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EVE161: Microbial Phylogenomics - Class 4 - Phylogeny

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Slides for EVE161 at UC Davis.
"Microbial Phylogenomics"
Taught by Jonathan Eisen and Cassie Ettinger.
Winter 2018.

Published in: Science
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EVE161: Microbial Phylogenomics - Class 4 - Phylogeny

  1. 1. Class 1: EVE 161:
 Microbial Phylogenomics Class #4: Phylogeny UC Davis, Winter 2018 Instructor: Jonathan Eisen Teaching Assistant: Cassie Ettinger !1
  2. 2. Where we are going and where we have been • Previous Class: !3. rRNA • Current Class: !4. Phylogeny • Next Class: !5. Tree of Life !2
  3. 3. Phylogeny • Eisen Make Up Office Hours Tomorrow • Storer 5331 10:30-11:30 • Cassie Ettinger Office Hours • Today Storer 5331 10:30-11:30
  4. 4. Phylogeny Phylogeny
  5. 5. First Phylogenetic Tree?
  6. 6. Internal nodes represent hypothetical ancestral taxa a b c d e f g h root, root node terminal (or tip) taxa internal nodes internal branches u v w x y z t Terminal branches Parts of a phylogenetic tree !6
  7. 7. Branch Rotation
  8. 8. Types of Trees
  9. 9. Phylogram (Tree with Lengths)
  10. 10. Phylogenetic Groups
  11. 11. Phylogenetic Groups Monophyletic Paraphyletic Polyphyletic
  12. 12. Branch rotation
  13. 13. Characters • A heritable feature of an organism is known as a character (also character trait or trait). • The form that a character takes is known as its state (also known as character state). ! Note: Presence/absence can be a state • Example: ! Character = heart ! Character state = present/absent ! Character state = # of chambers !13
  14. 14. Characters ancestry is critical to understand • Characters that are inherited from a common ancestor are homologous. • Species change over time ! Known (generally) as divergence, or divergent evolution. ! Species change over time due to the combined processes of mutation, recombination, drift, selection, etc !14
  15. 15. Homology vs. Orthology vs. Paralogy
  16. 16. Data matrices !16
  17. 17. Alignment
  18. 18. Alignment with Gaps
  19. 19. Sequence Alignment 19
  20. 20. Alignment Scoring (BLAST)
  21. 21. DNA substitution matrix
  22. 22. Blosum Matrix
  23. 23. Guide Tree for Alignment
  24. 24. Refining Alignment
  25. 25. Structure Guided Alignment
  26. 26. Structure Guided Alignment
  27. 27. HMM Alignment
  28. 28. Tree reconstruction methods 28
  29. 29. Distance Phylogenetics • Calculate distances between taxa • Use an algorithm to infer a tree from those distances • Based on principle that divergence occurs after organisms separate
  30. 30. Parimony Phylogenetics • Based on Principle of Parsimony / Occam’s Razor • Possible trees are given a score of the fewest number of sequence changes required to fit data into tree • Score for all possible trees
  31. 31. Likelihood Phylogenetics • Based on Bayes’ Theorem • Trying to calculate the Probability of the Data, Given a Hypothesis • For each tree, calculate probability that the data (e.g., sequence alignment) could come from that tree • Score for all possible trees • Prob(H|D) = Prob(H and D) ÷ Prob(D) • Prob(H|D) = Prob(D|H) x Prob(H) ÷ Prob(D)
  32. 32. Bayesian Phylogenetics • Based on Bayes’ Theorem • Trying to calculate the Probability of the Hypothesis, Given the Data • For each tree, calculate probability that the tree could come from that data ((e.g., sequence alignment) • Score for all possible trees • Prob(H|D) = Prob(H and D) ÷ Prob(D) • Prob(H|D) = Prob(D|H) x Prob(H) ÷ Prob(D)
  33. 33. Bayesian • Based on Bayes’ Theorem • Prob(H|D) = Prob(H and D) ÷ Prob(D) • Prob(H|D) = Prob(D|H) x Prob(H) ÷ Prob(D)
  34. 34. Many possible trees
  35. 35. Other Tree Related Issues
  36. 36. Bootstrapping
  37. 37. Bootstrapping !37
  38. 38. Jacknifing !38
  39. 39. Congruence !39
  40. 40. Masking !40
  41. 41. Concatenation !41
  42. 42. Homoplasy !42
  43. 43. Clustering vs. Distance Trees
  44. 44. UPGMA Unweighted Pair Group Method with Arithmetic mean (UPGMA) algorithm
  45. 45. The True Tree
  46. 46. Distance Matrix For True Tree
  47. 47. Collapse Diagonal
  48. 48. Identify Lowest D OTUs A B C D E B 2 C 4 4 D 6 6 6 E 6 6 6 4 F 8 8 8 8 8
  49. 49. Join Those Two Taxa • Create branch with length = D • 2 • A--------------B
  50. 50. Make D from Node Equal
  51. 51. Create New Distance Matrix • Merge Two OTUs joined in previous step (AB) • Dx, AB = 0.5 * (Dx, A + Dx, B)
  52. 52. New Matrix
  53. 53. UPGMA
  54. 54. Compare to True Tree
  55. 55. But … • What is evolutionary rates not equal
  56. 56. Unequal rates
  57. 57. UPGMA with Unequal rates
  58. 58. Compare to True Tree
  59. 59. Neighbor Joining
  60. 60. Start with Star Tree
  61. 61. Calculate S • For each OTU, calculate a measure (S) as follows. • S is the sum of the distances (D) between that OTU and every other OTU, divided by N-2 where N is the total number of OTUs. • This is a measure of the distance an OTU is from all other OTUs
  62. 62. Calculate Pairwise Distances • Calculate the distance Dij between each OTU pair (e.g., I and J).
  63. 63. Identify Closest Pair • Identify the pair of OTUs with the minimum value of Dij – Si – Sj
  64. 64. Joining Taxa • As in UPGMA, join these two taxa at a node in a subtree.
  65. 65. Calculate Branches • Calculate branch lengths. Unlike UPGMA, neighbor joining does not force the branch lengths from node X to I (Dxi) and to J (Dxj) to be equal, i.e., does not force the rate of change in those branches to be equal. Instead, these distances are calculated according to the following formulas • Dxi = 1/2 Dij + 1/2 (Si – Sj) • Dxj = 1/2 Dij + 1/2 (Sj – Si)
  66. 66. Calculate New Matrix • Calculate a new distance matrix with I and J merged and replaced by the node (X) that joins them. Calculate the distances from this node to the other tips (K) by: • Dxk = (Dik + Djk – Dij)/2
  67. 67. Distance Matrix
  68. 68. S • SA = (5+4+7+6+8) / 4 = 7.5 • SB = (5+7+10+9+11) / 4 = 10.5 • SC = (4+7+7+6+8) / 4 = 8 • SD= (7+10+7+5+9) / 4 = 9.5 • SE= (6+9+6+5+8) / 4 = 8.5 • SF= (8+11+8+9+8) / 4 = 11
  69. 69. M • Mij = Dij – Si - Sj • Smallest are • MAB = 5 – 7.5 – 10.5 = -13 • MDE = 5 – 9.5 – 8.5 = -13 • Choose one of these (AB here)
  70. 70. New Tree • Create a node (U) that joins pair with lowest Mij such that • SIU = DIJ/2 + (SI – SJ) / 2 • Merge U with other taxa • Join I and J according to S above and make all other taxa in form of a star
  71. 71. C D E F U1 B A 4 1
  72. 72. New Matrix • DXU = DIX + DJX – DIJ where I and J are those selected from above.
  73. 73. Table 11
  74. 74. Compare to True Tree C D E F U1 B A 4 1 U2 3 2 2 1 U3 U4 5
  75. 75. Long branch attraction !75
  76. 76. Rooting !76
  77. 77. Rooting TOL Review

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