Title: Recombination and Pedigrees
1Recombination and Pedigrees
Genealogies and Recombination The
ARG Recombination Parsimony The ARG and
Data Pedigrees Models and Data Pedigrees
ARGs Challenges Empirical Investigations Open
Questions
2Recombination Histories Global Pedigrees
Acknowledgements Yun Song - Rune
Lyngsø - Mike Steel
3Hudson Kaplans RM
0 0 0 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0
0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1
1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 0
1 1 1 1 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
1 1 0 1
If you equate RM with expected number of
recombinations, this could be used as an
estimator. Unfortunately, RM is a gross
underestimate of the real number of
recombinations.
4Local Inference of Recombinations
5Finding Minimal Recombination Histories
64 Bodmer Edwards Parsimony defined as
reconstruction principle 85 Hudson Kaplan uses
minimal recombination histories as observed
recombinations
- Attempts to find minimal histories of sequences
- Definition of recombination as Subtree Prune
Regraft operations
- J.J.Hein Reconstructing the history of
sequences subject to Gene Conversion and
Recombination. Mathematical Biosciences. (1990)
98.185-200. - J.J.Hein A Heuristic Method to Reconstruct the
History of Sequences Subject to Recombination.
J.Mol.Evol. 20.402-411. 1993 - Hein,J.J., T.Jiang, L.Wang K.Zhang (1996) "On
the complexity of comparing evolutionary trees"
Discrete Applied Mathematics 71.153-169 - Song, Y.S. (2003) On the combinatorics of rooted
binary phylogenetic trees. Annals of
Combinatorics, 7365379 - Song, Y.S. Hein, J. (2005) Constructing
Minimal Ancestral Recombination Graphs. J. Comp.
Biol., 12147169 - Song, Y.S. Hein, J. (2004) On the minimum
number of recombination events in the
evolutionary history of DNA sequences. J. Math.
Biol., 48160186. - Song, Y.S. Hein, J. (2003) Parsimonious
reconstruction of sequence evolution and
haplotype blocks finding the minimum number of
recombination events, Lecture Notes in
Bioinformatics, Proceedings of WABI'03,
2812287302. - Lyngsø, Song and Hein (2005) Minimal
Recombination Histories by Branch and Bound WABI
6Minimal Number of Recombinations
The Kreitman data (1983) 11 sequences, 3200bp,
43(28) recoded, 9 different
Bi-partitions
How many neighbors?
7Two Adjacent Columns
1. RecDistT1,T2 is hard for large leaf number,
but can be automatically calculated by adding
DiamRec trivial columns and only considering 1
recombination neighbors.
2. Infinite Site Assumption Local Trees must
contain Local Bipartition
8Metrics on Trees based on subtree transfers.
9Tree Combinatorics and Neighborhoods
Observe that the size of the unit-neighbourhood
of a tree does not grow nearly as fast as the
number of trees
101
4
2
3
5
6
7
11The Minimal Recombination History for the
Kreitman Data
Methods of rec events obtained
Hudson Kaplan (1985) 5
Myers Griffiths (2003) 6
Song Hein (2004). Set theory based approach. 7
Song Hein (2003). Tree scanning using DP Lyngsø, Song Hein (2006). Massive Acceleration using Branch and Bound Algorithm. Lyngsø, Song Hein (2006). Minimal number of Gene Conversions (in prep.) 7 7 5-2/6-1
12- recombination 27 ACs
recombination 3108 ACs
13Ancestral configurations to 2 sequences with 2
segregating sites
14Counting Recursion
15Counting Branch and Bound Algorithm
16Time versus Spatial Coalescent-Recombination
(Griffiths, 1981 Hudson, 1983 - Wiuf Hein,
1999)
Temporal Process
Spatial Process
17Time versus Spatial 2 Pedigrees
Elston-Stewart (1971) -Temporal Peeling
Algorithm
Father
Mother
Condition on parental states Recombination and
mutation are Markovian
Lander-Green (1987) - Genotype Scanning
Algorithm
Father
Mother
Condition on paternal/maternal inheritance Recombi
nation and mutation are Markovian
18Time versus Spatial 3 Phylogenetic Alignment
- Optimisation Algorithms
- indels of length 1 (David Sankoff, 1973)
Spatial - indels of length k (Bjarne Knudsen, 2003)
Temporal - Statistical Alignment
Temporal
Spatial
19minARGs Recombination Events Local Trees
20Likelihood Calculations on the e-ARG
010 010 101 101 110
Example
21(No Transcript)
22Reconstructing global pedigrees
Superpedigrees Steel and Hein, 2005
The gender-labeled pedigrees for all pairs,
defines global pedigree
Gender-unlabeled pedigrees doesnt!!
23Reconstructing global pedigrees Links and lassos
Steel and Hein, 2005
Gender-labeled links and lassos determine the
global pedigree.
24Benevolent Mutation and Recombination Process
- All embedded phylogenies are observable
- Do they determine the pedigree?
Counter example
25Summary and Future
- Minimal Recombination Histories
- Likelihood Calculations
- Global Pedigrees Inferring Pedigrees from
Genomes
Recombination Remove infinite site assumption
Investigate MCMC algorithms Pedigrees Data
Analysis Algorithms
Presentation can be found at
http//mathgen.stats.ox.ac.uk/bioinformatics/
26To Do
- Hudson Slide
- Neighbor trees
- Literature and History