Recombination Histories

1
Recombination Histories Global Pedigrees
Acknowledgements Yun Song - Rune
Lyngsø - Mike Steel
2
Basic Evolutionary Events
3
Local Inference of Recombinations
4
Hudson 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.
5
Minimal Number of Recombinations
The Kreitman data (1983) 11 sequences, 3200bp,
43(28) recoded, 9 different
Bi-partitions
How many neighbors?
6
Metrics on Trees based on subtree transfers.
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Tree 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
8
1
4
2
3
5
6
7
9
The 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
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- recombination 27 ACs
recombination 3108 ACs
11
Ancestral configurations to 2 sequences with 2
segregating sites
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Counting Branch and Bound Algorithm
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minARGs Recombination Events Local Trees
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Reconstructing global pedigrees
Superpedigrees Steel and Hein, 2005
The gender-labeled pedigrees for all pairs,
defines global pedigree
Gender-unlabeled pedigrees doesnt!!
15
Benevolent Mutation and Recombination Process

• All embedded phylogenies are observable
• Do they determine the pedigree?

Counter example