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Phylogenetic trees

rodney avatar
rodney
54 diapositives · 764 Views · Sep 09, 2014

Phylogenetic trees. Trees. Gorilla. Human. Chimp. Human. Chimp. Gorilla. =. Gorilla. Chimp. Human. =. =. Chimp. Human. Gorilla. Terminology. A branch = An edge. The root. Internal nodes. Chicken. Gorilla. Human. Chimp. External node - leaf. Ingroup / Outgroup:. Chicken.

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  1. Phylogenetic trees

  2. Trees Gorilla Human Chimp Human Chimp Gorilla = Gorilla Chimp Human = = Chimp Human Gorilla

  3. Terminology A branch =An edge The root Internal nodes Chicken Gorilla Human Chimp External node - leaf

  4. Ingroup / Outgroup: Chicken Gorilla Human Chimp OUTGROUP INGROUP

  5. The maximum parsimony principle. (The shortest path) Modified from Inferring Phylogenies (Book), Author: Prof. Joe Felsenstein

  6. Evaluate this tree… s2 s1 s4 s3 s5

  7. s2 s1 s4 s3 s5 1

  8. s2 s1 s4 s3 s5 1 0

  9. s2 s1 s4 s3 s5 1 1 0

  10. Gene number 1 s2 s1 s4 s3 s5 1 1 1 0 0

  11. Gene number 1. The most parsimonious ancestral character states 1 0 1 s1 s4 s3 s2 s5 1 1 1 0 0

  12. 1 0 Gene number 1, Option number 1. 1 1 s1 s4 s3 s2 s5 1 1 1 0 0

  13. 0 1 0 1 1 1 1 0 0 Gene number 1, Option number 2. s1 s4 s3 s2 s5 Minimal number of changes for gene 1 (character 1) = 1

  14. Gene number 2, s2 s1 s4 s3 s5 0 0

  15. 0 1 0 1 0 1 1 0 0 Gene number 2, Option number 1. s2 s1 s4 s3 s5

  16. 1 1 0 1 0 1 1 0 0 Gene number 2, Option number 2. Gene number 2, Option number 2. s2 s1 s4 s3 s5

  17. 0 0 0 0 0 1 1 0 0 Gene number 2, Option number 3. Number of changes for gene 2 (character 2) = 2 s2 s1 s4 s3 s5

  18. Sum of changes = 9

  19. Sum of changes = 9 Can we do better?

  20. Sum of changes = 9 Sum of changes = 8 YES WE CAN! The MP (most parsimonious) tree:

  21. The MP (most parsimonious) tree: s2 s1 s4 s3 s5 Sum of changes for this tree topology = 8

  22. Intermediate Summary MP tree = one for which minimal number of changes are needed to explain the data We can now search for the best tree under the MP criterion

  23. Challenges Evaluating big tree “by hand” can be problematic. We want the computer to do it. Going over all the trees? How many trees are there? Can we generalize to nucleotides? To amino acids? Is the parsimony criterion ideal?

  24. MP for nucleotides

  25. s1AAGTAA s2CAAAAC s3CAGGAA s4AAATAC s5GCGCCA

  26. Position number 1 s2 s1 s4 s3 s5 A A C C G

  27. Position number 1 C C Number of changes for position 1 = 2 A C s2 s1 s4 s3 s5 A A C C G

  28. Find the MP score of the tree for these sequences Exercise CAAG GAAA GCGA GACA GGGA Chicken Duck Gorilla Human Chimp

  29. How to efficiently compute the MP score of a tree

  30. The Fitch algorithm (1971): {A,C} {A,C,G} {A,G} {A,C} C Chicken A Duck C Gorilla A Human Chimp G Postorder tree scan. In each node, if the intersection between the leaves is empty: we apply a union operator. Otherwise, an intersection.

  31. {A,C} {A,C,G} {A,G} {A,C} C Chicken A Duck C Gorilla A Human Chimp G Total number of changes = number of union operators.

  32. Rooting the tree From Wiki commons

  33. H C G C H G G C H A A A A A A A A A Total number of changes = 0 For all 3 possible tree topologies

  34. H C G C H G G C H A A C A A C C A A Total number of changes = 1 For all 3 possible tree topologies

  35. H C G C H G G C H G T A T G A A T G Total number of changes = 2 For all 3 possible tree topologies

  36. H C G C H G G C H Total number of changes is always the same for all 3 possible tree topologies

  37. With 4 taxa Orangutan

  38. O G C H O H C G H C O H O G C O G H C G O G C H O G C H C O H O H G O C G C H G O G C H O G C H C H G O H C G O H G O C

  39. O O H C G H C G G H C O H O C G C G O H

  40. O O H C G H C G 1 O 4 3 G 5 H 2 C H G O C G C O H C G O H

  41. Conclusion The position of the root does not affect the MP score.

  42. Rooting does not change MP score Orangutan G C Gorilla G G Chimp A G Human G G After “bending” the trees, the association of changes and branches does not change! G C A G G

  43. Rooting does not change MP score Orangutan G C Gorilla G C Chimp C G Human C G After “bending” the trees, the association of changes and branches does not change! C C C G G

  44. Using an outgroup Back to solving the relationships between human, chimp and gorilla…

  45. No MP with 3 species 3 1 2 3 1 2

  46. Using an outgroup Back to solving the relationships between human, chimp and gorilla…

  47. Human Human Human Chicken Chimp Chimp Gorilla Chicken Gorilla Chimp Gorilla Chicken With 4 taxa, there are 3 difference unrooted trees.

  48. Human Human Human Chicken Chimp Chimp Gorilla Chicken Gorilla Chimp Gorilla Chicken One tree gets a better score (less changes) than the other trees.