Association Mapping by Local Genealogies Bioinformatics Research Center University of Aarhus Thomas Mailund

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)

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----

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

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

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

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

The Ancestral Recombination Graph Mutations (Hudson 1990, Griffith&Marjoram 1996)

(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

(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

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

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

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

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

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

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

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

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

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

--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

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

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

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)

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)

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

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

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

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

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

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)

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)

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)

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)

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)

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: Phased: Unphased:

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

Scoring trees Mailund et al 2006

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

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

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

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,...

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

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

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

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:

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

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

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

Fine mapping example...

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

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

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

Comparison with Margarita Unphased data; Min markers: 5

Comparison with Margarita Phased data; Min markers: 5

Comparison with Margarita Unphased data; Min markers: 9

Comparison with Margarita Phased data; Min markers: 9

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 Blossoc unphased: -fH -fB -fA -fG -fP -fX m = 1: m = 2: m = 3: m = 4: m = 5: m = 6: m = 7: m = 8: m = 9:

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

Comparison with HPM (Toivonen et al. 2000)

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)

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

Comparison with HapCluster (Waldron et al. 2006)

Implementation freely available Homepage: Command line and graphical user interface...

The end Thank you! More at

References A cladistic analysis of phenotypic associations with haplotypes inferred from restriction endonuclease mapping – A.R. Templeton, E. Boerwinkle, and C.F. Sing; Genetics Gene genealogies and the coalescent process – R.R. Hudson; Oxford Surveys in Evolutionary Biology Ancestral inference from samples of DNA sequences with recombination – R.C. Griffith and P. Majoram; J Comput Biol 3: 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 Gene mapping via the ancestral recombination graph – F. Larribe, S. Lessard, and N.J. Schork; Theor Popul Biol 62: Haplotyping as Perfect Phylogeny: Conceptual Framework and Efficient Solutions – D. Gusfield; RECOMB 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: Minimum Recombination Histories by Branch and Bound – R.B. Lyngsø, Y.S. Song and J. Hein; WABI 2005, LNCS , 2005 A linear-time algorithm for the perfect phylogeny haplotyping (PPH) problem – Z. Ding, V. Filkov and D. Gusfield; RECOMB Haplotype-based linkage disequilibrium mapping via direct data mining – J Li and T Jiang; Bioinformatics 21(24) Fine mapping of disease genes via haplotype clustering – E.R.B. Waldron, J.C. Whittaker, and D.J. Balding; Genet Epidemiol 30: Whole genome association mapping by incompatibilities and local perfect phylogenies – T. Mailund, S. Besenbacher, and M.H. Schierup; BMC Bioinformatics 7: TreeDT: Tree pattern mining for gene mapping – P. Sevon, H. Toivonen, V. Ollikainen; IEEE/ACM Transactions on Computational Biology and Bioinformatics A tutorial on statistical methods for population association studies – D.J. Balding; Nat Rev Genet 7: 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