Comparing demographic models using ABC

Report
Comparing demographic models
using ABC
Roger Butlin
University of Sheffield
Maroja et al. 2009 Evolution
10 loci – do they all behave in the same way?
Accessory gland
proteins with other
evidence of selection
We need a flexible method to fit complex demographic (and
adaptive?) models with a variety of marker types…
Ideally, we would model drift and selection together, rather than
fitting one first.
Approximate Bayesian Computation (ABC) may be the answer!
ABC outline
Model
N1
N2
m21
Ts
Coalescent
Simulations
m12
Na
6 parameters
(Hey & Nielsen, 2004)
prior
Ts
Beaumont 2010 Annu. Rev. Ecol. Evol. Syst. 41: 379-406
ABC outline
Model
N1
N2
m21
Ts
Coalescent
Simulations
Molecular
data
(sequences,
microsatellites)
m12
Na
6 parameters
Statistics of population
genetics (differentiation and
polymorphism)
posterior
(Hey & Nielsen, 2004)
Rejection step (keep only good simulations)
Inferences
Regression between statistics
and parameter values from
retained simulations.
Ts
ABC model comparison
Molecular
data
Model1
simulations
Model2
simulations
(sequences,
microsatellites)
Statistics of population
genetics (differentiation and
polymorphism)
Rejection - Regression
Posterior probability of
model 1
Posterior probability of
model 2
ABC tools
DIYABC
http://www1.montpellier.inra.fr/CBGP/diyabc/
http://code.google.com/p/popabc/
ABC toolbox
http://www.cmpg.iee.unibe.ch/content/softwares__services/computer_programs/abctoolbox/index_eng.html
Tools in R
http://cran.r-project.org/web/packages/abc/index.html
Practical steps
1.
2.
3.
4.
5.
6.
7.
8.
9.
Choose models
Choose summary statistics (and whether to transform)
Define priors
Choose simulator
Choose standard, MCMC or Population MC
Choose rejection and regression parameters
Choose model comparison method
Validate
Interpret results!
Duvaux et al. 2011 Molecular Ecology
A successful example!
Present
Migration
period
Divergence
time
past
•
•
•
10 individuals sampled from each subspecies for their full respective
distribution areas + 2 outgroups
61 autosomal loci (Sanger sequencing of around 48 kb of aligned
sequences)
15 summary statistics: mean and sd of π, Fst, Da, Dxy, counts of fixed,
shared polymorphic and f-s substitutions
Mus m. domesticus
Mus m. musculus
Mus spretus
MOL (Japan)
Mus Famulus
(India)
European hybrid
zone center
Model comparison
Posterior probabilities
(6M simulations for each model)
Isolation
model
Isolation-withmigration
Sympatric
differentiation
0.000
0.295
0.008
Secondary
contact
0.697
The secondary contact scenario is the most probable
Parameters of interest
1. duration of isolation period
domesticus
musculus
74% of the divergence time in isolation
(allopatry)
Parameters of interest
2. Secondary contact
domesticus
musculus
Tm≈0.22 Mya
(0.048-1.452 Mya)
Secondary contact older than the European hybrid zone
setting up (2.000 ya)
Parameters of interest
3. Migration rate asymmetry
domesticus
musculus
2Nmmus=0.105 & 2Nmdom=0.050
Migration is twice as strong toward M. m. musculus
Allowing two classes of loci (low and high
migration rate) improves the fit….
Littorina saxatilis ecotypes
UK
SPAIN
small
thin-shelled
bigger
thick-shelled
SWEDEN
3 Nations project – Sampling design
Tj ä rno
Lysekil
• 4 genes sequenced per individual:
Dunbar
Thornwick
• 3 nDNA genes
• 1 mtDNA region
• and 462 AFLP loci
•2 sampling sites per country
• 2 ecotypes per sampling site
Burela
Silleiro
• 16 individuals per ecotype
What was the demographic setting for ecotype formation?
Did it occur in parallel in each locality?
Models of divergence for L. saxatilis
ecotypes
Old divergence
W1
W2
C1
C2
‘Old divergence model’
Scenario for ancestral
divergence of ecotypes
within one country
Vs
Parallel divergence
Models of divergence for L. saxatilis
ecotypes
Old divergence with
allopatric phase
W1
W2
C1
C2
‘Old divergence model’
Scenario for ancestral
divergence of ecotypes
within one country, with a
period of allopatry
Vs
Parallel divergence
Models of divergence for L. saxatilis
ecotypes
Old divergence
Vs
Parallel divergence
W1
C1
W2
C2
‘Parallel model’
Scenario for parallel
divergence of ecotypes
within a country
Models of divergence for L. saxatilis
ecotypes
Old divergence
W1
W2
C1
Vs
C2
Parallel divergence
W1
C1
W2
Split
Splitbetween
betweensampling
ecotypessites
‘Old divergence model’
‘Parallel model’
C2
Parameterize the Models
Model + parameters
Prior distribution of parameters
MLG
W1
C1
W2
C2
NL
TEC
MEC
MLG
NE
‘Parallel model’
TLG
AFLP data / Sequence data
2
1
W1
W2
C1
Old divergence
C2
W1
C1
3
W2
C2
Parallel divergence
W1
W2
C1
C2
Old divergence with
allopatry
Model choice
AFLP
Spa
0.0200
0.0100
0.0000
Model1
Model2
Swe
0.0100
Marginal Density
0.0300
Marginal Density
Marginal Density
Gbr
0.0050
0.0000
Model3
Model1
Model2
0.3000
0.2000
0.1000
0.0000
Model1 Model2 Model3
Model3
Sequence – all 4 loci
2E-08
1.9E-08
1.8E-08
Swe
5E-08
Marginal Density
2.1E-08
Spa
Marginal Density
Marginal Density
Gbr
4E-08
3E-08
2E-08
1E-08
0
1.7E-08
Model1 Model2 Model3
Model1
Model2
Model3
0.0000004
0.0000003
0.0000002
0.0000001
0
Model1
Model2
Model3
Spain model 2 AFLP
MLG
W1
C1
W2
C2
NL
TEC
MEC
TLG
MLG
Spain model 2 sequence (minus ThioPer)
NE
‘Parallel model’
Black=prior
Blue=post-rejection
Red=posterior
Sympatric
speciation!!
It’s TRUE!

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