Comparing demographic models using ABC

1. Comparing demographic models using ABC Roger Butlin University of Sheffield

2. Maroja et al. 2009 Evolution 10 loci – do they all behave in the same way?

3. Accessory gland proteins with other evidence of selection

4. 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!

5. Coalescent Simulations ABC outline Model N1 N2 m21 m12 Ts Na 6 parameters (Hey & Nielsen, 2004) prior Ts Beaumont 2010 Annu. Rev. Ecol. Evol. Syst. 41: 379-406

6. Molecular data Coalescent Simulations (sequences, microsatellites) Statistics of population genetics (differentiation and polymorphism) Rejection step (keep only good simulations) Inferences Regression between statistics and parameter values from retained simulations. ABC outline Model N1 N2 m21 m12 Ts Na 6 parameters posterior (Hey & Nielsen, 2004) Ts

8. Molecular data Model1 simulations Model2 simulations (sequences, microsatellites) Statistics of population genetics (differentiation and polymorphism) Rejection - Regression ABC model comparison Posterior probability of model 1 Posterior probability of model 2

9. 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

10. Practical steps 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!

11. Duvaux et al. 2011 Molecular Ecology A successful example! Present Migration period Divergence time past

12. Mus m. domesticus Mus m. musculus Mus spretus MOL (Japan) Mus Famulus (India) European hybrid zone center • 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

13. Model comparison Posterior probabilities (6M simulations for each model) Isolation-with-migration Sympatric differentiation Secondary contact Isolation model 0.295 0.008 0.000 0.697 The secondary contact scenario is the most probable

14. Parameters of interest 1. duration of isolation period 74% of the divergence time in isolation (allopatry) domesticus musculus

15. Parameters of interest 2. Secondary contact Tm≈0.22 Mya (0.048-1.452 Mya) domesticus musculus Secondary contact older than the European hybrid zone setting up (2.000 ya)

16. 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….

17. Littorinasaxatilisecotypes UK SWEDEN SPAIN bigger thick-shelled small thin-shelled

18. 3 Nations project – Sampling design • 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 Tj Tj ä ä rno rno Lysekil Lysekil Dunbar Dunbar Thornwick Thornwick Burela Burela Silleiro Silleiro What was the demographic setting for ecotype formation? Did it occur in parallel in each locality?

19. Models of divergence for L. saxatilisecotypes Vs W1 W2 C1 C2 Old divergence Parallel divergence ‘Old divergence model’ Scenario for ancestral divergence of ecotypes within one country

20. Models of divergence for L. saxatilisecotypes Vs Old divergence with allopatric phase Parallel divergence W1 W2 C1 C2 ‘Old divergence model’ Scenario for ancestral divergence of ecotypes within one country, with a period of allopatry

21. Models of divergence for L. saxatilisecotypes Vs W1 C1 W2 C2 Old divergence Parallel divergence ‘Parallel model’ Scenario for parallel divergence of ecotypes within a country

22. Models of divergence for L. saxatilisecotypes Vs W1 C1 W2 C2 W1 W2 C1 C2 Old divergence Parallel divergence Split between sampling sites Split between ecotypes ‘Parallel model’ ‘Old divergence model’

23. Parameterize the Models W1 C1 W2 C2 MLG NL TEC MEC TLG Model + parameters Prior distribution of parameters MLG NE ‘Parallel model’

24. AFLP data / Sequence data W1 C1 W2 C2 W1 W2 C1 C2 2 3 1 W1 W2 C1 C2 Parallel divergence Old divergence Old divergence with allopatry

25. Model choice Sequence – all 4 loci AFLP

26. W1 C1 W2 C2 Spain model 2 AFLP MLG NL TEC MEC TLG MLG NE Spain model 2 sequence (minus ThioPer) ‘Parallel model’ Black=prior Blue=post-rejection Red=posterior

27. Sympatric speciation!! It’s TRUE!