A not too technical explanation of coalescence HMMs and the divergence time between human and apes

1. Monkey Business Bioinformatics Research Center University of Aarhus Thomas Mailund Joint work with Asger Hobolth, Ole F. Christiansen and Mikkel H. Schierup

2. Paper:

3. Dating speciation events Relationship between great apes:

4. Dating speciation events Relationship between great apes: How do we know this is the relationship?

5. Dating speciation events Relationship between great apes: How do we know this is the relationship? How do we date the speciation events?

6. Fossil record Good fossil record for humans, less so for other apes... Jobling et al. 2004 Common ancestor human-chimp?

7. Fossil record Good fossil record for humans, less so for other apes... Enter: molecular genetics methods! Jobling et al. 2004 Common ancestor human-chimp?

11. Mutations and a molecular clock HIV sequence: Accumulation of mutations over time

12. Mutations and a molecular clock

13. Mutations and a molecular clock Estimation using observed number of mutations

14. Mutations and a molecular clock Back mutations complicate matters slightly, but we can compensate for this by solving a simple differential equation...

15. Mutations and a molecular clock Back mutations complicate matters slightly, but we can compensate for this by solving a simple differential equation...

16. Mutations and a molecular clock The time estimate is known up to a mutation-rate factor... ...that e.g. can be calibrated using fossil evidence.

17. Dating divergence... So we can estimate pairwise divergence in units of time... 14 My 36 My

18. Dating divergence... So we can estimate pairwise divergence in units of time... ...although this over-estimates the number of mutations (does not take shared mutations into account) 14 My 36 My

19. Dating divergence... So we can estimate pairwise divergence in units of time... ...possible to construct a tree and infer branch lengths from this... 14 My 36 My

20. Dating divergence... aactg agctg aggtg atatg agctg aactg So we can estimate pairwise divergence in units of time... ...possible to construct a tree and infer branch lengths from this... ...or take a statistical approach and deal with unobserved sequences in a mathematical model.

21. Dating divergence... aactg agctg aggtg atatg agctg aactg t 1 t 2 t 3

22. Dating divergence... aactg agctg aggtg atatg agctg aactg Can be computed efficiently using a dynamic programming algorithm. t 1 t 2 t 3

23. Dating divergence... aactg agctg aggtg atatg agctg aactg Time parameters can then be estimated by maximizing the likelihood. t 1 t 2 t 3

27. Populations and species Individuals A funny thing happens if the population size is large relative to the splitting time...

28. Populations and species Populations Individuals

29. Populations and species Individuals Populations

30. Populations and species Individuals Populations join at population join time join much later than population

31. Populations and species Individuals Populations

32. Populations and species A funny thing happens if the population size is large relative to the splitting time... ...for speciation, the time is too long...

33. Populations and species A funny thing happens if the population size is large relative to the splitting time... ...for speciation, the time is too long... ...and no human is closer related to chimps than any other human!

37. Recombination  genome  species Physical position along genome Divergence time Adapted from Patterson et al. 2006

38. Species and segment trees Human Chimp Gorilla Case A: Only Human and Chimp can coalesce here. Always consistent with species tree. Case B: All species can coalesce here. Only a third consistent with species tree.

39. Species and segment trees Human Chimp Gorilla Case A: Only Human and Chimp can coalesce here. Always consistent with species tree. Case B: All species can coalesce here. Only a third consistent with species tree. We can get the probability of A or B based on split times and population size t 1 t 1 + t 2 N HC N HCG

40. Species and segment trees We can express the probability of either of these trees in terms of splitting times and effective population sizes...

41. Species and segment trees We can express the probability of either of these trees in terms of splitting times and effective population sizes... ...or alternatively get the time parameters from the tree probabilities.

42. Species and segment trees We obtain the tree probabilities from an approximation to the coalescence process: a hidden Markov model

43. Markov models A Markov model is an automaton where transitions are probabilistic, i.e. each transition to the next state is taken with a certain probability. A run is a sequence of states generated by the model.

44. Hidden Markov models (HMMs) A hidden Markov model in addition has emission symbols and probabilities. In each state it emits symbols with certain probabilities. A run is a sequence of both states and emissions. We only observe the emissions.

46. A coalescence HMM A

47. A coalescence HMM A a a c a a c

48. A coalescence HMM A B1 a a c

49. A coalescence HMM A B1 a c a c c c c c c

50. A coalescence HMM A B1 B1 a c a a c t c c a a t a

51. A coalescence HMM A B1 B1 B1 a c a a a c t a c c a a a a a

52. A coalescence HMM A B1 B1 B1 B3 a c a a g a c t a c c c a a c g c c

53. A coalescence HMM A B1 B1 B1 B3 B3 B3 A A A a c a a g a t c a c a c t a c t c t a c c c a a c t c t a c c c c

54. A coalescence HMM A B1 B1 B1 B3 B3 B3 A A A a c a a g a t c a c a c t a c t c t a c c c a a c t c t a c

56. Results t 1 t 2

57. Annotation in the CoalHMM Posterior probabilities of each tree (probability of being in a particular tree given the sequence data) along a genomic region:

59. The end Thank you! http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1802818&rendertype=abstract