1. Association Mapping by Local Genealogies Bioinformatics Research Center University of Aarhus http://www.birc.au.dk/~mailund mailund@birc.au.dk Thomas Mailund

2. Disease mapping... --A--------C--------A----G---X----T---C---A---- --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- Locate disease locus  Unlikely to be among our genotyped markers  Use information from available markers Cases (affected) Controls (unaffected)

3. Indirect signal for causal locus --T--------G--------A----G---X----C---C---A---- --A--------G--------G----G---X----C---C---A---- --A--------C--------A----G---X----T---C---A---- --T--------C--------A----G---X----T---C---A---- --T--------C--------A----T---X----T---A---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------A----G---X----T---C---G---- --T--------C--------A----T---X----T---C---A---- --A--------C--------A----G---X----T---C---A---- --A--------C--------G----T---X----C---A---A---- --A--------C--------A----G---X----C---C---G---- The markers are not independent  Knowing one marker is partial knowledge of others  This dependency decreases with distance --A--------C--------A----G---X----T---C---A----

4. The Ancestral Recombination Graph Locally, the genealogy of a small genomic region is the Ancestral Recombination Graph (ARG)‏ (Hudson 1990, Griffith&Marjoram 1996)

5. The Ancestral Recombination Graph Sampled sequences MRCA (Hudson 1990, Griffith&Marjoram 1996)

6. The Ancestral Recombination Graph Recombination Coalescence (Hudson 1990, Griffith&Marjoram 1996)

7. The Ancestral Recombination Graph Non-ancestral material Non- ancestral material Ancestral material (Hudson 1990, Griffith&Marjoram 1996)

8. The Ancestral Recombination Graph Mutations 1 23 4 (Hudson 1990, Griffith&Marjoram 1996)

9. (Larribe, Lessard and Schork, 2002) The unknown ARG, mutation locus and disease status can be explored using statistical sampling methods This is very CPU demanding! The Ancestral Recombination Graph

10. (Lyngsø, Song and Hein, 2005; Minichiello and Durbin, 2006) The unknown ARG, mutation locus and disease status can be explored using statistical sampling methods This is very CPU demanding! Sampling only (near-) minimal ARGs improves matters  Still CPU demanding The Ancestral Recombination Graph

11. Local trees For each “point” on the chromosome, the ARG determines a (local) tree:

12. Local trees For each “point” on the chromosome, the ARG determines a (local) tree:

13. Local trees For each “point” on the chromosome, the ARG determines a (local) tree:

14. Local trees For each “point” on the chromosome, the ARG determines a (local) tree:

15. Local trees Type 1: No change Type 2: Change in branch lengths Type 3: Change in topology From Hein et al. 2005

16. Local trees Recombination rate From Hein et al. 2005 Tree measure: where

17. Using the local trees Tree genealogies  Each site a different genealogy  Nearby genealogies only slightly different --T--------G--------A----G---X----C----C-----A-- --A--------G--------G----G---X----C----C-----A-- --A--------C--------A----G---X----T----C-----A-- --T--------C--------A----G---X----T----C-----A-- --T--------C--------A----T---X----T----A-----A-- --A--------C--------A----G---X----T----C-----A-- AAATTTCCGGCC AAAGAAGGGGGTTTCCTTCCCCCAAAAAAA A nearby tree is an imperfect local tree

18. Tree at disease site:  “Perfect” setup  Incomplete penetrance  Other disease causes HHHHHHHH DDDDD HHHHHHHH DDDHD HDHHHDHH DDDHD Templeton et al 1987 Using the local trees

19. At the disease site:  A significant clustering of diseased/healthy HDHHHDHH DDDHD Using the local trees Templeton et al 1987

20. --T--------G--------A----G---X----C----C-----A-- --A--------G--------G----G---X----C----C-----A-- --A--------C--------A----G---X----T----C-----A-- --T--------C--------A----G---X----T----C-----A-- --T--------C--------A----T---X----T----A-----A-- --A--------C--------A----G---X----T----C-----A-- AAATTT CCGGCCAAAGAAGGGGGTTTCCTTCCCCCAAAAAAA Tree at disease site resembles neighbours Using the local trees

21. Near the disease site:  A significant clustering of diseased/healthy HDHHHDHH DDDHD Using the local trees Zöllner and Pritchard 2005; Mailund et al 2006 ; Sevon et al 2006

22. Approach:  Infer trees over regions  Score the regions wrt their clustering HDHHHDHH DDDHD Zöllner and Pritchard 2005; Mailund et al 2006 ; Sevon et al 2006 Using the local trees

23. In the infinite sites model:  Each mutation occurs only once  Each mutation splits the sample in two  A consistent tree can efficiently be inferred for a recombination free region Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

24. Use the four-gamete test to find regions, around each locus, that can be explained by a tree Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

25. Build a tree for each such region Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

26. Build a tree for each such region Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

27. Build a tree for each such region Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

28. Build a tree for each such region Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

29. Score the tree, and assign the score to the locus Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

30. If there are too many incompatibilities, we just cheat (but try to keep the cheating low in the tree) Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

31. If there are too many incompatibilities, we just cheat (but try to keep the cheating low in the tree) Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

32. If there are too many incompatibilities, we just cheat (but try to keep the cheating low in the tree) Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

33. If there are too many incompatibilities, we just cheat (but try to keep the cheating low in the tree) Mailund et al 2006 BLOck aSSOCiation (BLOSSOC)

34. Ding et al 2007 The tree construction is more complicated – but still possible and still efficient – for un-phased sequence data The Perfect Phylogeny Haplotyping (PPH) problem  Gusfield 2002; Ding et al 2005 (The “cheating” still requires local phasing; the most time consuming step)

35. BLOck aSSOCiation (BLOSSOC) Ding et al 2007 The tree construction is more complicated – but still possible and still efficient – for un-phased sequence data The Perfect Phylogeny Haplotyping (PPH) problem  Gusfield 2002; Ding et al 2005 (The “cheating” still requires local phasing; the most time consuming step) Min markers: 1 2 3 4 5 6 7 8 9 Phased: 4 4 4 4 4 4 5 5 7 Unphased: 26 66 248 596 905 1194 1419 1624 1844

36. Scoring trees Red=cases Green=controls Are the case chromosomes significantly overrepresented in some sub-trees? Mailund et al 2006

37. Scoring trees Mailund et al 2006

38. Scoring trees Mutation We can place “mutations” on the tree edges and partition chromosomes into “mutants” and “wild-types”... Mailund et al 2006 Mutants Wild-types

39. Scoring trees...and assign different risks based on the implied genotypes Mutants Wild-types Likelihoods Haploid data: Null model: Diploid data: Mailund et al 2006

40. Scoring trees Generalizes to more mutations in the obvious way Likelihoods Haploid data: Null model: Diploid data: Mailund et al 2006 Wild-types Mutant A Mutant B

41. Scoring trees Tree score Mailund et al 2006 Wild-types Mutant A Mutant B Likelihood Number of parameters Penalty weight Depending on penalty weight we get Akaiki Information Criteria, Bayesian Information Criteria, Hanna and Quinn Criteria,...

42. Scoring trees Tree score Mailund et al 2006 Wild-types Mutant A Mutant B Likelihood Number of parameters Penalty weight For efficiency reasons, we only explore the mutations top down, stopping when the score no longer improves

43. Scoring trees Mailund et al 2006; Ding et al 2007 Mutants Wild-types Likelihoods Haploid data: Null model: Diploid data:

44. Scoring trees Using an uninformative Beta prior, β (1,1), we can integrate the risk parameters out Mailund et al 2006; Ding et al 2007 Mutants Wild-types Marginal likelihoods Haploid data: Null model: Diploid data: Balding 2006 ; Waldron et al 2006

45. Scoring trees For the tree, we take the mean score over all edges. The score is the Bayes factor of the tree likelihood vs the null model likelihood. Mailund et al 2006; Ding et al 2007 Mutants Wild-types Null model: Tree model: Score:

46. Scoring trees This generalises to several mutations (more complicated implied genotypes; computationally slower) Through Bayes factors we can test for the number of mutations. Mailund et al 2006; Ding et al 2007

47. Scoring trees Generalises to quantitative traits as well with minor changes to the scoring approach... Besenbacher et al. 2007

48. Fine mapping example... 500 cases / 500 controls 100 SNPs on 100 Kbp 2 mutations at same locus with same risk P(case|aa) = 5% ; GRR = 2

49. Fine mapping example...

51. Localization accuracy 1 causal mutation Max BF / min p-val used as point estimate

52. Localization accuracy 2 causal mutations Max BF / min p-val used as point estimate

53. Comparison with Margarita Margarita is the (near-)minimal ARG method of Minichiello and Durbin Data sets:  1000 cases / 1000 controls  300 markers Comparisons with both phased and unphased data Acknowledgment:  Experiments done by Yun S. Song

54. Comparison with Margarita Unphased data; Min markers: 5

55. Comparison with Margarita Phased data; Min markers: 5

56. Comparison with Margarita Unphased data; Min markers: 9

57. Comparison with Margarita Phased data; Min markers: 9

58. Comparison with Margarita How did we do?  Generally between single-marker test and Margarita  Depends heavily on the scoring function  Quite well on time: Margarita: phased unphased 118620 300512 Blossoc unphased: -fH -fB -fA -fG -fP -fX m = 1: 26 26 25 26 2827 m = 2: 66 66 66 66 68 67 m = 3: 248 248 248 248 250 248 m = 4: 596 596 597 596 598 595 m = 5: 905 904 904 904 906 905 m = 6: 1194 1194 1195 1195 1196 1195 m = 7: 1419 1418 1416 1415 1419 1416 m = 8: 1624 1626 1623 1626 1628 1627 m = 9: 1844 1847 1845 1842 1851 1852

59. Choice of scoring function Is one scoring function generally better than the rest?  Unfortunately not  Simulations show a (small) trend:  Small datasets(<1000 individuals)-fP  Medium datasets(~1000 individuals)-fH  Larger datasets(>1000 individuals)-fA

60. Comparison with HPM (Toivonen et al. 2000)

61. Comparison with HapMiner P(case|AA)=15%; P(case|Aa)=10%; P(case|aa)=5% 200 markers, rho=40, 500 cases / 500 controls, P(A)=18-22% P(case|AA)=20%; P(case|Aa)=8%; P(case|aa)=5% (Li and Jiang 2005)

62. Comparison with HapMiner P(case|AA)=15%; P(case|Aa)=10%; P(case|aa)=5% 200 markers, rho=40, 500 cases / 500 controls, P(A)=18-22% P(case|AA)=20%; P(case|Aa)=8%; P(case|aa)=5% (Li and Jiang 2005) Blossoc: ~5 sec per data set HapMiner: ~40 min per data set

63. Comparison with HapCluster (Waldron et al. 2006)

64. Implementation freely available Homepage: www.birc.au.dk/~mailund/Blossoc Command line and graphical user interface...

65. The end Thank you! More at http://www.birc.au.dk/~mailund/association-mapping/

66. References A cladistic analysis of phenotypic associations with haplotypes inferred from restriction endonuclease mapping – A.R. Templeton, E. Boerwinkle, and C.F. Sing; Genetics 117 343-351 1987 Gene genealogies and the coalescent process – R.R. Hudson; Oxford Surveys in Evolutionary Biology 7 1-44 1990 Ancestral inference from samples of DNA sequences with recombination – R.C. Griffith and P. Majoram; J Comput Biol 3:4 479-502 1996 Data Mining Applied to Linkage Disequilibrium Mapping – H.T.T. Toivonen, P. Onkamo, K. Vasko, V. Ollikainen, P. Sevon, H. Mannila, M. Herr and J. Kere; Am J. of Human Gen 67 133-145 2000 Gene mapping via the ancestral recombination graph – F. Larribe, S. Lessard, and N.J. Schork; Theor Popul Biol 62:2 215-229 2002 Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions – D. Gusfield; RECOMB 2002 166-175 2002 Gene genealogies, variation, and evolution – J. Hein, M.H. Schierup, and C. Wiuf; Oxford University Press 2005 Coalescent-based association mapping and fine mapping of complex trait loci – S. Zöllner and J.K. Pritchard; Genetics 169:2 1071-1092 2005 Minimum Recombination Histories by Branch and Bound – R.B. Lyngsø, Y.S. Song and J. Hein; WABI 2005, LNCS 3692 239- 250, 2005 A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem – Z. Ding, V. Filkov and D. Gusfield; RECOMB 2005 585-600 2005 Haplotype-based linkage disequilibrium mapping via direct data mining – J Li and T Jiang; Bioinformatics 21(24) 4384-4393 2005 Fine mapping of disease genes via haplotype clustering – E.R.B. Waldron, J.C. Whittaker, and D.J. Balding; Genet Epidemiol 30:2 170-179 2006 Whole genome association mapping by incompatibilities and local perfect phylogenies – T. Mailund, S. Besenbacher, and M.H. Schierup; BMC Bioinformatics 7:454 2006 TreeDT: Tree pattern mining for gene mapping – P. Sevon, H. Toivonen, V. Ollikainen; IEEE/ACM Transactions on Computational Biology and Bioinformatics 3 174-185 2006 A tutorial on statistical methods for population association studies – D.J. Balding; Nat Rev Genet 7:10 781-791 2006 Mapping Trait Loci by Use of Inferred Ancestral Recombination Graphs – M. Minichiello and R. Durbin; Am J. of Human Gen 2006 Using unphased perfect phylogenies for efficient whole-genome association mapping – Z. Ding, T. Mailund and Y.S. Song; In preparation 2007