Inference of Complex Genealogical Histories In Populations and Application in Mapping Complex Traits

1
Inference of Complex Genealogical Histories In
Populations and Application in Mapping Complex
Traits

• Yufeng Wu
• Dept. of Computer Science and Engineering
• University of Connecticut

2
Genealogy Evolutionary History of Genomic
Sequences

• Tells how sequences in a population are related
• Helps to explain diseases disease mutations
  occur on branches and all descendents carry the
  mutations
• Genealogy unknown. Only have SNP haplotypes
  (binary sequences).
• Problem Inference of genealogy for unrelated
  haplotypes
• Not easy partly due to recombination

Diseased (case)
Healthy (control)
Sequences in current population
3
Recombination

• One of the principle genetic forces shaping
  sequence variations within species
• Two equal length sequences generate a third new
  equal length sequence in genealogy
• Spatial order is important different parts of
  genome inherit from different ancestors.

110001111111001
1100 00000001111
000110000001111
4
Ancestral Recombination Graph (ARG)
Mutations
Recombination
10
01
00
10
01
00
11
S1 00 S2 01 S3 10 S4 11
Assumption At most one mutation per site
S1 00 S2 01 S3 10 S4 10
5
What is the Use of an ARG
May look at the ARG directly. But for noisy
data another way of using ARGs an ARG
represents a set of local trees!
Data 0000 0101 0110 1110 1010
0000
0000
0100
0010
Local trees evolutionary history for different
genomic regions between recombination breakpoints.
1010
0110
0101
1010
0000
0110
1110
6
At which Local Tree Did Disease Mutations Occur

• Clear separation of cases/controls not expected
  for complex diseases

Case
Control
7
How to infer ARGs

• But we do not know the true ARG!
• Goal infer ARGs from haplotypes
• First practical ARG association mapping method
  (Minichiello and Durbin 2006)
• Use plausible ARGs heuristic
• Less complex disease model implicitly assume one
  disease mutation with major effects.
• My results (Wu RECOMB 2007)
• Generate ARGs with a provable property and works
  on a well-defined complex disease model
• Focus on parsimonious history

8
Simulation Results (Wu 2007)

• TMARG/MARGARITA sample ARGs decompose to
  local trees and look for association signals.
• LATAG infer local trees at focal points.
• Average mapping error for 50 simulated datasets
  from Zollner and Pritchard

Comparison TMARG (minARGs) TMARG (near
minARGs) LATAG (Z. P.) MARGARITA (M.
D.). TMARG (my program) and MARGRITA are much
faster than LATAG.
9
Preliminary Results GAW16 Data

• GAW16 data from the North American Rheumatoid
  Arthritis Consortium (NARAC) 868 cases and 1194
  controls. Chromosome one 40929 SNPs.
• Running TMARG on large-scale data
• Break into non-overlapping windows
• Run fastPHASE (Scheet and Stephens 06) to
  obtain haplotypes
• Run TMARG with Chi-square mode

Caution more investigation needed.
10
A Related ProblemInference of Local Tree
Topologies Directly (Wu 2008 Submitted)
11
Inference of Local Tree Topologies

• Recall ARG represents a set of local trees.
• Question given SNP haplotypes infer local tree
  topologies (one tree for each SNP site ignore
  branch length)
• Hein (1990 1993)
• Song and Hein (20032005) enumerate all possible
  tree topologies at each site
• Parsimony-based

12
Local Tree Topologies

• Key technical difficulty enumerate all tree
  topologies
• Brute-force enumeration of local tree topologies
  not feasible when number of sequences gt 9
• Trivial solution create a tree for a SNP
  containing the single split induced by the SNP.
• Always correct (assume one mutation per site)
• But not very informative need more refined trees!

A 0 B 0 C 1 D 0 E 1 F 0 G 1 H 0
13
How to do better Neighboring Local Trees are
Similar!

• Nearby SNP sites provide hints!
• Near-by local trees are often topologically
  similar
• Recombination often only alters small parts of
  the trees
• Key idea reconstruct local trees by combining
  information from multiple nearby SNPs

14
RENT REfining Neighboring Trees

• Maintain for each SNP site a (possibly
  non-binary) tree topology
• Initialize to a tree containing the split induced
  by the SNP
• Gradually refining trees by adding new splits to
  the trees
• Splits found by a set of rules (later)
• Splits added early may be more reliable
• Stop when binary trees or enough information is
  recovered

15
A Little Background Compatibility
1 2 3
a b c d e
0 0 0 1 0 0 0 0 1 1 0 1 0 1 1
Sites 1 and 2 are compatible but 1 and 3 are
incompatible.
M

• Two sites (columns) p q are incompatible if
  columns pq contains all four ordered pairs
  (gametes) 00 01 10 11. Otherwise p and q are
  compatible.
• Easily extended to splits.
• A split s is incompatible with tree T if s is
  incompatible with any one split in T. Two trees
  are compatible if their splits are pairwise
  compatible.

16
Fully-Compatible Region Simple Case

• A region of consecutive SNP sites where these
  SNPs are pairwise compatible.
• May indicate no topology-altering recombination
  occurred within the region
• Rule for site s add any such split to tree at
  s.
• Compatibility very strong property and unlikely
  arise due to chance.

17
Split Propagation More General Rule

• Three consecutive sites 12 and 3. Sites 1 and 2
  are incompatible. Does site 3 matter for tree at
  site 1
• Trees at site 1 and 2 are different.
• Suppose site 3 is compatible with sites 1 and 2.
  Then
• Site 3 may indicate a shared subtree in both
  trees at sites 1 and 2.
• Rule a split propagates to both directions until
  reaching a incompatible tree.

18
One Subtree-Prune-Regraft (SPR) Event

• Recombination simulated by SPR.
• The rest of two trees (without pruned subtrees)
  remain the same
• Rule find compatible subtree Ts in neighboring
  trees T1 and T2 s.t. the rest of T1 and T2 (Ts
  removed) are compatible. Then joint refine T1- Ts
  and T2- Ts before adding back Ts.

More complex rules possible.
19
Simulation

• Hudsons program MS (with known coalescent local
  tree topologies) 100 datasets for each settings.
• Data much larger and perform better or similarly
  for small data than Song and Heins method.
• Test local tree topology recovery scored by Song
  and Heins shared-split measure

15
50
20
Acknowledgement

• More information available at http//www.engr.uco
  nn.edu/ywu
• I want to thank
• Dan Gusfield
• Yun S. Song
• Charles Langley
• Dan Brown
• And National Science Foundation and UConn
  Research Foundation