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Inferring Local Tree Topologies for SNP Sequences Under Recombination in a Population. Yufeng Wu Dept. of Computer Science and Engineering University of Connecticut, USA. Sites. 00100 01010 00101 00010 11101. Haplotypes. Genetic Variations. Sites.

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inferring local tree topologies for snp sequences under recombination in a population

Inferring Local Tree Topologies for SNP Sequences Under Recombination in a Population

Yufeng Wu

Dept. of Computer Science and Engineering

University of Connecticut, USA

MIEP 2008

genetic variations

Sites

00100

01010

00101

00010

11101

Haplotypes

Genetic Variations

Sites

  • Single-nucleotide polymorphism (SNP): a site (genomic location) where two types of nucleotides occur frequently in the population.
    • Haplotype, a binary vector of SNPs (encoded as 0/1).
  • Haplotypes: offer hints on genealogy.

AATGTAGCCGA

AATATAACCTA

AATGTAGCCGT

AATGTAACCTA

CATATAGCCGT

AATGTAGCCGA

AATATAACCTA

AATGTAGCCGT

AATGTAACCTA

CATATAGCCGT

Each SNP induces a split

DNA sequences

genealogy evolutionary history of genomic sequences

Disease mutation

Genealogy: Evolutionary History of Genomic Sequences
  • Tells how individuals in a population are related
  • Helps to explain diseases: disease mutations occur on branches and all descendents carry the mutations
  • Problem: How to determine the genealogy for “unrelated” individuals?
  • Complicated by recombination

Diseased (case)

Healthy (control)

Individuals in current population

recombination

Suffix

Prefix

11000

0000001111

Breakpoint

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

000110000001111

ancestral recombination graph arg

00

10

Ancestral Recombination Graph (ARG)

Mutations

Recombination

1 0

0 1

1 1

10

01

00

10

11

01

00

S1 = 00

S2 = 01

S3 = 10

S4 = 11

Assumption:

At most one mutation per site

S1 = 00

S2 = 01

S3 = 10

S4 = 10

local trees
Local Trees

ARG

  • ARG represents a set of local trees.
  • Each tree for a continuous genomic region.
  • No recombination between two sites  same local trees for the two sites
  • Local tree topology: informative and useful

Local tree near site 2

Local tree to the right of site 3

Local tree near sites 1 and 2

inference of local tree topologies
Inference of Local Tree Topologies
    • Question: given SNP haplotypes, infer local tree topologies (one tree for each SNP site, ignore branch length)
    • Hein (1990, 1993)
  • Enumerate all possible tree topologies at each site
    • Song and Hein (2003,2005)
    • Parsimony-based
  • Local tree reconstruction can be formulated as inference on a hidden Markov model.
local tree topologies
Local Tree Topologies
  • Key technical difficulty
    • Brute-force enumeration of local tree topologies: not feasible when number of sequences > 9
  • Can not enumerate all tree topologies
  • 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

A

C

B

E

D

F

G

H

how to do better neighboring local trees are similar
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: reconstructing local trees by combining information from multiple nearby SNPs
rent refining neighboring trees
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
a little background compatibility
A Little Background: Compatibility

1 2 3 4 5

a

b

c

d

e

f

g

0 0 0 1 0

1 0 0 1 0

0 0 1 0 0

1 0 1 0 0

0 1 1 0 0

0 1 1 0 1

0 0 1 0 1

Sites 1 and 2 are compatible, but 1 and 3 are incompatible.

M

  • Two sites (columns) p, q are incompatible if columns p,q 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.
fully compatible region simple case
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.
split propagation more general rule
Split Propagation: More General Rule
  • Three consecutive sites 1,2 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 subtreein both trees at sites 1 and 2.
  • Rule: a split propagates to both directions until reaching a incompatible tree.
unique refinement
Unique Refinement
  • Consider the subtree with leaves 1,2 and 3.
    • Which refinement is more likely?
    • Add split of 1 and 2: the only split that is compatible with neighboring T2.
  • Rule: refine a non-binary node by the only compatible split with neighboring trees

?

1

3

2

one subtree prune regraft spr event
One Subtree-Prune-Regraft (SPR) Event
  • Recombination: simulated by SPR.
    • The rest of two trees (without pruned subtrees) remain the same
  • Rule: find identicalsubtree 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.

Subtree to prune

More complex rules possible.

simulation
Simulation
  • Hudson’s 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 Hein’s method.
  • Test local tree topology recovery scored by Song and Hein’s shared-split measure

 = 15

 = 50

acknowledgement
Acknowledgement
  • Software available upon request.
  • More information available at: http://www.engr.uconn.edu/~ywu
  • I want to thank
    • Yun S. Song
    • Dan Gusfield