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How to estimate phylogenies? On parsimony, likelihood and probability.

How to estimate phylogenies? On parsimony, likelihood and probability. Duur Aanen. Overview. Basics What is a phylogenetic tree Rooted, unrooted, monophyletic group Distance methods Maximum parsimony Likelihood methods Maximum likelihood Bayesian analysis Differences

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How to estimate phylogenies? On parsimony, likelihood and probability.

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  1. How to estimate phylogenies?On parsimony, likelihood and probability. Duur Aanen

  2. Overview • Basics • What is a phylogenetic tree • Rooted, unrooted, monophyletic group • Distance methods • Maximum parsimony • Likelihood methods • Maximum likelihood • Bayesian analysis • Differences • Example: the evolution of fungus-growing termites and their mutualistic fungal symbionts

  3. A B C Basics • Phylogeny = evolutionary history of a group • Phylogenetic tree: graphical representation • (phylogenetic reconstruction

  4. Unrooted tree A C B

  5. A B C Rooted tree

  6. A C B

  7. A B C A C B

  8. A C B A A B C C B

  9. B C A A A B C C B A C B

  10. B C A A A B C C B A C B

  11. How do we know where the root is? • Usually by including an outgroup in the analysis: a species that falls outside the group you study (the ingroup) Examples: ingroup birds, outgroup crocodile ingroup rodents, outgroup gorilla

  12. rat hamster mouse rat mouse hamster mouse hamster rat rat mouse hamster

  13. Gorilla ?

  14. gorilla rat mouse hamster rat rat hamster mouse mouse hamster mouse hamster rat

  15. gorilla gorilla rat mouse hamster ! rat rat hamster mouse mouse hamster mouse hamster rat

  16. A B C AB: monophyletic group: A and B share a uniquecommon ancestor

  17. A B C BC: no monophyletic group: B and C do not share a uniquecommon ancestor

  18. Example: evolutionary history of three species: Outgroup: slide after Fredrik Ronquist

  19. Three possible trees: A C B slide after Fredrik Ronquist

  20. How to decide? • Not known • Estimate! • Use (some kind of) similarity to estimate: • Similarity based on characters: • Morphology • DNA! • Method to come from character to tree

  21. DNA characters 111 123456789012 Chimp ATTCGAGTAGCT Human ATTCGAGTAGCT Gorilla ATGCGAGTAGCT Orang-utan ATGCGAGAAGCT

  22. Methods to estimate tree from data • Maximum parsimony • Distance based methods • Likelihood based methods • Maximum likelihood • Bayesian inference

  23. 111 123456789012 Chimp ATTCGAGTAGCT Human ATTCGAGTAGCT Gorilla ATGCGAGTAGCT Orang-utan ATGCGAGAAGCT

  24. Most parsimonious solution: 2 steps 3:GT 7:AT

  25. 111 123456789012 Chimp ATTCGAGTAGCT Human ATTCGAGTAGCT Gorilla ATGCGAGTAGCT Orang-utan ATGCGAGAAGCT

  26. Distance based 0 0 1 2 0 1 2 0 1 0

  27. Maximum likelihood • The tree that maximizes the likelihood of observing the data from that tree is the best tree • Requires evolutionary model of sequence evolution • Calculation takes lot of computer time

  28. Maximum Likelihood estimate: the coin is biased! Example (coin tossing) • 10 coins, 1 is biased (p=0.8) but we don’t know which one • Experiment: 10 tosses with 1 of the 10 coins: HHHHHHHHHH • Likelihood: Pr [data | hypothesis] • Pr [10H | biased] = 0.810 = 0.107 • Pr [10H | fair] = 0.510 = 0.00098

  29. ’The best tree?’ • How can we know for sure? • Unlikely that we can decide for sure which tree • Often unlikely that we can find it

  30. No. of possible rooted trees no. sequences no. possible rooted trees 2 1 3 3 4 15 5 105 6 945 7 10.395 8 135.135 9 2.027.025 10 34.469.425 . . . 20. 8.200.794.532.637.891.559.000 . . . 135 2113354829308321145237289349456774432829304974 6389294775489579847592843759314562131843276117 4912347721241323233245569964443827487648712865 2143778687234129346123462394984237415736553232 2518798537837558885200938452003255000329843122 001192827437745585983493487551798753932 !!!

  31. Phylogeny as a statistical problem... • Many possible trees, with different likelihoods • Estimate the probability distribution of trees

  32. Bayesian methods... Bayes’ theorem: Posterior probability = probability of a hypothesis given the data For trees: probability of a tree given the DNA sequences and model of sequence evolution (likelihood is probability of data given a hypothesis, or of the DNA sequences given the tree)

  33. Example (coin tossing) • 10 coins, 1 is biased (p=0.8) but we don’t know which one • Prior probability biased coin = 0.1 • Experiment: 10 tosses with one of the 10 coins: HHHHHHHHHH • Bayes’ theorem: Posterior probability of biased coin given 10H = pr[10H|biased]*pr[biased]/ [pr[10H|biased]*pr[biased] + pr[10H|biased]*pr[unbiased]]  Posterior probability that coin is biased = 0.92 (Remember: Likelihood: Pr [data | hypothesis], Pr [10H | biased] = 0.810 = 0.107, Pr [10H | fair] = 0.510 = 0.00098)

  34. For trees... • Pr[tree|data] • Impossible to calculate: • Tree • Branch lengths • Evolutionary model with many parameters... •  estimation using Markow Chain Monte Carlo (MCMC) simulation • Start with a random tree • Propose new tree by changing current tree • Accept or reject with some criterion (likelihood and chance implemented in criterion) • Many generations • Save sample of trees

  35. slide after: François Lutzoni

  36. Different starting tree...

  37. slide after: François Lutzoni

  38. Example: 40 termite species, 937 nucleotides • Analysed with MrBayes (GTR + SSR) • 1.500.000 generations, sampled every 50th tree ( 30.000 trees) • The first 10 trees sampled...

  39. Microtermes sp. 103 tree 1 Macrotermes subhyalinus 64 Microtermes sp. 3 Odontotermes lateritius 39 Odontotermes billitori 168 Odontotermes sp. 303 Ancistrotermes cavitorax 46 Macrotermes bellicosus 19 Acanthotermes acanthotorax Pauls Protermes minutus 567 Odontotermes lateritius 81 Odontotermes sp.4 110 Odontotermes nilensis 93 Odontotermes sp.3 126 Odontotermes minutus 161 Odontotermes sarawakensis 167 Odontotermes javanicus 165 Macrotermes lilljeborgi 143 Macrotermes muelleri Corinnes Macrotermes nobilis 569 Pseudacanthotermes militaris 134 Macrotermes subhyalinus 5 Macrotermes bellicosus 8 Acanthotermes acanthotorax 136 Hypotermes xenotermitis 166 Macrotermes malacensis 160 Odontotermes silvicolus 6 Microtermes sp. 146 Synacanthotermes heterodon 118 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Odontotermes sp.1 130 Macrotermes ahmadi pe5 Ancistrotermes sp. 140 Protermes minutus 129 Ancistrotermes cavitorax 34 Labritermes butelreepeni 169 Microtermes sp. 38 Microtermes sp. 107 Foraminitermes sp. 159

  40. Microtermes sp. 103 tree 2 Microtermes sp. 107 Protermes minutus 567 Odontotermes nilensis 93 Pseudacanthotermes militaris 134 Ancistrotermes cavitorax 46 Synacanthotermes heterodon 118 Labritermes butelreepeni 169 Odontotermes minutus 161 Macrotermes nobilis 569 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Odontotermes silvicolus 6 Odontotermes sp.1 130 Ancistrotermes sp. 140 Macrotermes malacensis 160 Odontotermes lateritius 39 Microtermes sp. 3 Microtermes sp. 146 Odontotermes sp.4 110 Macrotermes subhyalinus 64 Odontotermes sp. 303 Macrotermes bellicosus 19 Acanthotermes acanthotorax 136 Macrotermes muelleri Corinnes Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 34 Protermes minutus 129 Odontotermes javanicus 165 Odontotermes oblongatus 162 Macrotermes subhyalinus 5 Hypotermes xenotermitis 166 Macrotermes bellicosus 8 Macrotermes ahmadi pe5 Microtermes sp. 38 Odontotermes billitori 168 Odontotermes lateritius 81 Odontotermes sp.3 126 Ancistro Odonto sp. 164 Foraminitermes sp. 159

  41. Microtermes sp. 103 tree 3 Microtermes sp. 107 Protermes minutus 567 Odontotermes nilensis 93 Pseudacanthotermes militaris 134 Ancistrotermes cavitorax 46 Synacanthotermes heterodon 118 Labritermes butelreepeni 169 Macrotermes nobilis 569 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Odontotermes silvicolus 6 Odontotermes sp.1 130 Odontotermes lateritius 39 Macrotermes malacensis 160 Ancistrotermes sp. 140 Microtermes sp. 3 Microtermes sp. 146 Odontotermes minutus 161 Odontotermes sp.4 110 Macrotermes subhyalinus 64 Odontotermes sp. 303 Macrotermes bellicosus 19 Acanthotermes acanthotorax 136 Macrotermes muelleri Corinnes Microtermes sp. 38 Odontotermes billitori 168 Macrotermes bellicosus 8 Macrotermes ahmadi pe5 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 34 Odontotermes javanicus 165 Protermes minutus 129 Odontotermes oblongatus 162 Hypotermes xenotermitis 166 Macrotermes subhyalinus 5 Odontotermes lateritius 81 Odontotermes sp.3 126 Ancistro Odonto sp. 164 Foraminitermes sp. 159

  42. Microtermes sp. 103 tree 4 Pseudacanthotermes militaris 134 Protermes minutus 567 Odontotermes minutus 161 Odontotermes sp.1 130 Macrotermes lilljeborgi 143 Macrotermes bellicosus 19 Microtermes sp. 38 Ancistrotermes sp. 140 Macrotermes subhyalinus 64 Odontotermes silvicolus 6 Acanthotermes acanthotorax Pauls Odontotermes sp.4 110 Odontotermes sp. 303 Odontotermes oblongatus 162 Odontotermes sarawakensis 167 Macrotermes bellicosus 8 Odontotermes billitori 168 Macrotermes malacensis 160 Macrotermes nobilis 569 Microtermes sp. 107 Macrotermes muelleri Corinnes Microtermes sp. 3 Macrotermes ahmadi pe5 Macrotermes subhyalinus 5 Protermes minutus 129 Ancistrotermes cavitorax 34 Synacanthotermes heterodon 118 Labritermes butelreepeni 169 Odontotermes javanicus 165 Microtermes sp. 146 Odontotermes nilensis 93 Odontotermes lateritius 39 Ancistrotermes cavitorax 46 Odontotermes lateritius 81 Acanthotermes acanthotorax 136 Hypotermes xenotermitis 166 Ancistro Odonto sp. 164 Odontotermes sp.3 126 Foraminitermes sp. 159

  43. Microtermes sp. 103 tree 5 Macrotermes subhyalinus 64 Microtermes sp. 3 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes sp.4 110 Odontotermes nilensis 93 Odontotermes sp.3 126 Macrotermes bellicosus 19 Odontotermes minutus 161 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Hypotermes xenotermitis 166 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Odontotermes silvicolus 6 Microtermes sp. 146 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Synacanthotermes heterodon 118 Odontotermes sp.1 130 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Ancistrotermes cavitorax 34 Labritermes butelreepeni 169 Microtermes sp. 38 Microtermes sp. 107 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  44. Microtermes sp. 103 tree 6 Macrotermes subhyalinus 64 Microtermes sp. 3 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes sp.4 110 Odontotermes nilensis 93 Odontotermes sp.3 126 Macrotermes bellicosus 19 Odontotermes minutus 161 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Hypotermes xenotermitis 166 Synacanthotermes heterodon 118 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Odontotermes silvicolus 6 Microtermes sp. 146 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Odontotermes sp.1 130 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Ancistrotermes cavitorax 34 Labritermes butelreepeni 169 Microtermes sp. 38 Microtermes sp. 107 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  45. Microtermes sp. 103 tree 7 Macrotermes subhyalinus 64 Microtermes sp. 3 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Macrotermes bellicosus 19 Odontotermes minutus 161 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes sp.4 110 Odontotermes nilensis 93 Odontotermes sp.3 126 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Synacanthotermes heterodon 118 Hypotermes xenotermitis 166 Odontotermes silvicolus 6 Microtermes sp. 146 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Odontotermes sp.1 130 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Labritermes butelreepeni 169 Ancistrotermes cavitorax 34 Microtermes sp. 38 Microtermes sp. 107 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  46. Microtermes sp. 103 tree 8 Macrotermes subhyalinus 64 Macrotermes bellicosus 19 Odontotermes minutus 161 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes nilensis 93 Odontotermes sp.4 110 Odontotermes sp.3 126 Microtermes sp. 3 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Hypotermes xenotermitis 166 Synacanthotermes heterodon 118 Odontotermes silvicolus 6 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Microtermes sp. 146 Odontotermes sp.1 130 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Labritermes butelreepeni 169 Ancistrotermes cavitorax 34 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Microtermes sp. 38 Microtermes sp. 107 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  47. Microtermes sp. 103 tree 9 Macrotermes subhyalinus 64 Macrotermes bellicosus 19 Odontotermes minutus 161 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes nilensis 93 Odontotermes sp.4 110 Odontotermes sp.3 126 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Microtermes sp. 3 Microtermes sp. 107 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Hypotermes xenotermitis 166 Synacanthotermes heterodon 118 Odontotermes silvicolus 6 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Odontotermes sp.1 130 Microtermes sp. 146 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Labritermes butelreepeni 169 Ancistrotermes cavitorax 34 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Microtermes sp. 38 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  48. Microtermes sp. 103 tree 10 Macrotermes subhyalinus 64 Macrotermes bellicosus 19 Odontotermes minutus 161 Protermes minutus 567 Odontotermes lateritius 81 Odontotermes nilensis 93 Odontotermes sp.4 110 Odontotermes lateritius 39 Odontotermes sp. 303 Odontotermes billitori 168 Odontotermes sp.3 126 Microtermes sp. 3 Microtermes sp. 107 Macrotermes muelleri Corinnes Macrotermes malacensis 160 Synacanthotermes heterodon 118 Odontotermes silvicolus 6 Odontotermes oblongatus 162 Ancistro Odonto sp. 164 Odontotermes sp.1 130 Microtermes sp. 146 Hypotermes xenotermitis 166 Macrotermes nobilis 569 Macrotermes subhyalinus 5 Pseudacanthotermes militaris 134 Acanthotermes acanthotorax 136 Macrotermes bellicosus 8 Labritermes butelreepeni 169 Ancistrotermes cavitorax 34 Protermes minutus 129 Ancistrotermes sp. 140 Macrotermes ahmadi pe5 Microtermes sp. 38 Acanthotermes acanthotorax Pauls Ancistrotermes cavitorax 46 Odontotermes javanicus 165 Odontotermes sarawakensis 167 Macrotermes lilljeborgi 143 Foraminitermes sp. 159

  49. Not very stable... • Does it get more stable? • Plot likelihoods against the number of generations...

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