Coalescents

Joe Felsenstein

GENOME 453, Autumn 2015

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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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