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Maximum parsimony

Maximum parsimony. Kai Müller. P hylogenetic trees. Cladogram Branch lenghts without meaning Slanted / rectangular Network/ unrooted Parenthetical notation ( Newick ). P hylogenetic trees. Phylogram. Chronogram. character changes. time. an ultrametric tree.

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Maximum parsimony

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  1. Maximum parsimony Kai Müller

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

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

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

  5. Phylogenetic trees

  6. Polytomies - multifurcations • Polytomies • hard • soft

  7. Order within polytomies without meaning =

  8. 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

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

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

  11. Whymanycharacters?

  12. Different types of sequence homology

  13. 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

  14. Alignment

  15. Alignment

  16. Alignment formats

  17. Alignment

  18. Issues

  19. Overview: treebuilding methods

  20. Data types: discretecharacters vs. distances

  21. 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

  22. Parsimony-informative characters

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

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

  25. Character conflict: example char 1 char 4

  26. Character conflict: example

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

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

  29. 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

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

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

  32. 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

  33. Character types

  34. Character types

  35. 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

  36. 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,

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

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

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

  40. 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

  41. Tree searching: exhaustive search • branch addition algorithm

  42. 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

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

  44. Star decomposition

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

  46. 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

  47. 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)

  48. 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

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

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