accommodatethe complex genetic relationships in thepopulation.

Mixed models are particularly suitable(GenStat).Suite of GenStat procedures developed to

run different models for LD mapping.Procedures can be run from the GUI.


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A mixed model for LD mapping

P = genotype + error

),0(~),0(~ 22 N error N G genotype

P = marker + genotype* + error

iii GP

iiii G xP

MMif 1

Mmif 0

mmif 1

i

i

i

x

x

x


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A naive mixed model for LD mapping

This model assumes UNRELATED genotypes

Standard assumption:

),0(~),0(~22

N error N G genotype

Relationship matrix K=I

),0(~ 2genotype I N G

This model ignores genetic relatedness/ population structure

1000

10010

1

K


iiii G xP


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K should be in the model to correct for relatedness

Now the relationship matrix (K) is in the modelK = kinship matrix derived from pedigree/marker

information

Change model assumption:

),0(~)2,0(~ 22 N error K N G g

Relationship matrix K I

II I I I

K

321

332313

2212

11


iiii G xP


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LD mapping using eigenanalysis

The PC scores represent relatedness / populationstructurePCs impose approximate covariance structure

Computationally less intensive than full structuring ofVCOV(G)

) ,0( N ~error ) ,0( N ~G) ,0( N ~C 22genotype2scores

P = marker + PCs + genotype* + error

ii M

m ,iii GC xP


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Population structure

This model imposes a common covariance between genotypes withina groupGenotypes from different groups are still assumed unrelatedGroups from STRUCTURE or clustering

),0(~),0(~),0(~ 222 N error N G N C genotypegroup

Relationship matrix K I

Group 1 Group 2

P = marker + group + genotype + error

ik ik ii GC xP )(


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LD mapping in GenStat 13


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Correcting for genetic relatedness: kinship vsnull


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Correcting for genetic relatedness: PC scores vs null


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LD decay plots


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LD decay plots

No correction Correction for population structure

Response marker =predictor marker +error

Response marker =PC scores / groups +predictor marker +error


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LD image plots

No correction Correction for population structure


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Genetic relatedness in segregating populations

Segregating populationsNo selectionNo mutation

No genetic driftSimple model does notwork

More complex residualstructure

F1

100-1000 offsprings

Parent 2Parent 1

QTL = Quantitative Trait Locus


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Modelling genetic relatedness for QTL detection

yi quantitative trait responsex

i genotypic covariable (marker information)additive marker effectResidual random variation consists of

Genetic residual with a correlation structure

Relationship matrix ij coefficient of coancestry between genotypes i and j

Standard independent residual (experimental error)

iiii G x y *

),0(~)2,0(~

2

2

*

*

N K N G

i

Gi

II I I I

G

321

332313

2212

11

2*


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Chi-square test for segregation distortions

Allele frequencies show deviations from expectation


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Genome-wide scan: plant height

Model includinggenetic relatedness(kinship)information)

Model ignoringrelatedness(kinship)information)


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Conclusions

Study of genetic relatedness crucial in LD

mappingKinshipEigenanalysisClustering methods (including STRUCTURE)

Need to control for genetic relatedness whenassessing:

Marker marker association (LD decay)

Marker trait association (LD mapping)GenStat procedures / GUI can be used to run allthese types of analyses

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8 Association Mapping

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