Doug Brutlag Professor Emeritus Biochemistry & Medicine (by courtesy)

1. Computational Molecular BiologyBiochem 218 – BioMedical Informatics 231http://biochem218.stanford.edu/ Phylogenies Doug Brutlag Professor Emeritus Biochemistry & Medicine (by courtesy)

2. Cladogram Representation of Phylogenies 100 0 Years x 106 Years x 106 0 100 A B C D E F G H I J L M N O P Q

3. Dendrogram Representation of Phylogenies GrowTree Phylogram February 1, 2010 Substitutions per 100 Residues 100.00

4. Cladogram

5. Phenogram

6. Curve-O-Gram

7. Eurogram

8. RadialGram

9. Methods for Determining Phylogenies • Parsimony (character based) • Assigns mutations to branches • Minimize number of edits • Topology maximizes similarity of neighboring leaves • Distance methods • Branch lengths = D(i,j)/2 for sequences i, j • Distances must be at least metric • Distances can reflect time or edits • Distance must be relatively constant per unit branch length A B C D E F G H I J L M N O P Q

10. Methods for Determining Phylogenies • Parsimony • Minimum mutation (Fitch, PAUP) • Minimal length encoding • Probabilistic • Branch and Bound • Maximum likelihood • Distance methods • Ultrametric Trees • Additive Trees • UPGMA • Neighbor Joining A B C D E F G H I J L M N O P Q

11. Properties of Trees • Rooted or Unrooted • Nodes and Branches • Internal Nodes • External Nodes - leaves • Operational Taxonomic Units • Outgroups • Topology • One path/pair • Distances 1 X 3 Y 2 Z 4 R2 3 Y 5 4 R1 Z 1 5 X 2 1 2 X R1 R2 Z 3 Y 5 4

12. Orthologous Evolution

13. Paralogous Evolution hemoglobins

14. Challenges Making Trees:Gene Duplication versus Speciation

15. Orthology and Paralogy Orthologs:Derived by speciation Paralogs: Gene Duplications Yeast HA1 Human HA2 Human WA Worm HB Human WB Worm Thanks to Seraphim Batzoglou

16. Challenges Making Trees:Gene Conversion A A T C G C G A T A G C A T C A A T T C C C T C Thanks to Maryellen Ruvolo

17. Challenges Making Trees:Gene Conversion A A T C G C G A T A G C A T C C G C G A T C TC A T C A A T T C C C T C Thanks to Maryellen Ruvolo

18. A B C D A B C D Challenges Making Trees:Gene Conversion Orthologs:Derived by speciation Paralogs: Gene Duplications Gene M Gene N Thanks to Maryellen Ruvolo

19. Challenges Making Trees:CM Has Been Converted from CN Orthologs:Derived by speciation Paralogs: Gene Duplications AM BM DM AN BN CMCN DN Gene N Gene M Thanks to Maryellen Ruvolo

20. Consensus CG/LH Tree Thanks to Maryellen Ruvolo

21. Gene conversion between1st & 2nd exons of LH, CG2 Genes 15nt LH Gene 168 nt Conversion No Conversion CG2 Gene 168 nt Thank Thanks to Maryellen Ruvolo

22. Challenges Making Trees: Varying Rates of Mutation

23. Challenges Making Trees:Horizontal Gene Transfer

24. Maximum Ultrametric Distance Trees Matrix D Tree T 8 5 3 3 A E D B C • Matrix D is ultrametric for tree T if: • If D is a symmetric n by n matrix of distances • T contains n leaves, one from each row or column • Each node of T labeled by one entry from D • Numbers from root to leaves strictly decrease • For any two leaves i, j, D(i,j) labels nearest common ancestor of i and j in tree

25. Maximum Ultrametric Distance Trees A symmetric matrix D is ultrametric if and only if for every three leaves i, j, and k, there is a tie for the maximum distance between D(i,j), D(i,k) and D(j,k). U V I J K

26. Additive Distance Trees Tree T Matrix D A C 2 2 3 1 4 B D

27. Distance Metrics Obey theTriangle Inequality • D(i,j) ≤ D(i,k) +D(j,k) for all i, j, k • (Max Score - Smith-Waterman Score) is a Metric if • If Gap-penalty ≥ 1+ Gap-size/(n-1) • Assuming match = 1 and mismatch = -1

28. Three Leaf Tree 1 L1,A A L3,A 3 Observe D1,2 D1,3 D2,3 L2,A 2 Calculate L1,A L2,A L3,A

29. Three Leaf Tree 1 L1,A L3,A A 3 L2,A Observe D1,2 D1,3 D2,3 2 Calculate L1,A L2,A L3,A D1,2=L1,A+L2,A D1,3=L1,A+L3,A D2,3=L2,A+L3,A

30. Solution to Three Species Tree 1 L1,A A L3,A 3 L2,A 2

31. 1 3 4 Four Species Tree L1,A L3,A B A A,B L2,A L4,A Observe D1,2 D1,3 D1,4 D2,3 D2,4 D3,4 2 Calculate L1,A L2,A L3,B L4,B, LA,B

32. Four Species Topology 1 3 L1,A L3,A B A LA,B L2,A L4,A 4 2 Label species 1, 2, 3, and 4 so that: D(1,2) + D(3,4) ≤ D(1,3) + D(2,4) = D(1,4) + D(2,3)

33. Solution for Four Species 3 1 L1,A L3,A A LA,B B L4,A L2,A 4 2 L1,A = 1/4*(D1,3 + D1,4 - D2,3 -D2,4) + 1/2*D1,2 L2,A = 1/4*(D2,3 + D2,4 - D1,3 - D1,4) + 1/2*D1,2 LB,3 = 1/4*(D1,3 + D2,3 - D1,4 - D2,4) + 1/2*D3,4 LB,4 = 1/4*(D1,4 + D2,4 - D1,3 - D2,3) + 1/2*D3,4 LA,B = 1/4*(D1,3 + D1,4 + D2,3 + D2,4) - 1/2*(D1,2 + D3,4)

34. 1 1 3 2 4 4 2 3 1 3 4 2 Four Species =>Three Topologies A B B A A

35. Species, Distances, Branches & Topologies

36. Species, Distances, Branches & Topologies

37. Number of Topologies for n Species

38. 1 3 2 4 1 34 2 UPGMA: Unweighted Pair GroupMethod with Arithmetic Average Where D1,(34) = (D1,3+D1,4)/2 and D2,(34) = (D2,3+D2,4)/2

39. 1 2 3 4 UPGMA Dendrogram 1 3 4 2

40. UPGMA Clustering

41. Neighbor Joining Method n n-1 1 n n-2 n-1 2 n-2 i X Y n-3 3 ... j n-4 3 4 2 1 n-5 5 . . .

42. Nearest Neighbor Dendrogram R Y X Z W D E C A B

43. New Hampshire Standard Tree

44. SeqWeb GrowTree Programhttp://seqweb.stanford.edu:81/gcg-bin/analysis.cgi?program=evolution-prot

45. GrowTree Parameters

46. GrowTree Distanceshttp://seqweb.stanford.edu:81/gcg-bin/analysis.cgi?program=evolution-prot

47. GrowTree Phylogram (UPGMA)

48. GrowTree Alignment

49. GrowTree Neighbor Joining Treehttp://seqweb.stanford.edu:81/gcg-bin/analysis.cgi?program=evolution-prot

50. GrowTree VegF Inputhttp://seqweb.stanford.edu:81/gcg-bin/analysis.cgi?program=evolution-prot