Mapping QTL to a phylogenetic tree
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1 Mapping QTL to a phylogenetic tree Karl W Broman Department of Biostatistics & Medical Informatics University of Wisconsin Madison
2
3 Human vs mouse 3
4 Intercross P 1 P 2 F 1 F 1 F 2 4
5 A tree A B C D E 5
6 A QTL on a tree A B C D E 6
7 QTL mapping QTL = Quantitative Trait Locus QTL mapping data: Set of intercross individuals Quantitative phenotype for each Marker genotype data Genetic map 7
8 QTL mapping data Broman et al., Genetics, 174: , 2006 Owens et al., Hum Mol Genet, 14: ,
9 ANOVA at marker loci Split mice into groups according to genotype at a marker D5NCNP4 (Chr 5) 17.0 WILSET (Chr 9) Do a t-test / ANOVA. Repeat for each marker. Average gut length Average gut length CC CB BB Genotype CC CB BB Genotype 9
10 LOD curves 6 5 LOD score Chromosome 10
11 LOD curves 6 5 LOD score 4 3 5% Chromosome 11
12 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 12
13 QTL on a tree No epistasis Assumptions Ave. phenotype Single diallelic QTL No epistasis or background effects No variation in recombination Known tree LL LH HH Genotype 13
14 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 14
15 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 15
16 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 16
17 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 17
18 QTL on a tree Assumptions Single diallelic QTL No epistasis or background effects No variation in recombination A B C D Known tree 18
19 QTL on a tree Assumptions A B C D Single diallelic QTL No epistasis or background effects No variation in recombination Known tree 19
20 QTL on a tree 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) 20
21 QTL on a tree 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) 21
22 Li et al., Genetics 169: , 2005 Combining crosses 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
23 Diallelic QTL Macdonald and Long, Genetics 176: , 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 10 Ave. phenotype G D C A F H E B Genotype 23
24 Diallelic QTL Macdonald and Long, Genetics 176: , 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 10 Ave. phenotype G D C A F H E B Genotype 24
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) 25
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) 26
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) 27
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) 28
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) 29
30 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) 30
31 Simulated example Individual crosses Combined analysis 8 8 LOD = 2.7 A BCD B ACD C ABD D ABC AB CD 6 6 LOD score 4 LOD score Map position (cm) Map position (cm) 31
32 Four taxa One diallelic QTL with h 2 = 10% All 6 intercrosses; 100 individuals per cross 10,000 simulation replicates Does it work? 100 Power 100 Not determined 100 False positive rate Power (%) Not determined (%) A BCD B ACD C ABD D ABC AB CD A BCD B ACD C ABD D ABC AB CD A BCD B ACD C ABD D ABC AB CD False positive rate (%) Truth Truth Truth 32
33 Four taxa One diallelic QTL with h 2 = 10% All 6 intercrosses; 100 individuals per cross 10,000 simulation replicates Does it work? 100 Power 100 Not determined 100 False positive rate Crude method Power (%) Fancy method Not determined (%) Fancy method Crude method A BCD B ACD C ABD D ABC AB CD A BCD B ACD C ABD D ABC AB CD A BCD B ACD C ABD D ABC AB CD False positive rate (%) Truth Truth Truth 33
34 Does it work? 100 ROC curves Fancy method 80 Power (%) Crude method A BCD B ACD C ABD D ABC AB CD False positive rate (%) 34
35 Does it work? 100 ROC curves Fancy method 80 Power (%) Crude method A BCD B ACD C ABD D ABC AB CD False positive rate (%) 35
36 All partitions? 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) (AC BD) (AD BC) 36
37 All partitions? 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) (AC BD) (AD BC) 37
38 Minimal crosses 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) 38
39 Minimal crosses 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) 39
40 Minimal crosses 5 A D B A B C D C QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) 40
41 Minimal crosses 5 A D B A B C D C QTL position (partition of taxa) Cross 1 (A BCD) 2 (B ACD) 3 (C ABD) 4 (D ABC) 5 (AB CD) 41
42 Minimal crosses Tree Crosses B D A E works C A B C D E B D A E doesn't work C 42
43 Minimal crosses Tree Crosses E D B A works (sort of) C F A B C D E F 43
44 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
45 All or some crosses? 3 taxa All crosses, 100 individuals each, or 2 crosses, 150 individuals each? A B C QTL with 10% heritability; A BC pattern 45
46 All or some crosses? 3 taxa All crosses, 100 individuals each, or 2 crosses, 150 individuals each? A B C QTL with 10% heritability; A BC pattern 100 Power (%) All Crosses 46
47 All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? A B C D QTL with 10% heritability Consider all 7 partitions 47
48 All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? A B C D QTL with 10% heritability Consider all 7 partitions Power (%) A BCD B ACD C ABD D ABC AB CD True pattern 48
49 All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? A B C D QTL with 10% heritability Consider all 7 partitions Power (%) A BCD B ACD C ABD D ABC AB CD True pattern 49
50 All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? A B C D QTL with 10% heritability Consider all 7 partitions Power (%) A BCD B ACD C ABD D ABC AB CD True pattern 50
51 All or some crosses? 4 taxa All crosses, 100 individuals each, or 3 crosses, 200 individuals each? A B C D QTL with 10% heritability Consider the 5 partitions induced by the tree Power (%) A BCD B ACD C ABD D ABC AB CD True pattern 51
52 Which crosses? Considering all partitions Power (%) AB CD D ABC C ABD B ACD A BCD Crosses 52
53 Which crosses? Considering all partitions Power (%) AB CD D ABC C ABD B ACD A BCD Crosses 53
54 Which crosses? Considering all partitions Simulated example Power (%) AB CD LOD score Crosses Map position (cm) Partition of taxa Cross A BCD B ACD C ABD D ABC AB CD AC BD AD BC 54
55 Which crosses? Considering all partitions Simulated example Power (%) AB CD LOD score Crosses Map position (cm) Partition of taxa Cross A BCD B ACD C ABD D ABC AB CD AC BD AD BC 55
56 Which crosses? Considering all partitions Simulated example Power (%) AB CD LOD score Crosses Map position (cm) Partition of taxa Cross A BCD B ACD C ABD D ABC AB CD AC BD AD BC
57 Which crosses? Considering all partitions Simulated example Power (%) AB CD LOD score Crosses Map position (cm) Partition of taxa Cross A BCD B ACD C ABD D ABC AB CD AC BD AD BC
58 Which crosses? Considering all partitions Power (%) AB CD D ABC C ABD B ACD A BCD Crosses 58
59 Which crosses? Considering the 5 partitions induced by the tree Power (%) AB CD D ABC C ABD B ACD A BCD Crosses 59
60 Caveats Epistasis Multiple linked QTL More than two alleles 60
61 Future work Software Application Paper Sensitivity to departures from assumptions Multiple linked loci Jointly consider multiple unlinked regions 61
62 Acknowledgments Bret Payseur Cécile Ané Sungjin Kim Genetics, UW Madison Statistics and Botany, UW Madison Statistics, UW Madison NIH/NIGMS R01 GM
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