P1252109395ODoxS

1
Book Tutorials
Hein, Schierup Wiuf Genealogies, Variation
Evolution. www.stats.ox.ac.uk/hein/lectures
www.coalescent.dk (mheide_at_birc.dk)
Contents H The Basic Coalescent H The
Coalescent with Recombination S The Coalescent
with History, Geography Selection S The
Coalescent Gene Mapping H The Coalescent
Combinatorics W The Coalescent Ancestral
Analysis W Parameter Estimation Hypothesis
Testing H The Coalescent Human Evolution
2
The Coalescent with Geography, History,
Selection www.stats.ox.ac.uk/hein/lectures
www.coalescent.dk (mheide_at_birc.dk)
Review Coalescence/Recombination
Geography History Selection
Scenarios Detection
3
Continuous-Time Coalescent
1.0 corresponds to 2N generations
Discrete
Continuous
2N
1.0
0
1
0.0
4
3
2
5
6
4
Recombination-Coalescence Illustration
Intensities Coales. Recomb.
Copied from Hudson 1990
0 ?
1 (1b)?
b
3 (2b)?
6 2?
3 2?
1 2?
5
History Scenarios.
Simple Deterministic Models of Population Size.
Logistic growth
Bottleneck
Size jump
Exponential growth
T
LB
Bottleneck Severity LB/Ne
Bottleneck Age T/Ne
Stochastic Fluctuations of Population Size.
6
The Coalescent Population Growth
Growth will elongate leaf edges relative to deep
edges! If the population size is known as
function of time N(t), time can be scaled as
for
exponential growth eat, this gives
7
Tests of History.
Distortion of branch lengths towards the
present. Tajima (1989) - Fu and Li
(1993) Mismatch Distribution Pairwise Distances
Rogers Harpending,1992. Likelihood
Models Beerli Felsenstein,1999
8
Mismatch distributions Rogers Harpending,1992,
Slatkin and Hudson, 1991
9
Wattersons Estimator
ACCTGAACGTAGTTCGAAG ACCTGAACGTAGTTCGAAT ACCTGACCGT
AGTACGAAT ACATGAACGTAGTACGAAT ACATGAACGTAGTACGAAT

A
A
B
D
C
C
B
D
1
3
2
5
4
Expected Number Segregating Sites ???????????(1
1/2 1/(k-1)) ??????????W Segr/(11/2
1/(k-1)) 4/ 11/624/112.1818
Var(segr)
10
Pairwise Distance Estimator
ACCTGAACGTAGTTCGAAG ACCTGAACGTAGTTCGAAT ACCTGACCGT
AGTACGAAT ACATGAACGTAGTACGAAT ACATGAACGTAGTACGAAT

6
B
A
C
D
A
C
6
B
4
D
4
4
4
4
A mutation on a (n,n-k) branch will be counted
n(n-k) times. I.e. deep branches have higher
weights.
???PD Average Pairwise Distance (above
2.166) ??Var??PD) ?(n1)/3(n-1) ?2
2(n2n3)/9n(n-1)
11
Tajimas Test
?D (?PD -???W)/Sd(?PD -???W)
A large value indicates shortened tips A small
value indicates shortened deep branches.
Mitochondria (Ingman et al. 2000) Remade from
McVean 52 complete molecules 521 segregating
sites ?PD 44.2 ???W 115.3 V(D) 31.8
D -2.23
12
Geography Scenarios.
2 Demes Same Size Continent Island N
Demes with structure stepping stone 1-
dimension stepping stone 2 dimensions Continu
ous Geography 1 Dimension 2 Dimensions
13
Two Demes
Symmetric
Island/Continent
M1
M2
14
Distribution of MRCA in d-deme model.
d5
1/d
m
2 alleles. T(2,0) time to coalesce if in
different demes T(0,1) time
to coalesce if in the same demes
Recursions
Solutions
15
Distribution of coalescence times within/between
demes
From Hudson, 1990
16
Population subdivision - two demes
17
Stepping stone models
Line (1-Dim)
Plane (2-Dim)
18
Continuous Geography (Wright 43, Malecot 48,
Felsenstein 75, Barton 96 02)
1 dimensional
2 dimensional - plane or torus (wrapped rectangle)

• These models can be obtained by
• A limit of stepping stone models
• Directly by a Brownian Motion model of movement.

Sequences can only find common ancestors when at
the same place. This doesnt happen in the
continuous models for dim gt1. A neighborhood
has to be defined.
19
Continuous Geography (Barton Wilson 96)
Several artifacts in this model. Increasing
lumping over time.
20
Testing Geography.
Hudson, Boos Slatkins (1990) Permutation
test Maddison Slatkin (1989) Assignment of
ancestral geography. Likelihood Bahlo
Griffiths (2000) Pritchards Structure
(2000) Kuhner et al. (2000)
21
Selection Scenarios.
Alleles A a
Haploid Selection Directional Frequency
Dependent Diploid Balancing Selection
Directional Selection Allelic Types
Fitnesses 1 1-s
Fitnesses 1-pA 1-pa
Genotypes AA AA aa
Fitnesses 1 1s 1
Fitnesses 1 1hs 1s
s?Ns In the coalescent scaling
22
The 1983 Kreitman Data (M. Kreitman 1983 Nature)
from Hartl Clark, 1997
11 alleles 3200 bp long. 43 segregating sites
(columns with variation). 1 amino replacement
event 1 insertion-deletion (indel)
23
Two locus balancing selection model Hudson,
Darden Kaplan,88-89
q
p
k1
k2
P(A)p, P(B)q, we sample k1 A alleles and k2 B
alleles
Two cases Strong selection with fixed
ancestral frequencies Weaker selection with
fluctuating ancestral frequencies.
24
Directional Selection/ Bottlenecks
25
Geography ?? Selection
26
The ancestral selection graph Krone Neuhauser,
1997
Two alleles, A and a, A has an advantage of
s Mutation rate between types u
27
Construction of the ancestral selection graph
28
Recovery of the coalescent tree with directional
selection
Krone Neuhauser, 97
29
A Coalescent relating Allele Classes. (Takahata,19
90)
Examples Major Histocompatibility Genes
Self-incompatibility Alleles in plants.
30
Allelic genealogy in the self-incompatibility
system of Solanaceae
From Vekemans, 1998
31
Tests of Selection
Tajimas D (1989) (Fus test) Hudson, Kreitman
Aquade (1987) HKA Kreitman-MacDonald test
(1990) Likelihood tests
32
HKA-Test (Hudson, Kreitman Aquade) Hudson,Kreitm
an Aquade,1987
Gene 2
Gene 1
MRCA2
MRCA1
Speciation, T
Speciation, T
Q2
Q1
Specie 2
Specie 2
Specie 1
Specie 1
The original data set ADH 5 prime region, D.
sechellia D.melanogaster d210 (MRCA1)

d18 (MRCA2) S9
(Lk1Q1)
S8 (Lk2Q2) Q1
2.7 Q20.7 T13.4Ne Rejection.
Are the 2 loci linked or unlinked?
33
Kreitman/McDonald-Test Kreitman/McDonald,1990
Eanes, 1994
Replacement
Synonymous
Between Specie
21 BR
26 BS
36 WS
2 WR
Within Specie
Specie 2
Specie 1
Rejection
Tested by 22 indendence in contingency
table. Parameter estimation not necessary.
34
Summary of Coalescent with HGS
History Geography Selection
Scenarios Detection
35
References.
(Balding,D. et al. (2000) Handbook of
Statistical Genetics Wiley Articles by Rousset,
Nordborg, Stephens, Hudson, Barton,NH, Depaulis
Etheridge (2002) Neutral Evolution in Spatially
Continuous Populations Theor.Pop.Biol.
61.31-48. Barton, N. I.Wilson (1996)
Genealogies and Geography in New uses for New
Phylogenies eds. Harvey et al. OUP Donnelly,P.,
Nordborg, M. Joyce,P. (2001) Likelihoods and
Simulation Methods for Classes of Non-neutral
Population Genetics Models. Genetics
159.853-867. Golding,B. (ed.) (1994)
Non-Neutral Evolution Chapman Hall articles
by Eanes, Aquadro,.Hudson, McDonald, Hein,JJ
(2002) Slides www.stats.ox.ac.uk/hein/lectures
Hudson, Boos Kaplan (1992) A Statistical Test
for Detecting Geographical Subdivision
Mol.Biol.Evol. 9.1.138-151 Hudson, Kreitman
Aquade (1987) A test of Neutral Molecular
Evolution Based on Nuclear Data. Genetics
116.153-9 Hudson, Darden Kaplan (1988)
Hudson and Kaplan (1988) The Coalescent
Process in Models with Selection and
Recombination Genetics 120.831-840. Krone
Neuhauser (1997) McVean,G. (2002) course
www.stats.ox.ac.uk/mcvean Neuhauser Krone
(1997) The Genealogy of Samples in Models with
Selection Genetics 145.519-534. Nordborg,
M.(1997) Structured Coalescent Processes on
Different Time Scales Genetics
146.1501-1514. Pybus,OG et al(2000) An
Integrated Framework for the Inference of Viral
Population History from Reconstructed
Genealogies. Genetics 155.1429-1437. Schierup,
M. et al.(2002) Coalescent Simulator
www.coalescent.dk Slatkin (1991) Inbreeding
Coeffecients and Coalescence Times. Genet. Res.
Camb. 58.167-175. Slatkin Hudson (1992) Slade
(2000) Simulation of Selected Genealogies
Theor.Pop.Biol. 57.35-49 Takahata,N.(1990) A
simple genealogical structure of strongly
balanced allelic lines of transpecies evolution
of polymorphism. PNAS 87.2419-23. Wiuf, C. and
J.Hein (2000) The Coalescent with Gene
Conversion Genetics 155.451-462.
36
FSTs Geography Coalescent.
37
History of Coalescent with HGS
Stepping Stone Model introduced by Wright Krone
Neuhauser introduces Selection Graph
38
Evidence against background selection
From Aquadro, 1994
39
Evidence for genetic hitch-hiking
From Aquadro, 1994
40
Variation in recombination rate in Drosophila,
chromosome 3
From Aquadro, 1994
41
Selective Sweeps/Background Selection.
42
Mismatch distributions in human populations
Excoffier, 2000
43
Fus Test From Li,1997
External (e) versus Internal (?) Branches. ?e
and ?i the number of mutations in external and
internal branches. E(e) 2 E(i) Lk-2
E(?e ) ?????????? V(?e ) ???????????? ????
E(?i ) (Lk-2)? V(?i ) (Lk-2)??????????/(n-1
) c ?? 1 if n 2 c
b
2nLk - 2(n-1)/(n-1)(n-2)
44
Waiting intensities in general model of
population subdivision