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Coalescents
Joe Felsenstein
GENOME 453, Autumn 2015
Coalescents – p.1/48
Cann, Stoneking, and Wilson
Becky Cann Mark Stoneking the late Allan Wilson
Cann, R. L., M. Stoneking, and A. C. Wilson. 1987. Mitochondrial DNAand human evolution. Nature 325:a 31-36.
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Mitochondrial Eve
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Genealogy of gene copies in a random-mating population
Time
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Untangling this genealogy by left-right swappings ...
Time
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Genealogy of a sample of gene copies
Time
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Ancestry of a sample in the population pedigree
Time
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Why lineages coalesce
each gene comes from a random copyin the previous generation
a chance of 1 out of 2N that anotherone comes from the same copy
hence it takes about 2N generations fortwo lineages to coalesce
under the Wright−Fisher model
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Sir John Kingman
J. F. C. Kingman in about 1983
Currently Emeritus Professor of Mathematics at Cambridge University,U.K., and former head of the Isaac Newton Institute of MathematicalSciences.
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Kingman’s coalescent
u9u
8u
7u6u
5
u4
u3
u2
Random collision of lineages as go back in time (sans recombination)Collision is faster the smaller the effective population size
Average time for k copies to coalesce to k−1 = k(k−1)
4Ne
Average time for n 1 − 1n ( generations (copies to coalesce = 4Ne
Average time for two copies to coalesce = generationse2N
In a diploid population of effective population size eN
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An accurate analogy: Bugs In A Box
There is a box ...
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An accurate analogy: Bugs In A Box
with bugs that are ...
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An accurate analogy: Bugs In A Box
... hyperactive ...
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An accurate analogy: Bugs In A Box
... indiscriminate ...
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An accurate analogy: Bugs In A Box
... voracious ...
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An accurate analogy: Bugs In A Box
... (eats other bug) ...
Gulp!
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An accurate analogy: Bugs In A Box
... and insatiable.
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Random coalescents from the same population
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Two sources of variability
can reduce variability by looking at(i) more gene copies, or(ii) more loci
(2) Randomness of coalescence of lineages
can reduce variance of
branch by examining more sitesnumber of mutations per site per
affected by the u
(1) Randomness of mutation
Necoalescence times allow estimation of
Neaffected by effective population size
mutation rate
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Coalescent with population growth
During a population bottleneckthere is expected to be aburst of coalescence
Down near the root of the treeeffects of population sizebecome difficult to see
size of population
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Coalescent with migration
Time
population #1 population #2
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Coalescent with migration, untangled
Time
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My ancestor?
Joe
Eleanor Jake
Helen Will Sheimdel Lev
Cornelia John Maud William Itzhak Jacob
1850s
1880s
1910s
1942
747
about 44 more generations
bornCharles the Great
(Charlemagne)
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Chromosome 1, back up one lineage
now
−1
−2
−3
−4
−5
−6 (none)
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Coalescent with recombination
Recomb.
Different markers have slightly different coalescent trees
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Coalescent with recombination
1 142 143 417 418 562
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A phylogeographic study
The rotifer Brachionus plicatilis
Mills, S., D. H. Lunt, and A. Gomez 2007. Global isolation by distancedespite strong regional phylogeography in a small metazoan. BMCEvolutionary Biology 7: 225 .
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A phylogeographic study
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Why mitochondrial eve? The Out-Of-Africa Hypothesis
Africa
Europe Asia
(vertical scale is not time or evolutionary change)
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Genomes from Neanderthals, and more
Svante Pääbo
Krings, M., H. Geisert, R. W. Schmitz, H. Krainitzki, and S. Paabo. 1999.DNA sequence of the mitochondrial hypervariable region II from theneandertal type specimen. Proceedings of the Natonal Academy of SciencesUSA 96: 5581-5585.
Green, R., 54 others, and S. Pääbo. 2010. A draft sequence of theNeanderthal genome. Science 7 May 2010: 710-722.
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Neanderthals, Denisovans, and us
But ... can you make trees from closely-related genomes?Coalescents – p.42/48
Coalescents in related speciesTree of gene copies, compared with the phylogeny of the species
for the case in which effective population size is smallcompared to the number of generations between speciations
The tree of gene copies has topology consistent with the phylogeny
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Coalescents in related species
Tree of gene copies, compared with the phylogeny of the species
compared to the number of generations between speciationsfor the case in which effective population size is large
The tree of gene copies has topology inconsistent with the phylogeny
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Hey and Kliman
Jody Hey Rich Kliman and friendKliman, R. M., and J. Hey. 1993. DNA sequence variation at the periodlocus within and among species of the Drosophila melanogaster complex.Genetics 133: 375-87Hey, J. and R. M. Kliman. 1993. Population genetics and phylogenetics ofDNA sequence variation at multiple loci within the Drosophilamelanogaster species complex. Molecular Biology Evolution 10: 804-822.
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Ranges of East African Drosophila species
East Africa
D. melanogaster
D. simulans
Madagascar
SeychellesD. seychellea
Mauritius
D. mauritianus
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Coalescent among Drosophila species
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Coalescent among Drosophila species
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