Transcript Lecture 21 : Introduction to Neutral Theory

Lecture 23 : Introduction to Coalescence
April 7, 2014
Last Time
Introduction to phylogenetics
Phylogeography
Limitations of phylogenetic analysis
Today
Gene trees versus species trees
Coalescence
Influence of demographic factors on
coalescence times
Coalescence and human origins
Gene Trees vs Species Trees
 Genes
(or loci) evolve at different rates
Why?
 Topology derived by a single gene may not match
topology based on whole genome, or morphological traits
Gene Tree
B
C A
Coalescence
 Retrospective tracing
of existing alleles to a
common ancestral allele
 A reverse reconstruction of the evolution of
modern variation
 Allows explicit simulation of sequence
evolution
 Incorporation of factors that cause deviation
from neutrality: selection, drift, and gene flow
9 generations in the history of a population of 14 gene copies
Time
present
Slide courtesy of Yoav Gilad
Individual alleles
Gene Trees vs Species Trees
Failure to coalesce within species
lineages drives divergence of
relationships between gene and species
trees
Divergent Gene
Tree:
Concordant Gene
Tree
b is closer to a than to c
a b
c
b is closer to c
than to a
a b
c
How to model this process?
Modeling from Theoretical Ancestors: Forward Evolution
Can model
populations in a
forward direction,
starting with
theoretical past
Fisher-Wright model
of neutral evolution
Very computationally
intensive for large
populations
Alternative: Start at the end and work your way back
Most recent common ancestor (MRCA)
Time
present
Slide courtesy of Yoav Gilad
Individual alleles
The genealogy of a sample of 5 gene copies
Most recent common ancestor (MRCA)
Time
present
individuals
Slide courtesy of Yoav Gilad
The genealogy of a sample of 5 gene copies
Most recent common ancestor (MRCA)
Individual alleles
Slide courtesy of Yoav Gilad
Time
present
Examples of coalescent trees for a sample of 6
Time
Individual alleles
Slide courtesy of Yoav Gilad
Coalescence Advantages
 Don’t
have to model dead ends
 Only consider lineages that survive to modern
day: computationally efficient
 Based on actual observations
 Can simulate different evolutionary scenarios
to see what best fits the observed data
Coalescent Tree Example

Coalescence:
Merging of two
lineages in the
Most Recent
Common Ancestor
(MRCA)

Waiting Time:
time to
coalescence for
two lineages

Increases with
each coalescent
event
Probability of Coalescence
 For any two lineages, function of population
size
Pcoalescence
1

2Ne
 Also a function of number of lineages
Pcoalescence
k (k  1) 1

2
2 Ne
where k is number of lineages
Probability of Coalescence
 Probability declines over time
 Lineages decrease in number
 Can be estimated based on negative
exponential
Pcoalescence  e
 k ( k 1) 1
 t 
2
2 Ne




where k is number of lineages
Time to Coalescence Affected by Population
History
Bottleneck
Time to Coalescence Affected by Population
History
Population Growth
How will population structure
affect coalescence times?
Time to Coalescence Affected by Population
Structure
Applications of the Coalescent Approach
 Framework for efficiently testing alternative
models for evolution
 Inferences about effective population size
 Detection of population structure
 Signatures of selection (coming attraction)
 Reconstructing history of populations
Origins of Modern Humans
 Most fossil evidence points to origins in Africa and subsequent migrations
Skulls found in Omo Valley, Ethiopia
Dated at ~195K
Omo 1
Modern
http://wwwv1.amnh.org/exhibitions/
permanent/humanorigins
/history/origin.php
http://www.dhushara.com/book/unraveltree/unravel.htm
Human Phylogeography:
mtDNA
Most ancient and
diverse haplotypes in
Africa (dots)
Migration and
admixture is evident
from presence of
African haplotypes in
other clades
Complexities to Human Phylogeography
 Some genes show evidence of Asian origin
 Sequence of X-linked ribonucleotide reductase M2 pseudogene 4 (RRM2P4)
Garrigan 2007 Nature Reviews Genetics 7:669
Why might some X-linked genes
show a human origin in Africa
(e.g., PDHA1), while others
suggest an Asian origin e.g.,
(RRM2P4)?
Evidence of Population Structure in Ancient
Humans
Garrigan and Hammer 2006 Nature Reviews Genetics 7:669
Time to Coalescence Affected by
Population Structure
Evidence for Ancient Population Structure in Nuclear
but not Mitochondrial Trees
Garrigan and Hammer 2006 Nature Reviews Genetics 7:669
Why does mitochondrion show
shorter coalescence times than
nuclear loci?
Why does rate vary much more
for nuclear loci?