Maximum parsimony

1. Maximum parsimony Kai Müller

3. Phylogenetic trees • Cladogram • Branchlenghtswithoutmeaning • Slanted/rectangular • Network/unrooted • Parentheticalnotation(Newick)

4. Phylogenetic trees Phylogram Chronogram character changes time an ultrametric tree

5. Free rotation around all nodes a phylogram the same phylogram =

6. Phylogenetic trees

7. Polytomies - multifurcations • Polytomies • hard • soft

8. Order within polytomies without meaning =

9. A B C A D B D A B A D B C C C E D A B D E A B D A E B D E A B D A E B C C C C C How many trees are there? • for n taxa, there arepossible rooted trees

10. A B C A C B C A B C A B Too many! • for n taxa, there arepossible rooted trees

11. Typesofcharacters • Morphological • Molecular • DNA sequences • Aminoacidsequences • Presence of genes in Genome • Genomicrearrangements • Presence ofintrons • Single substitutions (SNP, RFLP, AFLP etc.)

12. Whymanycharacters?

13. Different types of sequence homology

14. Different types of sequence homology • Imagineweareunawareofthegeneduplicationand sample onlyalpha-chick,alpha-frog, beta-mouse: != true organismal relationships erroneously inferred by a mixture of paralogous & orthologous sequences

15. Alignment

16. Alignment

17. Alignment formats

18. Alignment

19. Issues

20. Overview: treebuilding methods

21. Data types: discretecharacters vs. distances

22. Maximum parsimony • parsimony principle • most parsimonious explanation should be preferred to others • Ockham‘s razor • parsimony analysis ~= cladistics • the oldest phyl. reconstr. method • still widely used because • principle/optimality criterion easy to grasp • quick • without convincing alternatives for morphological data

23. Parsimony-informative characters

24. Parsimony-informative characters • >= 2 states, >= 2 ofwhichoccur in >=2 taxa

25. Character conflict • character state distributions of different characters do not all support the same topology • example for the following tree:

26. Character conflict: example char 1 char 4

27. Character conflict: example

28. Character conflict: example • suggested topology No 1: 10 steps

29. Character conflict: example • suggested topology No 2: 9 steps

30. The shortest tree • length of tree = #steps = #character state transitions • out of the two trees tried, 9 is the best score • trying all other out of the 15 possible trees shows: there are more that require 9, but non with fewer steps

31. Consensus trees • strict • loose (semi-strict) • majority rule • Adams . . . • supertrees

32. Consensus trees strict/semistrict 50% Majority-rule Adams

33. Types of parsimony • different types of parsimony • Wagner parsimony • binary or ordered multistate characters • i.e, states are on a scale and changes occur via intermediate steps only • free reversibel, 01 = 10 • Fitch parsimony • binary or unordered multistate characters • not on a scale, no intermediate steps required: cost(02)= cost(01) • free reversibel • Dollo parsimony • polarity: ancestral/primitive vs. derived states defined a priori • derived states may occur only once on a tree, but can undergo >1 reversals • Generalized parsimony • cost (step) matrices define state transition costs

34. Character types

35. Character types

36. Weighted parsimony • differential weight given to each character • relative importance of upweighted characters grows • other tree length results: • different trees may be preferred now • successive weighting • problematic • risk of circularity

37. Calculatingtreelength • initialize L=0; root arbitrarily (root taxon); • postorder traversal: assign each node i a state set Siand adjust L: • the set for terminal nodes contains the state of this leaf • cycle through all internal nodes k for which Sk has not yet been defined, unlike for its child nodes m and n; if • if k is parent node to root node, stop; if state at root node not in current Sk,

38. Calculatingtreelength 1 tax1T tax2 G tax3 T tax4 A tax5 A 1) + 1 Example: tax6 A L:

39. Calculatingtreelength 1 tax1T tax2 G tax3 T tax4 A tax5 A 1) + 1 Example: 2 tax6 A L: 2) + 0

40. Calculatingtreelength 1 3 tax1T tax2 G tax3 T tax4 A tax5 A 1) + 1 3) + 0 Example: 2 tax6 A L: 2) + 0

41. Calculatingtreelength 4 1 3 tax1T tax2 G tax3 T tax4 A tax5 A 1) + 1 = 2 3) + 0 4) + 1 Example: 2 tax6 A L: 2) + 0

42. Tree searching: exhaustive search • branch addition algorithm

43. Branch and bound • Lmin=L(random tree) • „search tree“ as in branch addition • at each level, if L < Lmin go back one level to try another path • if at last level, Lmin=L and go back to first level unless all paths have been tried already

44. Heuristicsearches best • stepwise addition • as branch addition, but on each level only the path that follows the shortest tree at this level is searched

45. Star decomposition

46. Branchswapping NNI: nearest neighbour interchanges SPR: subtree pruning and regrafting TBR: tree bisection and reconnection

47. Tree inference with many terminals • general problem of getting trapped in local optima • searches under parsimony: parsimony ratchet • searches under likelihood: estimation of • substitution model parameters • branch lengths • topology

48. Parsimonyratchet • generate start tree • TBR on this and the original matrix • perturbe characters by randomly upweighting 5-25%. TBR on best tree found under 2). Go to 2) [200+ times] • once more TBR on current best tree & original matrix • get best trees from those collected in steps 2) and 4)

49. Bootstrapping • estimates properties of an estimator (such as its variance) by constructing a number of resamples of the observed dataset (and of equal size to the observed dataset), each of which is obtained by random sampling with replacement from the original dataset

50. Bootstrapping • variants • FWR (Frequencies within replicates) • SC (strict consensus)