Lecture 23 : Introduction to Coalescence

April 7, 2014

Last Time

Introduction to phylogenetics

Phylogeography

Limitations of phylogenetic analysis

TodayGene 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

ACB

Gene Tree

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

present

Time

Individual alleles

9 generations in the history of a population of 14 gene copies

Slide courtesy of Yoav Gilad

a b c

Concordant Gene Treeb is closer to a than to c

Failure to coalesce within species lineages drives divergence of relationships between gene and species trees

Gene Trees vs Species Trees

a b c

Divergent Gene Tree:b is closer to c than to a

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

present

Most recent common ancestor (MRCA)

Time

Individual allelesSlide courtesy of Yoav Gilad

present

Most recent common ancestor (MRCA)

The genealogy of a sample of 5 gene copies

Time

individualsSlide courtesy of Yoav Gilad

present

Most recent common ancestor (MRCA)

The genealogy of a sample of 5 gene copies

Time

Individual allelesSlide courtesy of Yoav Gilad

Examples of coalescent trees for a sample of 6

Time

Individual allelesSlide courtesy of Yoav Gilad

Coalescence AdvantagesDon’t have to model dead endsOnly consider lineages that survive to modern

day: computationally efficientBased on actual observationsCan 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

eecoalescenc N

P2

1

Also a function of number of lineages

eecoalescenc N

kkP

2

1

2

)1(

where k is number of lineages

Probability of Coalescence

Probability declines over time

Lineages decrease in number

Can be estimated based on negative exponential

where k is number of lineages

eN

kkt

ecoalescenc eP 2

1

2

)1(

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

http://www.dhushara.com/book/unraveltree/unravel.htm

Skulls found in Omo Valley, EthiopiaDated at ~195K

http://www-v1.amnh.org/exhibitions/permanent/humanorigins/history/origin.php

Omo 1 Modern

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?