why you should know about experimental crosses
DESCRIPTION
Why you should know about experimental crosses. Why you should know about experimental crosses. To save you from embarrassment. Why you should know about experimental crosses. To save you from embarrassment To help you understand and analyse human genetic data. - PowerPoint PPT PresentationTRANSCRIPT
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Why you should know about experimental crosses
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Why you should know about experimental crosses
To save you from embarrassment
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Why you should know about experimental crosses
To save you from embarrassment
To help you understand and analyse human genetic data
![Page 4: Why you should know about experimental crosses](https://reader036.vdocument.in/reader036/viewer/2022062322/5681472e550346895db46af8/html5/thumbnails/4.jpg)
Why you should know about experimental crosses
To save you from embarrassment
To help you understand and analyse human genetic data
It’s interesting
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Experimental crosses
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Experimental crosses
Inbred strain crosses
Recombinant inbreds
Alternatives
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Inbred Strain Cross
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Backcross
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F2 cross
F2
F1
F0
Generation
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Data conventions
AA = A
BB = B
AB = H
Missing data = -
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Data conventions
ID M1 M2 M3A01231 A A AA07612 B - HA01812 H H A
Genotype file
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Data conventions
ID M1 M2 M3A01231 A A AA07612 B - HA01812 H H A
ID Phenotype CovariateA01231 10 FA07612 - FA01812 8 M
Genotype file
Phenotype file
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Data conventions
ID M1 M2 M3A01231 A A AA07612 B - HA01812 H H A
ID Phenotype CovariateA01231 10 FA07612 - FA01812 8 M
Genotype file
Phenotype file
Map file
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Map file
Use the latest mouse build and convert physical to genetic distance: 1 Mb = 1.6 cM
Use our genetic map: http://gscan.well.ox.ac.uk/
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Analysis
If you can’t see the effect it probably isn’t there
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0
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ABAA BB
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Red = Hom
Blue = Het
Backcross genotypes
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Statistical analysis
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Linear models
Also known as
ANOVA
ANCOVA
regression
multiple regression
linear regression
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QTL snp
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QTL snp
-1
0
+1
x
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QTL snp
axy
-1
0
+1
x
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QTL snp
axy
-1
0
+1
x
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QTL snp
axy
-1
0
+1
x
a
a
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axy
a
a
qq qQ QQ
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QTL snp
-1
0
+1
Ax
0
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0
Dx
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QTL snp
-1
0
+1
Ax
0
1
0
Dx DA dxaxy
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qq qQ QQ
DA dxaxy
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qq qQ QQ
DA dxaxy
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Hypothesis testing
axy
yH0:
H1:
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Hypothesis testing
H0: y ~1
H1: y ~ 1 + x axy
y
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Hypothesis testing
H0: y ~ 1
H1: y ~ 1 + x axy
y
H1 vs H0 : Does x explain a significant amount of the variation?
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Hypothesis testing
H0: y ~ 1
H1: y ~ 1 + x axy
y
H1 vs H0 : Does x explain a significant amount of the variation?
likelihoodratio
LOD score
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Hypothesis testing
H0: y ~ 1
H1: y ~ 1 + x axy
y
H1 vs H0 : Does x explain a significant amount of the variation?
likelihoodratio
Chi Squaretest
p-value logP
LOD score
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Hypothesis testing
H0: y ~ 1
H1: y ~ 1 + x axy
y
H1 vs H0 : Does x explain a significant amount of the variation?
likelihoodratio
Chi Squaretest
p-value logP
SS explained /SS unexplained
F-test(or t-test)
linearmodels
only
LOD score
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Hypothesis testing
H0: y ~ 1 + x
H1: y ~ 1 + x + x2
axy
DA dxaxy
H1 vs H0 : Does x2 explain a significant extra amount of the variation?
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H0: phenotype ~ 1
H1: phenotype ~ a
Test:H1 vs H0
H2 vs H1
H2 vs H0
PRACTICAL: hypothesis test for identifying QTLs
H2: phenotype ~ a + d
To start:1. Copy the folder faculty\valdar\AnimalModelsPractical to your own directory.2. Start R3. File -> Change Dir… and change directory to your AnimalModelsPracticaldirectory4. Open Firefox, then File -> Open File, and open “f2cross_and_thresholds.R”in the AnimalModelsPractical directory
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PRACTICAL: Chromosome scan of F2 cross
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Two problems in QTL analysis
Missing genotype problem
Model selection problem
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Missing genotype problem
M1 M2 M3 Q M4 M5H A A - A AH H H - A AB B - - H H
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Solutions to the missing genotype problem
Maximum likelihood interval mapping
Haley-Knott regression
Multiple imputation
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Interval mapping
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ANOVA
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Interval mappingqq genotype 10
qQ genotype 20
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Interval mapping 2
1Pr qq
21Pr qQ
qq genotype 10
qQ genotype 20
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Interval mapping
Which is the true situation?
21Pr qq
21Pr qQ
qq genotype 10
qQ genotype 20
10y
20y
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Interval mapping
Which is the true situation?
21Pr qq
21Pr qQ
qq genotype 10
qQ genotype 20
10y
20y
0.5
0.5
“mixture” model
Fit both situations and then weight them
ML interval mapping
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Interval mapping
Which is the true situation?
21Pr qq
21Pr qQ
qq genotype 10
qQ genotype 20
10y
20y
0.5
0.5
“mixture” model
Fit both situations and then weight them
Fit the “average” situation(which is technically false, but quicker)
15y
ML interval mapping
Haley-Knott regression
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Imputation
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Imputation
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Key referencesMaximum likelihood methods
Linear regression
Imputation
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r/qtl
http://www.rqtl.org/Broman, Sen & Churchill
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Is interval mapping necessary?
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QTL
logP score
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QTL
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QTL
logP score
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Significance Thresholds
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Significance Thresholds
Suggestive Significant Mapping method P LOD P LOD Backcross 3.40E-03 1.9 1.00E-04 3.3 Intercross (2 df) 1.60E-03 2.8 5.20E-05 4.3
Lander, E. Kruglyak, L. Genetic dissection of complex traits: guidelines for interpreting and reporting linkage results Nature Genetics. 11, 241-7, 1995
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Thresholds
Permutation test SUBJECT.NAME Sex Phenotype m1 m2 m3 m4 F2$798 F -0.738004 -1 1 1 -1 F2$364 F 0.413330 0 0 0 0 F2$367 F 1.417480 -1 1 1 -1 F2$287 F 0.811208 1 -1 -1 1 F2$205 M 1.198270 0 0 0 0
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Thresholds
Permutation test SUBJECT.NAME Sex Phenotype m1 m2 m3 m4 F2$798 F -0.738004 -1 1 1 -1 F2$364 F 0.413330 0 0 0 0 F2$367 F 1.417480 -1 1 1 -1 F2$287 F 0.811208 1 -1 -1 1 F2$205 M 1.198270 0 0 0 0
SUBJECT.NAME Sex Phenotype m1 m2 m3 m4 F2$798 F 0.413330 -1 1 1 -1 F2$364 F 1.417480 0 0 0 0 F2$367 F 1.198270 -1 1 1 -1 F2$287 F -0.738004 1 -1 -1 1 F2$205 M 0.811208 0 0 0 0
shuffle
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Permutation tests to establish thresholds
Empirical threshold values for quantitative trait mappingGA Churchill and RW Doerge
Genetics, 138, 963-971 1994
An empirical method is described, based on the concept of a permutation test, for estimating threshold values that are tailored to the experimental data at hand.
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PRACTICAL: significance thresholds by permutation
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Two problems in QTL analysis
Missing genotype problem
Model selection problem
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The model problem
How QTL genotypes combine to produce the phenotype
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The model problem
Linked QTL corrupt the position estimates
Unlinked QTL decreases the power of QTL detection
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Composite interval mapping
ZB Zeng Precision mapping of quantitative trait lociGenetics, Vol 136, 1457-1468, 1994
http://statgen.ncsu.edu/qtlcart/cartographer.html
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Composite interval mapping
M1 M2
M1 M2QQ Q
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Composite interval mapping
M-1 M1 M2 M3
M-1 M1 M2 M3QQ Q
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Model selection
Inclusion of covariates: gender, environment and other things too many too enumerate here
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Inclusion of covariates
H0: phenotype ~ covariates
H1: phenotype ~ covariates + LocusX
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Inclusion of covariates
H0: phenotype ~ covariates
H1: phenotype ~ covariates + LocusX
H1 vs H0 : how much extra does LocusX explain?
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Inclusion of covariates
H0: phenotype ~ covariates
H1: phenotype ~ covariates + LocusX
H0: startle ~ Sex + BodyWeight + TestChamber + Age
H1: startle ~ Sex + BodyWeight + TestChamber + Age + Locus432
H1 vs H0 : how much extra does LocusX explain?
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PRACTICAL: Inclusion of gender effects in a genome scan
To start:In Firefox, then File -> Open File, and open “gxe.R”
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Experimental crosses
Inbred strain crosses
Recombinant inbreds
Alternatives
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Recombinant InbredsF0 Parental Generation
F1 Generation
F2 Generation
Interbreeding for approximately 20 generations to produce recombinant inbreds
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RI strain genotypes
http://www.well.ox.ac.uk/mouse/INBREDS
SNP SELECTOR
http://gscan.well.ox.ac.uk/gs/strains.cgi
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RI strain phenotypes
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RI analysis
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Power of RIs
Effect size of a QTL that can be detected with RI strain sets, at P= 0.00013
Number Power QTL %Varexp
24 90 5550 45
37 90 3050 35
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Experimental crosses
Inbred strain crosses
Recombinant inbreds
Alternatives
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Why do we need alternatives?
Classical strategies don’t find genes because of poor resolution
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D
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One locus may contain many QTL
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New approaches
Chromosome substitution strains
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New approaches
Chromosome substitution strains
Collaborative cross
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New approaches
Chromosome substitution strains
Collaborative cross
In silico mapping
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Resources
R http://www.r-project.org/
R help http://news.gmane.org/gmane.comp.lang.r.general
R/qtl http://www.rqtl.org
Composite interval mapping (QTL Cartographer)
http://statgen.ncsu.edu/qtlcart/index.php
Markers http://www.well.ox.ac.uk/mouse/inbreds
Gscan (HAPPY and associated analyses) http://gscan.well.ox.ac.uk
General reading
Lynch & Walsh (1998) Genetics and analysis of quantitative traits (Sinauer).
Dalgaard (2002) Introductory statistics with R (Springer-Verlag).
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END SECTION
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New approaches
Advanced intercross lines
Genetically heterogeneous stocks
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F2 Intercross
x
Avg. Distance BetweenRecombinations
F1
F2F2 intercross
~30 cM
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Advanced intercross lines (AILs)
F0
F1
F2
F3
F4
Darvasi A, Soller M (1995) Advanced intercross lines, an experimental population for fine genetic mapping. Genetics 141: 1199-1207.
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Chromosome scan for F12
position along whole chromosome (Mb)
goodness of fit(logP)
0 100cM
significance threshold
QTL
Typicalchromosome
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PRACTICAL: AILs
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Genetically Heterogeneous Mice
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F2 Intercross
x
Avg. Distance BetweenRecombinations
F1
F2F2 intercross
~30 cM
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Pseudo-random matingfor 50 generations
Heterogeneous Stock F2 Intercross
x
Avg. Distance Between Recombinations:
F1
F2HS
~2 cMF2 intercross
~30 cM
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Pseudo-random matingfor 50 generations
Heterogeneous Stock F2 Intercross
x
Avg. Distance Between Recombinations:
F1
F2HS
~2 cMF2 intercross
~30 cM
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High resolution mapping
0
1
2
3
4
5
6
7
8
64 64.2 64.4 64.6 64.8 65 65.2
position (cM)
-logP
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Relation Between Marker and Genetic Effect
Observable effect
QTL Marker 1
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Relation Between Marker and Genetic Effect
Observable effect
QTLMarker 2 Marker 1
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Relation Between Marker and Genetic Effect
No effect
observableObservable
effect
QTLMarker 2 Marker 1
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Hidden Chromosome Structure
Observed chromosome structure
Multipoint method (HAPPY) calculates the probability that an allele descends from a founder
using multiple markers
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M1
Q
M2
m1
q
m2
M1
?
m2
recombination
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Haplotype reconstruction using HAPPY
m183 m184 m185
allele allele allele
A typical chromosome from an HS mouse
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Haplotype reconstruction using HAPPY
m183 m184 m185
allele allele allele
A typical chromosome from an HS mouse
actual path
another plausible path
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Haplotype reconstruction using HAPPY
m183 m184 m185
allele allele allele
A typical chromosome from an HS mouse
actual path
another plausible path
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Haplotype reconstruction using HAPPY
marker interval
m183 m184 m185
allele allele allele
A typical chromosome from an HS mouse
0.02
0.01
0.76
0.14
0.01
0.01
0.05
0
0 0.5 1
average over all paths
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Haplotype reconstruction using HAPPY
chromosome
genotypes
haplotypeproportionspredicted byHAPPY
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HAPPY model for additive effects
Strain f (strain)LP.J 0.04
DBA.2J 0.05CBA.J 0.03
C57BL.6J 0.07C3H.HeJ 0.36BALB.cJ 0.07AKR.J 0.03
A.J 0.36
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HAPPY model for additive effects
8
1s
sfsy
Phenotype y is modeled asStrain f (strain)LP.J 0.04
DBA.2J 0.05CBA.J 0.03
C57BL.6J 0.07C3H.HeJ 0.36BALB.cJ 0.07AKR.J 0.03
A.J 0.36 s is effect of strain s
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HAPPY effects models
8
1s
sfsy
8
1covariates sjj sfsy
Additive model
Additive model with covariate effects
tsj
j tsftsy,covariates
,,
Full (ie, additive & dominance) model with covariate effects
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Genome scans with HAPPY
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Many peaks
mean red cell volume
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Ghost peaks
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family effects, cage effects, odd breeding
…complex pattern of linkage disequilibrium
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How to select peaks: a simulated example
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How to select peaks: a simulated example
Simulate 7 x 5% QTLs
(ie, 35% genetic effect)
+ 20% shared environment effect
+ 45% noise
= 100% variance
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Simulated example: 1D scan
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Peaks from 1D scan
phenotype ~ covariates + ?
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1D scan: condition on 1 peak
phenotype ~ covariates + peak 1 + ?
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1D scan: condition on 2 peaks
phenotype ~ covariates + peak 1 + peak 2 + ?
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1D scan: condition on 3 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + ?
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1D scan: condition on 4 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 +peak 4 + ?
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1D scan: condition on 5 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + ?
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1D scan: condition on 6 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + ?
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1D scan: condition on 7 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + peak 7 + ?
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1D scan: condition on 8 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + peak 7 + peak 8 + ?
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1D scan: condition on 9 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + peak 7 + peak 8 + peak 9 + ?
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1D scan: condition on 10 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + peak 7 + peak 8 + peak 9 + peak 10 + ?
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1D scan: condition on 11 peaks
phenotype ~ covariates + peak 1 + peak 2 + peak 3 + peak 4 + peak 5 + peak 6 + peak 7 + peak 8 + peak 9 + peak 10 + peak 11 + ?
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Peaks chosen by forward selection
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Bootstrap sampling
1
2
3
4
5
6
7
8
9
10
10 subjects
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Bootstrap sampling
1
2
3
4
5
6
7
8
9
10
1
2
2
3
5
5
6
7
7
9
10 subjects
sample withreplacement
bootstrap samplefrom
10 subjects
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Forward selection on a bootstrap sample
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Forward selection on a bootstrap sample
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Forward selection on a bootstrap sample
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Bootstrap evidence mounts up…
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In 1000 bootstraps…
Bootstrap Posterior Probability(BPP)
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Model averaging by bootstrap aggregation
Choosing only one model:
very data-dependent, arbitrary
can’t get all the true QTLs in one model
Bootstrap aggregation averages over models
true QTLs get included more often than false ones
References:
Broman & Speed (2002)
Hackett et al (2001)
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PRACTICAL: http://gscan.well.ox.ac.uk
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ADDITIONAL SLIDES FROM HERE
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An individual’s phenotype follows a mixture of normal distributions
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m
Maternal chromosomePaternal chromosome
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mChromosome 1Chromosome 2
ABCDEF
Strains
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Markers
m
ABCDEF
Strains
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Markers
m
ABCDEF
Strains
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Markers
m
0.5 cM
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Markers
m
0.5 cM 1 cM
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Markers
m0.5 cM 1 cM
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Analysis
Probabilistic Ancestral Haplotype Reconstruction (descent mapping): implemented in HAPPY
http://www.well.ox.ac.uk/~rmott/happy.html
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M1
Q
M2
m1
q
m2
M1
?
m2
recombination
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M1
Q
M2
m1
q
m2
m1
Q
M2
M1
q
m2
M1
q
m2
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M1
Q
M2
m1
q
m2 M1
Q
m2
M1
Q
m2
m1
q
M2
m1
Q
M2
M1
q
m2
M1
q
m2
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M1
Q
M2
m1
q
m2
M1
m2
M1
m2
m1
m2
m1
M2
M1
m2
M1
m2
Q q
Q q q
Q
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M1
?
m2
m1
?
m2
1c
2c
cM distancesdetermineprobabilities
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0|Pr
5.0|Pr
5.0|Pr
2121
2121
2121
mmmMQQ
mmmMqQ
mmmMqq
M1
?
m2
m1
?
m2
1c
2c
cM distancesdetermineprobabilities
Eg,
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Interval mapping
M1 M2
m1 m2
M1m1
M2m2
LODscore
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Interval mapping
M1 M2
m1 m2
M1m1
M2m2
LODscore
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Interval mapping
M1 M2
m1 m2
M1m1
M2m2
LODscore
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Interval mapping
M1 M2
m1 m2
M1m1
M2m2
LODscore