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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
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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
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mmif 1
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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
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P = marker + genotype* + error
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
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P = marker + genotype* + error
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 *
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N K N G
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II I I I
G
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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