Coalescents - University of Washington
Transcript of Coalescents - University of Washington
![Page 1: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/1.jpg)
Coalescents
Joe Felsenstein
GENOME 453, Autumn 2015
Coalescents – p.1/48
![Page 2: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/2.jpg)
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.
Coalescents – p.2/48
![Page 3: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/3.jpg)
Mitochondrial Eve
Coalescents – p.3/48
![Page 4: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/4.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.4/48
![Page 5: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/5.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.5/48
![Page 6: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/6.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.6/48
![Page 7: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/7.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.7/48
![Page 8: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/8.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.8/48
![Page 9: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/9.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.9/48
![Page 10: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/10.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.10/48
![Page 11: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/11.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.11/48
![Page 12: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/12.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.12/48
![Page 13: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/13.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.13/48
![Page 14: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/14.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.14/48
![Page 15: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/15.jpg)
Genealogy of gene copies in a random-mating population
Time
Coalescents – p.15/48
![Page 16: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/16.jpg)
Untangling this genealogy by left-right swappings ...
Time
Coalescents – p.16/48
![Page 17: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/17.jpg)
Genealogy of a sample of gene copies
Time
Coalescents – p.17/48
![Page 18: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/18.jpg)
Ancestry of a sample in the population pedigree
Time
Coalescents – p.18/48
![Page 19: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/19.jpg)
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
Coalescents – p.19/48
![Page 20: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/20.jpg)
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.
Coalescents – p.20/48
![Page 21: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/21.jpg)
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
Coalescents – p.21/48
![Page 22: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/22.jpg)
An accurate analogy: Bugs In A Box
There is a box ...
Coalescents – p.22/48
![Page 23: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/23.jpg)
An accurate analogy: Bugs In A Box
with bugs that are ...
Coalescents – p.23/48
![Page 24: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/24.jpg)
An accurate analogy: Bugs In A Box
... hyperactive ...
Coalescents – p.24/48
![Page 25: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/25.jpg)
An accurate analogy: Bugs In A Box
... indiscriminate ...
Coalescents – p.25/48
![Page 26: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/26.jpg)
An accurate analogy: Bugs In A Box
... voracious ...
Coalescents – p.26/48
![Page 27: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/27.jpg)
An accurate analogy: Bugs In A Box
... (eats other bug) ...
Gulp!
Coalescents – p.27/48
![Page 28: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/28.jpg)
An accurate analogy: Bugs In A Box
... and insatiable.
Coalescents – p.28/48
![Page 29: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/29.jpg)
Random coalescents from the same population
Coalescents – p.29/48
![Page 30: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/30.jpg)
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
Coalescents – p.30/48
![Page 31: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/31.jpg)
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
Coalescents – p.31/48
![Page 32: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/32.jpg)
Coalescent with migration
Time
population #1 population #2
Coalescents – p.32/48
![Page 33: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/33.jpg)
Coalescent with migration, untangled
Time
Coalescents – p.33/48
![Page 34: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/34.jpg)
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)
Coalescents – p.34/48
![Page 35: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/35.jpg)
Chromosome 1, back up one lineage
now
−1
−2
−3
−4
−5
−6 (none)
Coalescents – p.35/48
![Page 36: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/36.jpg)
Coalescent with recombination
Recomb.
Different markers have slightly different coalescent trees
Coalescents – p.36/48
![Page 37: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/37.jpg)
Coalescent with recombination
1 142 143 417 418 562
Coalescents – p.37/48
![Page 38: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/38.jpg)
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 .
Coalescents – p.38/48
![Page 39: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/39.jpg)
A phylogeographic study
Coalescents – p.39/48
![Page 40: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/40.jpg)
Why mitochondrial eve? The Out-Of-Africa Hypothesis
Africa
Europe Asia
(vertical scale is not time or evolutionary change)
Coalescents – p.40/48
![Page 41: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/41.jpg)
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.
Coalescents – p.41/48
![Page 42: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/42.jpg)
Neanderthals, Denisovans, and us
But ... can you make trees from closely-related genomes?Coalescents – p.42/48
![Page 43: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/43.jpg)
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
Coalescents – p.43/48
![Page 44: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/44.jpg)
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
Coalescents – p.44/48
![Page 45: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/45.jpg)
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.
Coalescents – p.45/48
![Page 46: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/46.jpg)
Ranges of East African Drosophila species
East Africa
D. melanogaster
D. simulans
Madagascar
SeychellesD. seychellea
Mauritius
D. mauritianus
Coalescents – p.46/48
![Page 47: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/47.jpg)
Coalescent among Drosophila species
Coalescents – p.47/48
![Page 48: Coalescents - University of Washington](https://reader036.fdocuments.us/reader036/viewer/2022081619/62ce116f673fc86f1a3920cb/html5/thumbnails/48.jpg)
Coalescent among Drosophila species
Coalescents – p.48/48