Download - Comparing demographic models using ABC
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Comparing demographic models using ABC
Roger ButlinUniversity of Sheffield
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Maroja et al. 2009 Evolution
10 loci – do they all behave in the same way?
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Accessory gland proteins with other evidence of selection
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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!
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Model
6 parameters
Na
N1 N2
m12
m21
Coalescent Simulations
(Hey & Nielsen, 2004)
Ts
Ts
prior
ABC outline
Beaumont 2010 Annu. Rev. Ecol. Evol. Syst. 41: 379-406
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Statistics of population genetics (differentiation and
polymorphism)
Molecular data
(sequences, microsatellites)
Rejection step (keep only good simulations)
InferencesRegression between statistics and parameter values from retained simulations.
Coalescent Simulations
Ts
Model
6 parameters
Na
N1 N2
m12
m21
Ts
(Hey & Nielsen, 2004)posterior
ABC outline
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Model1 simulations
Model2 simulations
Molecular data
(sequences, microsatellites)
Rejection - Regression
Posterior probability of model 1
Posterior probability of model 2
Statistics of population genetics (differentiation and
polymorphism)
ABC model comparison
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ABC tools
DIYABChttp://www1.montpellier.inra.fr/CBGP/diyabc/
http://code.google.com/p/popabc/
ABC toolboxhttp://www.cmpg.iee.unibe.ch/content/softwares__services/computer_programs/abctoolbox/index_eng.html
Tools in Rhttp://cran.r-project.org/web/packages/abc/index.html
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Practical steps
1. Choose models2. Choose summary statistics (and whether to transform)3. Define priors4. Choose simulator5. Choose standard, MCMC or Population MC6. Choose rejection and regression parameters7. Choose model comparison method8. Validate9. Interpret results!
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Duvaux et al. 2011 Molecular Ecology
A successful example!
Divergence time
Migration period
past
Present
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• 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
MOL (Japan)
Mus Famulus (India)
Mus m. domesticus
Mus m. musculus
Mus spretus
European hybrid zone center
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Posterior probabilities(6M simulations for each model)
Isolation-with-migration
Sympatric differentiation
Secondary contact
Isolation model
0.000 0.295 0.008 0.697
The secondary contact scenario is the most probable
Model comparison
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74% of the divergence time in isolation (allopatry)
1. duration of isolation period
domesticus musculus
Parameters of interest
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Parameters of interest
Secondary contact older than the European hybrid zone setting up (2.000 ya)
2. Secondary contact
Tm≈0.22 Mya(0.048-1.452 Mya)
domesticus musculus
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Parameters of interest
Migration is twice as strong toward M. m. musculus
3. Migration rate asymmetry
domesticus musculus2Nmmus=0.105 & 2Nmdom=0.050
Allowing two classes of loci (low and high migration rate) improves the fit….
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Littorina saxatilis ecotypes
smallthin-shelled
biggerthick-shelled
UK
SWEDENSPAIN
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3 Nations project – Sampling design
Burela
Silleiro
Dunbar
Thornwick
Tj ä rno
Lysekil
Burela
Silleiro
Dunbar
Thornwick
Tj ä rno
Lysekil
• 4 genes sequenced per individual:
• 3 nDNA genes• 1 mtDNA region
• and 462 AFLP loci
•2 sampling sites per country
• 2 ecotypes per sampling site
• 16 individuals per ecotype
What was the demographic setting for ecotype formation?Did it occur in parallel in each locality?
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Models of divergence for L. saxatilis ecotypes
Old divergence Parallel divergenceVs
W1 C1W2 C2
Scenario for ancestral divergence of ecotypes within one country
‘Old divergence model’
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Models of divergence for L. saxatilis ecotypes
Old divergence with allopatric phase
W1 C1W2 C2
Scenario for ancestral divergence of ecotypes within one country, with a period of allopatry
‘Old divergence model’
Parallel divergenceVs
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Models of divergence for L. saxatilis ecotypes
Old divergence Parallel divergenceVs
W1 W2C1 C2
Scenario for parallel divergence of ecotypes within a country
‘Parallel model’
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Models of divergence for L. saxatilis ecotypes
Old divergence Parallel divergenceVs
W1 W2C1 C2
‘Parallel model’
W1 C1W2 C2
‘Old divergence model’
Split between sampling sitesSplit between ecotypes
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W1 W2C1 C2
NE
‘Parallel model’
TEC
TLG
MLG
MEC
NL
MLG
Model + parameters Prior distribution of parameters
Parameterize the Models
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W1 C1W2 C2
Old divergence
W1 C1W2 C2
Old divergence with allopatry
W1 W2C1 C2
Parallel divergence
1 2 3
AFLP data / Sequence data
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AFLP
Model1 Model2 Model30.00000.00500.01000.01500.02000.02500.0300
Gbr
Mar
gina
l Den
sity
Model1 Model2 Model30.00000.00200.00400.00600.00800.0100
Spa
Mar
gina
l Den
sity
Model1 Model2 Model30.00000.05000.10000.15000.20000.25000.3000
Swe
Mar
gina
l Den
sity
Sequence – all 4 loci
Model choice
Model1 Model2 Model30.000000017
0.00000001750.000000018
0.00000001850.000000019
0.00000001950.00000002
0.00000002050.000000021
Gbr
Mar
gina
l Den
sity
Model1 Model2 Model30
0.00000001
0.00000002
0.00000003
0.00000004
0.00000005
Spa
Mar
gina
l Den
sity
Model1 Model2 Model30
0.000000050.0000001
0.000000150.0000002
0.000000250.0000003
0.00000035
Swe
Mar
gina
l Den
sity
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W1 W2C1 C2
NE
‘Parallel model’
TEC
TLG
MLG
MEC
NL
MLG
Spain model 2 AFLP
Spain model 2 sequence (minus ThioPer)
Black=priorBlue=post-rejectionRed=posterior
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Sympatric speciation!!It’s TRUE!