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Fitness Landscapes & Dynamics of Adaptation
- 1. Fitness Landscapes & Dynamics of Adapta4on & … what can we infer from pa9erns of phenotypic and molecular evolu4on? Thomas Bataillon Bioinforma4cs Research Center (BiRC), Aarhus University, Denmark. ISEM, Universite de Montpellier ( Un4l July 2013)
- 2. Muta4on & Fitness landscapes & Evolu4on Why do I care ? Open ended vs. Close evolu6on Evolu6onary Poten6al Proper6es of beneficial muta6ons? • BIG or small effects ? à Distribu6on of fitness effects (DFE) • DOMINANT or recessive, etc? • Ecologically specialized or broadly beneficial ?
- 3. Which model can account for the proper4es of muta4ons that ma9er for adapta4on? à What data do we have to challenge models? Mutation fitness effect, s
- 4. Predic4ng DFE Heuristics “In a well adapted population, virtually (almost) all mutations with a measurable fitness effect will suck” à Extreme Value Theory • Gillespie’s seminal work (1984, …) • Orr (2002,…) Explicit fitness landscape models “Current level of adaptation matters as well as the genetic architecture underlying fitness” Fisher’s “geometric” landscape Other landscapes e.g. stick breaking
- 5. Distribu4ons of fitness effects and extreme value theory: look on the right … A. H. Orr, The Distribu,on of Fitness Effects Among Beneficial Muta,on, Gene6cs 2003. J. H. Gillespie, Molecular evolu,on over the muta,onal landscape, Evolu6on,1984 Extreme value theory Fitness
- 6. EVT limi4ng distribu4on: Generalized Pareto distribu4on κ< -‐1 κ=-‐1 Beisel et al Gene4cs 2007…
- 7. Explicit fitness landscape Genotypes à Fitness Genotypesà Phenotype(s) àFitness DFE Expected dynamics of fitness over 4me Expected level of molecular //ism etc. Martin & Lenormand Evolution 2006 Chevin et al Evolution 2010 Lourenço et al Evolution 2011
- 8. DFEs & Experimental Evolu4on data • What kind of data? – Fitness of strains differing by single step from an ancestral strain – Fitness trajectory over 4me – Snapshot of genomic diversity over 4me
- 9. Assaying collec4on of genotypes “one step” away from a wild type Selective Count 0 20 40 60 80 100 120 140 Permissive Absolute fitness 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 140 Kassen & Bataillon Nat Gen 2006, Bataillon et al Gene4cs 2011
- 10. EVT limi4ng distribu4on: Generalized Pareto distribu4on κ< -‐1 κ=-‐1 Beisel et al Gene4cs 2007…
- 11. Inferring the distribu4on of beneficial muta4ons fixed / on their way to fixa4on Schoustra et al PLOS Biol 2009
- 12. Inferring parameters of Fisher’s phenotypic landscape with Exp Evolu4on data with L. Perfeito A. Sousa & I Gordo (IGC, Portugal) • DATA (E. coli) • Patterns of fitness decline in a mutation accumulation experiment • 50 lines ca 230 gens • Patterns of fitness recovery over 240 generations • MODEL: Fisher’s geometric fitness landscape • PARAMETERS – Genome wide mutation rate U – Number of indep traits underlying fitness n – Mean effect of a mutation – Distance to opimum (here ZERO)
- 13. Temporal dynamics of fitness b d f Trindade et al Phil Trans Roy Soc 2010
- 14. ABC in a nutshell • Principle :approximate the likelihood or posterior distribu4on of the parameters • Replace the whole data D by a joint set of summary sta4s4cs • Simulate data under your (pet) model • Prac4ce • Choose summary sta4s4cs that have worked in known contexts • Use (crude) rejec4on sampling to approximate P(S) • Validate with simulated data
- 15. Proper4es of Fisher’s fitness landscape as inferred by experimental data
- 19. Fitness decline depends on star4ng fitness Δ fitness over 10 bo9lenecks
- 20. Fitness recovery also depends on ini4al fitness
- 21. DFEs predicted by the data under Fisher’s model
- 22. Sta4s4cal performance of the approx. Bayesian framework ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 5e−04 2e−03 5e−03 2e−02 5e−02 2e−01 5e−042e−035e−032e−025e−022e−01 Estimating U True U ABCestimateofU unbiased actual bias (lowess) Es4mated U True genome-‐wide muta4on rate (U)
- 23. ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !!! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 5 10 15 20 51015 Estimating Number of dimension (ndim) True ndim ABCestimateofndim unbiased actual bias (lowess) ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.00.10.20.30.40.5 Estimating Rmax True Rmax ABCestimateofRmax unbiased actual bias (lowess)
- 25. Inferring DFE from polymorphism and divergence (1) Assump4ons: 1. Synonymous muta4ons are to first approxima4on neutral 2. Non-‐synonymous muta4ons might be neutral deleterious or beneficialà DFE Bad muta4ons are ojen pre9y rare à examine site frequency spectrum (SFS) Hvilsom et al. PNAS 2012
- 26. Inferring DFE from polymorphism and divergence (2) • SFS based methods assume: – Stable popula4on or some explicit model – Neutral synonymous – Non-‐Synonymous polymorphism is always deleterious – a frac4on α of non-‐syn divergence are beneficial. (but see RSS models) Keightley & Eyre-‐Walker MBE 2009 |Ns|<1 1<|Ns|<10 10<|Ns|<100 |Ns|>100 Hvilsom et al. PNAS 2012
- 27. Puong it all together… can we steer way from dangerous assump4ons? −15 −10 −5 0 020406080100120 S=4Nes EPnorEDn φ(S) rescaled EPn EDn −15 −10 −5 0 5 020406080100 S=4Nes EPn(S)andEDn(S) EPs EPn ESn EDn
- 28. Single stat summaries of polymorphism & divergence alone are not good enough à SFS or MK counts Expecta6on for the direc6on Of Selec6on −100 −80 −60 −40 −20 0 −0.4−0.3−0.2−0.10.00.1 S DirectionOfSelection(dos) dos ≡ Dn Dn + Ds − Pn Pn + Ps Mean DOS var(DOS) Expecta6on for MK counts −15 −10 −5 0 5 020406080100 S=4Nes EPn(S)andEDn(S) EPs EPn ESn EDn
- 29. Structure of an extended MK model Data Pol Syn Frequency 0 5 10 15 20 25 0246810 Singleton Syn Frequency 2 4 6 8 10 12 051015 Diverg. Syn Frequency 0 5 10 15 20 25 30 02468 Pol Non Syn dataS$PNobs Frequency 0 5 10 15 20 25 024681012 Singleton Non Syn dataS$SNobs Frequency 0 5 10 15 051015 Diverg. Non Syn dataS$DNobs Frequency 0 5 10 20 30 02468 Hierarchical model for counts of polymorphism & divergence ξ η Δ are indepPoisson with means functions of Ne, r, Φµ Φs Φssmax,smean,Β s ΦΜΑ,Β Μ Θ Ne Η1, Η2,..., Ηn1 Sr Ξ1, Ξ2,..., Ξn1 syn ns
- 30. “Chimps in a nutshell” Gonder M K et al. PNAS 2011;108:4766-4771 12 wild-‐born unrelated chimpanzees (CENTRAL) Aboume Amelie Ayrton Bakoumba Benefice Chiquita Cindy Lalala Makokou Masuku Noemie Susi Pääbo, Nature 421, 409-‐412(23 January 2003) doi:10.1038/nature01400 6 Western 11 Eastern
- 31. (Chimp)Polymorphism (Chimp) divergence Chimpanzee Human (hg 19) Human – Chimp ancestor Divergence Orangutan
- 32. Numbers of coding SNPs and fixed differences with humans Autosome X chromosome Number of synonymous sites called 3287414 172476 Number of non-synonymous sites called 11380785 600624 Number of synonymous SNPs 32942 808 Number of non-synonymous SNPs 26462 617 Synonymous divergence with humans 32548 1223 Non-synonymous divergence with humans 20632 1054
- 33. DFEs inferred from exome polymorphism divergence −60 −40 −20 0 0.000.020.040.060.08 DFE inferred from exome Pol divergence S= 4Nes φ(S) Deleterious Beneficial chromosome X chromosome 4, 7, 9, 10 • n=87-‐90 windows comprising 10kb of called exon material • Varia4on in muta4on rate • Poor fit with 7 parameters rela4ve to a saturated model
- 34. fitness effects of deleterious muta4ons on autosomes Vs. X chromosome Purifying selec4on at least as efficient on the X chromosome ! !#$ !#% !# !#' !#( !#) !#* +,-./01,23- 4/5657 6151213/8,. 9151213/8,. :137 6151213/8,. ;3/=- ,38?1 Distribu4on of fitness effects in human popula4ons show weaker selec4on (values from Eyre-‐Walker and Keightley 2009) |Ns|1 1|Ns|10 10|Ns|100 |Ns|100
- 35. 0.005 0.010 0.015 0.020 050100150 ! Density prior MC approx Posterior −1 0 1 2 3 4 5 6 0.000.050.100.150.200.25 density.default(x = margPost, bw = 0.35) Smax Density
- 36. Many thanks to • Experimental Evolu4on – Rees Kassen, Sijmen Schoustra Gordo group – Guillaume Mar4n, Thomas Lenormand and Paul Joyce for numerous discussions • Pa9erns of molecular polymorphism divergence – Mikkel Schierup, Thomas Mailund, C. Hvilsom, Yu Qian (chimp exomes) – Nicolas Gal4er Sylvain Glemin (MK-‐DFE). • Money UM2, FNU, French Embassy in O9awa, ERC.
- 37. Cleaning of the exome data • Minimize rela4onship between coverage and human-‐chimpanzee divergence • Restrict analyses to exons with 20X and 100X coverage in all 12 individuals • Exclude exons in duplicated regions è 48% of all exons included. For these, genotypes of SNPs could be called in all individuals (12 Central Chimpanzees)
- 38. log10(length in bp) 4.5 5.0 5.5 6.0 6.5 7.0 7.5 050100150200250300350 A non sophis4cated survey for Sweeps • Bin exome data in con4guous windows comprising 10kb of exon (n=2069) • Use polymorphism and divergence to compute – Synonymous divergence (Ds) to control for varia4on in muta4on rate – Standardized measure of polymorphism per window – Index for direc4on of selec4on DoS = Dn/(Dn+Ds) -‐ Pn/(Pn+Ps)
- 39. ! ! MODEL Φssmax,smean,Β s ΦΜΑ,Β Μ Θ Ne Η1, Η2,..., Ηn1 Sr Ξ1, Ξ2,..., Ξn1 syn ns DATA
- 40. 40/37 Assaying 18 mutants in 96 new environments How specialized are beneficial mutations?
- 41. 41/37 Assaying Top 18 mutants in 96 new environments How specialized are mutants? → They are NOT
- 42. A non sophis4cated survey for Sweeps reveals a major Sweep on Chr 3 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ●● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● −0.40.0 ch3$start DOS −2.0−0.51.0 ch3$start Std.PolC −2.0−0.5 ch3$start Std.PolE 0 20 40 60 80 100 −3.0−1.0 Std.PolW
- 43. THE DATA : Experimental set up (P. fluorescens) • Use a single strain (SBW25) • Use an4bio4c resistance to trap new single step resistance muta4ons – 2016 popula4ons assayed – n = 673 mutants collected • Replicated assays to characterize pleiotropic fitness effects of muta4ons • Compare with the wild type … LB 500 cells ~ 108 cells Agar + nalidixic acid
- 44. What does natural selec4on see ? Selective Count 0 20 40 60 80 100 120 140 Permissive Absolute fitness 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0 20 40 60 80 100 120 140 Wild type Wild type has zero fitness LB + an6bio6c LB • 673 nalR mutants isolated (from 2016 screened) • 28 mutants fi9er than wild type Kassen Bataillon Nat Gen 2006
- 45. 45/37 BIOLOG Setting Assaying 18 mutants in 96 new environments How specialized are beneficial mutations? Are GxE important relative to a random set of mutation ? Random 63 Top 18
- 46. 46/37 Assaying Top 18 mutants in 96 new environments → A variety of shapes for fitness effect
- 47. Assaying Top 18 mutants in 96 new environments H0: muta4on effects are exponen4al Ha: muta4on effects are GPD pvalues Frequency 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 Combined p-‐values (Fisher s procedure) p=0.0002 95 Different carbon source +Water