Department Of Biostatistics & Medical Informatics University Of .
Mapping QTL to a phylogenetic tree Karl W Broman Department of Biostatistics & Medical Informatics University of Wisconsin – Madison www.biostat.wisc.edu/ kbroman
Human vs mouse www.daviddeen.com 3
Intercross P1 P2 F1 F1 F2 4
A tree A B C D E 5
A QTL on a tree A B C D E 6
QTL mapping QTL Quantitative Trait Locus QTL mapping data: Set of intercross individuals Quantitative phenotype for each Marker genotype data Genetic map 7
QTL mapping data Broman et al., Genetics, 174:2151–2158, 2006 Owens et al., Hum Mol Genet, 14:1549–1558, 2005 8
ANOVA at marker loci D5NCNP4 (Chr 5) Split mice into groups according to genotype at a marker. WILSET234151 (Chr 9) 17.0 17.0 Repeat for each marker. Average gut length Do a t-test / ANOVA. Average gut length 16.5 16.0 16.5 16.0 15.5 15.5 CC CB Genotype BB CC CB BB Genotype 9
LOD curves 6 5 LOD score 4 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Chromosome 10
LOD curves 6 5 LOD score 4 5% 3 2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Chromosome 11
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 12
QTL on a tree Assumptions No epistasis Ave. phenotype B C A D B D A C A B C D Single diallelic QTL No epistasis or background effects No variation in recombination Known tree LL LH HH Genotype 13
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 14
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 15
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 16
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 17
QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 18
QTL on a tree Assumptions Single diallelic QTL 5 No epistasis or background effects 1 A 3 2 B C 4 No variation in recombination D Known tree 19
QTL on a tree 5 1 A 3 2 B C 4 D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 20
QTL on a tree 5 1 A 3 2 B C 4 D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 21
Combining crosses Li et al., Genetics 169:1699–1709, 2005 Four mouse intercrosses, I P, P D, D C, C S I, D, S have low plasma HDL cholesterol P, C have high plasma HDL cholesterol Use results from individual crosses to determine partition Recode genotypes in each cross to L/H and combine (with the goal of increasing mapping precision) 22
Diallelic QTL Macdonald and Long, Genetics 176:1261–1281, 2007 Drosophila recombinant inbred lines (RIL) developed from 8 strains Assume an underlying diallelic QTL (that the 8 alleles are of two flavors) Approximate method for partitioning the 8 alleles into 2 groups Ave. phenotype 10 8 6 4 2 0 G D C A F H E B Genotype 23
Diallelic QTL Macdonald and Long, Genetics 176:1261–1281, 2007 Drosophila recombinant inbred lines (RIL) developed from 8 strains Assume an underlying diallelic QTL (that the 8 alleles are of two flavors) Approximate method for partitioning the 8 alleles into 2 groups Ave. phenotype 10 8 6 4 2 0 G D C A F H E B Genotype 24
The basic idea 5 1 A 3 2 B C 4 D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 25
The basic idea A B C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 26
The basic idea A B C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 27
The basic idea A B C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 28
The basic idea A B C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 29
The basic idea A B C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 30
Simulated example Individual crosses Combined analysis A B A C B D 8 A BCD B ACD C ABD D ABC AB CD 8 LOD 2.7 6 LOD score LOD score 6 4 4 2 2 0 0 0 20 40 60 Map position (cM) 80 100 0 20 40 60 80 100 Map position (cM) 31
Does it work? Four taxa One diallelic QTL with h2 10% All 6 intercrosses; 100 individuals per cross 10,000 simulation replicates Not determined False positive rate 80 80 80 Truth Truth AB CD AB CD D ABC C ABD B ACD 0 A BCD 0 AB CD 0 D ABC 20 C ABD 20 B ACD 20 D ABC 40 C ABD 40 60 B ACD 40 60 A BCD 60 False positive rate (%) 100 Not determined (%) 100 A BCD Power (%) Power 100 Truth 32
Does it work? Four taxa One diallelic QTL with h2 10% All 6 intercrosses; 100 individuals per cross 10,000 simulation replicates Power Not determined 100 False positive rate 100 100 Crude method 60 40 20 60 40 Fancy method 60 40 20 20 0 0 Truth Truth AB CD D ABC C ABD B ACD A BCD AB CD D ABC C ABD B ACD AB CD D ABC C ABD B ACD 0 A BCD Crude method A BCD Power (%) Fancy method 80 False positive rate (%) 80 Not determined (%) 80 Truth 33
Does it work? ROC curves 100 Fancy method Power (%) 80 A BCD B ACD C ABD D ABC AB CD 60 40 Crude method 20 0 0.0 0.5 1.0 1.5 2.0 2.5 False positive rate (%) 34
Does it work? ROC curves 100 Fancy method Power (%) 80 A BCD B ACD C ABD D ABC AB CD 60 40 Crude method 20 0 0.0 0.5 1.0 1.5 2.0 2.5 False positive rate (%) 35
All partitions? 5 1 A 3 2 B Cross A B A C A D B C B D C D C 4 D QTL position (partition of taxa) 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) (AC BD) (AD BC) 36
All partitions? 5 1 A 3 2 B Cross A B A C A D B C B D C D C 4 D QTL position (partition of taxa) 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) (AC BD) (AD BC) 37
Minimal crosses 5 1 A 3 2 B C 4 D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 38
Minimal crosses 5 1 A 3 2 B C 4 D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 39
Minimal crosses A 5 D 1 3 2 B 4 A B C C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 40
Minimal crosses A 5 D 1 3 2 B 4 A B C C D QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) A B A C A D B C B D C D 41
Minimal crosses Tree Crosses A B D E works E doesn't work C A B C D E A B D C 42
Minimal crosses Tree Crosses E D B A B C D E A works (sort of) C F F 43
Minimal crosses For n taxa, you need at least n – 1 crosses Crosses should involve all taxa Crosses should connect all taxa (if you consider all possible partitions) 44
All or some crosses? 3 taxa All crosses, 100 individuals each, or 2 crosses, 150 individuals each? QTL with 10% heritability; A BC pattern A B C 45
All or some crosses? 3 taxa All crosses, 100 individuals each, or 2 crosses, 150 individuals each? QTL with 10% heritability; A BC pattern B C Power (%) A 100 80 60 40 20 0 All A B A C A B B C A C B C Crosses 46
All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? QTL with 10% heritability A B C D Consider all 7 partitions 47
All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? QTL with 10% heritability B C D Consider all 7 partitions 100 Power (%) A 80 60 A BCD B ACD C ABD D ABC 40 20 0 AB CD True pattern 48
All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? QTL with 10% heritability B C D Consider all 7 partitions 100 Power (%) A 80 60 A BCD B ACD C ABD D ABC 40 20 0 AB CD True pattern 49
All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? QTL with 10% heritability B C D Consider all 7 partitions 100 Power (%) A 80 60 A BCD B ACD C ABD D ABC 40 20 0 AB CD True pattern 50
All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? QTL with 10% heritability B C D Consider the 5 partitions induced by the tree 100 Power (%) A 80 60 40 20 0 A BCD B ACD C ABD D ABC AB CD True pattern 51
Which crosses? Considering all partitions A BCD 75 50 25 B ACD C ABD 75 50 25 D ABC 75 50 25 75 50 25 AB CD Power (%) 75 50 25 A B A B A B A B A B A B A B A B A C A C A C A C A C A D A D A D A C A C A C A D A D B C B C B D A D A D B C B C B D B C B C B D A D B D C D B C C D B D C D C D B C B D B D C D C D B D C D C D Crosses 52
Which crosses? Considering all partitions A BCD 75 50 25 B ACD C ABD 75 50 25 D ABC 75 50 25 75 50 25 AB CD Power (%) 75 50 25 A B A B A B A B A B A B A B A B A C A C A C A C A C A D A D A D A C A C A C A D A D B C B C B D A D A D B C B C B D B C B C B D A D B D C D B C C D B D C D C D B C B D B D C D C D B D C D C D Crosses 53
Which crosses? Considering all partitions Simulated example 12 50 25 LOD score 10 75 AB CD Power (%) 100 8 6 4 2 0 0 A B A C A D 0 Crosses Cross A B A C A D B C B D C D 20 40 60 80 100 120 Map position (cM) Partition of taxa A BCD B ACD C ABD D ABC AB CD AC BD AD BC 54
Which crosses? Considering all partitions Simulated example 12 50 25 LOD score 10 75 AB CD Power (%) 100 8 6 4 2 0 0 A B A C B D 0 Crosses Cross A B A C A D B C B D C D 20 40 60 80 100 120 Map position (cM) Partition of taxa A BCD B ACD C ABD D ABC AB CD AC BD AD BC 55
Which crosses? Considering all partitions Simulated example 12 50 25 LOD score 10 75 AB CD Power (%) 100 8 6 4 2 0 0 A B A C B D 0 Crosses Cross A B A C A D B C B D C D 20 40 60 80 100 120 Map position (cM) Partition of taxa A BCD B ACD C ABD D ABC AB CD AC BD AD BC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 56
Which crosses? Considering all partitions Simulated example 12 50 25 LOD score 10 75 AB CD Power (%) 100 8 6 4 2 0 0 A B A C B D 0 Crosses Cross A B A C A D B C B D C D 20 40 60 80 100 120 Map position (cM) Partition of taxa A BCD B ACD C ABD D ABC AB CD AC BD AD BC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 57
Which crosses? Considering all partitions A BCD 75 50 25 B ACD C ABD 75 50 25 D ABC 75 50 25 75 50 25 AB CD Power (%) 75 50 25 A B A B A B A B A B A B A B A B A C A C A C A C A C A D A D A D A C A C A C A D A D B C B C B D A D A D B C B C B D B C B C B D A D B D C D B C C D B D C D C D B C B D B D C D C D B D C D C D Crosses 58
Which crosses? Considering the 5 partitions induced by the tree A BCD 75 50 25 B ACD C ABD 75 50 25 D ABC 75 50 25 75 50 25 AB CD Power (%) 75 50 25 A B A B A B A B A B A B A B A B A C A C A C A C A C A D A D A D A C A C A C A D A D B C B C B D A D A D B C B C B D B C B C B D A D B D C D B C C D B D C D C D B C B D B D C D C D B D C D C D Crosses 59
Caveats Epistasis Multiple linked QTL More than two alleles 60
Future work Software Application Paper Sensitivity to departures from assumptions Multiple linked loci Jointly consider multiple unlinked regions 61
Acknowledgments Bret Payseur Genetics, UW–Madison Cécile Ané Statistics and Botany, UW–Madison Sungjin Kim Statistics, UW–Madison NIH/NIGMS R01 GM074244 62
QTL mapping data Broman et al., Genetics, 174:2151-2158, 2006 Owens et al., Hum Mol Genet, 14:1549-1558, 2005 8
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Master of Science in Biostatistics (MSIBS) Master of Science in Biostatistics and Data Science (MSBDS) 1.1.2. Core Program Coursework for All Programs Statistical Computing with SAS , Introduction to R for Data Science, Biostatistics I, Biostatistics II, Study Design and Clinical Trials, Ethics for
19 Zhang, Ying MD, PhD Biostatistics Assistant Professor of Research 20 Zhao, Daniel Yan PhD Biostatistics Associate Professor NOTE: The annual report does not reflect the work of Drs. Raskob or George as their annual reviews are not performed by the Chair of the Department of Biostatistics and Epidemiology.
Department of Biostatistics Oversees biostatistics concentration in the MPH program; offers MS and PhD in Biostatistics Chair: Peihua Qiu, PhD 294-5911 MPH - Biostatistics Concentration Coordinator: Robert Parker, PhD 294-5906 Department of Environmental & Global Health 294 Oversees environmental health concentration in the MPH program Chair:
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