Molecular population genetics of adaptation from recurrent beneficial mutation

1. Molecular population genetics of adaptation from recurrent beneficial mutation Joachim Hermisson and Pleuni Pennings, LMU Munich

2. How can genetic variation be maintained in a population in the face of positive selection?

3. Selective sweepwith recombination

4. Selective sweep with recombination

5. Selective sweepwith recombination

6. Selective sweepwith recombination

7. Selective sweepwith recombination

8. Recurrent mutation Classical view: • Adaptive substitutions occur from a single mutational origin

9. Recurrent mutation Classical view: • Adaptive substitutions occur from a single mutational origin What happens if the same beneficial allele occurs recurrently in a population?

10. Soft sweepfrom recurrent mutation

11. Soft sweepfrom recurrent mutation

12. Soft sweepfrom recurrent mutation

13. Soft sweepfrom recurrent mutation

14. 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 Soft sweepfrom recurrent mutation frequency → time →

15. Is recurrent mutation relevant? • What is the probability of a soft sweep under recurrent mutation? • What is the impact on patterns of neutral polymorphism?

16. Model • Haploid population of constant size Ne • At selected locus: recurrent mutation of rate uto a beneficial allele (or a class of equivalent alleles) with selective advantage s • Scaled values: q = 2Ne u ,a = 2Ne s, R = 2Ne r • Generation update: Wright-Fisher model (fitness weighted multinomial sampling)

17. Coalescent viewGenealogy of a sample from a linked locus t +1 t • What can happen one generation back in time? 1- xt xt n lines

18. Coalescent viewCoalescence of two lines t +1 t • Rate per generation: 1- xt xt

19. Coalescent viewRecombination t +1 t • Rate per generation: 1- xt xt

20. Coalescent viewNew mutation at selected site t +1 t • Rate per generation: 1- xt xt

21. Coalescent view Problem: Rates for • coalescence • recombination • beneficial mutation depend on the frequency x of the selected allele: stochastic path

22. Coalescent viewClassic case: Coalescence and recombination • Probability for multiple haplotypes in a sample after a sweep due to recombination: (Higher orders: Etheridge, Pfaffelhuber, Wakolbinger) • small for large a (strong selection makes broad sweep patterns)

23. Coalescent viewCoalescence and mutation, sample of size 2 Probability for coalescence before mutation (single haplotype)

24. Coalescent viewCoalescence and mutation, sample of size 2 Probability for coalescence before mutation (single haplotype)

25. Coalescent viewCoalescence and mutation, sample of size 2 Probability for coalescence before mutation (single haplotype)

26. Coalescent viewCoalescence and mutation, sample of size 2 Probability for coalescence before mutation (single haplotype)

27. Coalescent viewCoalescence and mutation, sample of size 2 Probability for coalescence before mutation (single haplotype)

28. Coalescent viewCoalescence and mutation, sample of size 2 Probability for single or multiple haplotypes: T1: average time to the first coalescence or mutation-event

29. Coalescent viewCoalescence and mutation, sample of size 2 Sampling at time of fixation: 0 <T1 < Tfix

30. Coalescent viewCoalescence and mutation, sample of size 2 General: sampling Tobs generations after fixation: extra factor can be ignored for Tobs << Ne

31. Coalescent viewCoalescence and mutation, sample of size 2 Sampling at time of fixation: 0 <T1 < Tfix Tfix / Ne≈ 4 log(a) / a , a = 2Ne s(scaled selection strength)

32. Coalescent viewCoalescence and mutation, sample of size 2 Simulation results (θ = 0.4)

33. Coalescent viewCoalescence and mutation, sample of size 2 Fora > 500 : Tfix / Ne<< 1, thus • Corresponds to approximation:

34. Coalescent viewCoalescence and mutation, sample of size n

35. Coalescent viewCoalescence and mutation, sample of size n

36. Coalescent viewCoalescence and mutation, sample of size n Continuous time and time rescaling: Neutral coalescent !

37. Coalescent viewCoalescence and mutation, sample of size n • Problem independent of the path xt and all selection parameters

38. Coalescent viewCoalescence and mutation, sample of size n • Problem independent of the path xt and all selection parameters • Coalescent of the infinite alleles model • Forward in time: “Hoppe urn” or Yule process with immigration

39. Coalescent viewCoalescence and mutation, sample of size n • Problem independent of the path xt and all selection parameters • Coalescent of the infinite alleles model • Forward in time: “Hoppe urn” or Yule process with immigration The sampling distribution of ancestral haplotypes can be approximated by the distribution of family sizes in a Hoppe urn or a Yule process with immigration • Solved problem

40. ResultsEwens sampling formula • Probability for k haplotypes, occurring n1,…, nk times in a sample of size n:

41. ResultsEwens sampling formula • Probability for more than one ancestral haplotype in a sample (“soft sweep”):

42. Ewens approximation, sample size n = 20 >4 haplos 100% 4 haplos 80% 3 haplos 60% 2 haplos 40% 1 haplo 20% 0% q = 1 q = 4 q = 0.4 q = 0.04 q = 0.004 ResultsProbability of a soft sweep

43. ResultsProbability of a soft sweep Simulation (2Ne s = 10000, n = 20) >4 haplos 100% 4 haplos 80% 3 haplos 60% 2 haplos 40% 1 haplo 20% 0% q = 1 q = 4 q = 0.4 q = 0.04 q = 0.004

44. ResultsProbability of a soft sweep Simulation (2Ne s = 10000, n = 20) >4 haplos 100% 4 haplos 80% 3 haplos 60% 2 haplos 40% 1 haplo 20% 0% q = 1 q = 4 q = 0.4 q = 0.04 q = 0.004 Probability for multiple haplotypes> 5%forq > 0.01 >95% for q > 1

45. ResultsFrequency of major haplotype 0.5 Sample size 10 0.4 α =100 α =1000 0.3 α =10000 prediction 0.2 0.1 0 5/10 6/10 7/10 8/10 9/10

46. When should we expect soft sweeps?Multiple haplotypes due to recurrent beneficial mutations • Strong dependence on the mutation rate • More than 5% for q> 0.01 • E.g. African D. melanogaster: q≈ 0.05 (Li / Stephan 2006) • About 16% of all single-site adaptations “soft” • Particularly relevant for • Large populations (e.g. bacteria) • Adaptive (partial) loss-of-function mutations

47. Soft sweeps in data? • Drosophila • Schlenke and Begun (Genetics 2005): LD pattern at 3 immunity receptor genes in Californian D. simulans • Humans • Multiple origin of FY-0 Duffy allele (loss of function) • Plasmodium • Multiple origins of pyrimethamine resistance mutations

48. Generality of the resultmigration instead of mutation • Beneficial alleles enter by recurrent migration at rate M = 2Ne m from a genetically diverged source population • Coalescent analysis with migration rate

49. Generality of the resultmigration instead of mutation • Beneficial alleles enter by recurrent migration at rate M = 2Ne m from a genetically diverged source population • Coalescent analysis with migration rate • Directly proportional to coalescence rate (no factor 1- xt) • Approximation holds exactly in this case

50. Generality of the resultmigration instead of mutation M = 0.4 q = 0.4 a