Comparing demographic models using ABC

Roger ButlinUniversity 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!

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

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

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

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

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!

Duvaux et al. 2011 Molecular Ecology

A successful example!

Divergence time

Migration period

past

Present

• 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

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

74% of the divergence time in isolation (allopatry)

1. duration of isolation period

domesticus musculus

Parameters of interest

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

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….

Littorina saxatilis ecotypes

smallthin-shelled

biggerthick-shelled

UK

SWEDENSPAIN

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?

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’

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

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’

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

W1 W2C1 C2

NE

‘Parallel model’

TEC

TLG

MLG

MEC

NL

MLG

Model + parameters Prior distribution of parameters

Parameterize the Models

W1 C1W2 C2

Old divergence

W1 C1W2 C2

Old divergence with allopatry

W1 W2C1 C2

Parallel divergence

1 2 3

AFLP data / Sequence data

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

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

Sympatric speciation!!It’s TRUE!