1. Phylogenetic Trees

2. OUTLINE
Phylogeny
UPGMA
Neighbor Joining Method

3. Phylogeny Understanding life through time,
over long periods of past time,
the connections between all groups of organisms as understood by ancestor/descendant relationships,
Tree of life.

4. Phylogeny

5. Phylogeny
Rooted and Unrooted trees:

6. Phylogeny Rooted and Unrooted trees:
Most phylogenetic methods produce unrooted trees, because they detect differences between sequences, but have no means to orient residue changes relatively to time.

7. Phylogeny Rooted and Unrooted trees:
Two means to root an unrooted tree :
The outgroup method : include in the analysis a group of sequences known a priori to be external to the group under study; the root is by necessity on the branch joining the outgroup to other sequences.
Make the molecular clock hypothesis : all lineages are supposed to have evolved with the same speed since divergence from their common ancestor. Root the tree at the midway point between the two most distant taxa in the tree, as determined by branch lengths. The root is at the equidistant point from all tree leaves.

8. Phylogeny Rooted and Unrooted trees:
Two means to root an unrooted tree :

9. Phylogeny
Orthology / Paralogy:

10. Phylogeny Species Tree and Gene Tree:
E gene tree for Na+-K+ ion pump membrane protein family members
Evolutionary relationship between seven eukaryotes

11. Phylogeny
Species Tree and Gene Tree:

12. Phylogeny
Additive Tree:A distance matrix corresponding to a tree is called additive,
THEOREM: D is additive if and only if:
For every four indices i,j,k,l, the maximum and median of the three pairwise sums are identical:
Dij+Dkl < Dik+Djl = Dil+Djk

13. UPGMA Building Phylogenetic Trees by UPGMA:
Unweighted Pair – Group Method using arithmetic Averages,
Assume constant mutation rate,
The two sequences with with the shortest evolutionary distance between them are assumed to have been the last two diverge, and represented by the most racent internal node.

14. UPGMA Building Phylogenetic Trees by UPGMA:
The distance between two clusters:
Assume we have N sequences,
Cluster X has NX sequences, cluster Y has NY sequences,
dXY : the evlotionary distance between X and Y

15. UPGMA Building Phylogenetic Trees by UPGMA:
When cluster X and Y are combined to make a new cluster Z:
No need to use sequence – sequence distances,
Calculate the distance of each cluster (such as W) to the new cluster Z

16. UPGMA Building Phylogenetic Trees by UPGMA: Example:
The distance matrix

17. UPGMA
Building Phylogenetic Trees by UPGMA:
Example:

18. UPGMA Building Phylogenetic Trees by UPGMA: Example:
A – D becomes a new cluster lets say V,
We have to modify the distance matrix,
What are the distances between:
V and B,
V and C,
V and E,
V and F.

19. UPGMA Building Phylogenetic Trees by UPGMA: Example:
A – D becomes a new cluster lets say V,
We have to modify the distance matrix,
What are the distances between:
V and B (Calculate),

20. UPGMA Building Phylogenetic Trees by UPGMA: Example:
A – D becomes a new cluster lets say V,
We have to modify the distance matrix,
What are the distances between:
V and C (Calculate),

21. UPGMA Building Phylogenetic Trees by UPGMA: Example:
A – D becomes a new cluster lets say V,
We have to modify the distance matrix,
What are the distances between:
V and E (Calculate),

22. UPGMA Building Phylogenetic Trees by UPGMA: Example:
A – D becomes a new cluster lets say V,
We have to modify the distance matrix,
What are the distances between:
V and F (Calculate),

23. UPGMA
Building Phylogenetic Trees by UPGMA:
Example:
New matrix:

24. UPGMA Building Phylogenetic Trees by UPGMA: Example:
Cluster according to min distance:

25. UPGMA Building Phylogenetic Trees by UPGMA: Example:
V – E becomes a new cluster lets say W,
We have to modify the distance matrix,
What are the distances between:
W and B,
W and C,
W and F.

26. UPGMA Building Phylogenetic Trees by UPGMA: Example:
V – E becomes a new cluster lets say W,
We have to modify the distance matrix,
What are the distances between:
W and B (Calculate),

27. UPGMA Building Phylogenetic Trees by UPGMA: Example:
V – E becomes a new cluster lets say W,
We have to modify the distance matrix,
What are the distances between:
W and C (Calculate),

28. UPGMA Building Phylogenetic Trees by UPGMA: Example:
V – E becomes a new cluster lets say W,
We have to modify the distance matrix,
What are the distances between:
W and F (Calculate),

29. UPGMA
Building Phylogenetic Trees by UPGMA:
Example:
New matrix:

30. UPGMA Building Phylogenetic Trees by UPGMA: Example:
Cluster according to min distance:

31. UPGMA Building Phylogenetic Trees by UPGMA: Example:
F – B becomes a new cluster lets say X,
We have to modify the distance matrix,
What are the distance between:
W and X.

32. UPGMA Building Phylogenetic Trees by UPGMA: Example:
What are the distance between: W and X (Calculate).

33. UPGMA
Building Phylogenetic Trees by UPGMA:
Example:
New matrix:

34. UPGMA Building Phylogenetic Trees by UPGMA: Example:
Cluster according to min distance:

35. UPGMA Building Phylogenetic Trees by UPGMA: Example:
X – W becomes a new cluster lets say Y,
We have to modify the distance matrix,
What are the distance between:
Y and C.

36. UPGMA Building Phylogenetic Trees by UPGMA: Example:
What are the distance between: Y and C (Calculate).

37. UPGMA
Building Phylogenetic Trees by UPGMA:
Example:
New matrix:

38. UPGMA Building Phylogenetic Trees by UPGMA: Example:
Cluster according to min distance:

39. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Do not make the assumption of constant mutation rate,
Assume that the distances are additive.

40. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
The distances dij:

41. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
The branch lengths:

42. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
The distances between clusters are defined as UPGMA:

43. Fitch-Margoliash Method:

44. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example: A B C D E 22 39 41 43 18 20 10

45. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
D and E are the closest sequences A B C D E 22 39 41 43 18 20 10

46. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
D and E are the closest sequences A B C D E 22 39 41 43 18 20 10

47. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Name {A, B, C} as W, A B C D E 22 39 41 43 18 20 10

48. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Distance between W and D: A B C D E 22 39 41 43 18 20 10

49. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Distance between W and E: A B C D E 22 39 41 43 18 20 10

50. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Branches a, b and c:

51. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Branches a, b and c:

52. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Update the distance matrix: A B C
{D,E} 22 39 40 41 42 19 A B C D E 22 39 41 43 18 20 10

53. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
{D,E} and C are the closest sequences A B C
{D,E} 22 39 40 41 42 19

54. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Name {A, B} as W: A B C
{D,E} 22 39 40 41 42 19

55. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Distance between W and C: A B C D E 22 39 41 43 18 20 10

56. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Distance between W and {D,E} (name {D,E} as X): A B C D E 22 39 41 43 18 20 10

57. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Distance between C and {D,E} (name {D,E} as X): A B C D E 22 39 41 43 18 20 10

58. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Branches a, b and c:

59. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Branches a, b and c:

60. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Update the distance matrix: A B C
{D,E} 22 39 40 41 42 19 A B
{C,D,E} 22
39.5
41.5

61. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
Now we are in thee trivial case of 3 sequences (remember the previous example): A B
{C,D,E} 22
39.5
41.5

62. Fitch-Margoliash Method:
Building Phylogenetic Trees by Fitch-Margoliash:
Another Example:
FINAL TREE:

63. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
The true tree will be that for which the total branch length, S, is shortest,
Neighbors: a pair of nodes that are seperated by just one other node,

64. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
Algorithm (Given a distance matrix):
Iterate Until 2 Nodes are left:
For each node find
Choose pair (i, j) with smallest
Mege two nodes i and j with a new internal node Y, and find branch lengths by
Update the distance matrix using

65. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
Example:

66. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
Example:

67. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
Example:

68. The Neighbor-Joining Method:
Building Phylogenetic Trees by Neighbor-Joining:
Example:

69. References
M. Zvelebil, J. O. Baum, “Understanding Bioinformatics”, 2008, Garland Science
Andreas D. Baxevanis, B.F. Francis Ouellette, “Bioinformatics: A practical guide to the analysis of genes and proteins”, 2001, Wiley.
Barbara Resch, “Hidden Markov Models - A Tutorial for the Course Computational Intelligence”, 2010.