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The (Supertree) of Life: Procedures, Problems, and Prospects

The (Supertree) of Life: Procedures, Problems, and Prospects. Presented by Usman Roshan. Supertree Methods. Input: Set of trees Output: Tree leaf-labeled by where is the set of leaves of . Why supertree methods?.

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The (Supertree) of Life: Procedures, Problems, and Prospects

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  1. The (Supertree) of Life: Procedures, Problems, and Prospects Presented by Usman Roshan

  2. Supertree Methods • Input: Set of trees • Output: Tree leaf-labeled by where is the set of leaves of . • Why supertree methods?

  3. Motivation (1) • Supertree methods are used as part of divide-and-conquer method to solve NP-hard problems on large datasets

  4. Motivation (2) • Supertree methods are used when we have missing data

  5. Types of supertree methods (1) • Direct methods (e.g. strict consensus supertrees, MinCutSupertrees)

  6. Types of supertree methods (2) • Indirect methods (e.g. MRP, average consensus)

  7. Types of supertree methods (3) (MRP)

  8. Definitions • Contraction: • Restriction: • If then contains

  9. Optimization problems • Subtree Compatibility: Given set of trees ,does there exist tree ,such that, (we say contains ). • NP-hard (Steel 1992) • Special cases are poly-time (rooted trees, DCM) • MRP: also NP-hard

  10. Limitations of supertree methods Three desirable properties: • P1: Method can be applied to any unordered set of input trees • P2: Renaming the species does not change the constructed supertree • P3: If the input trees are compatible, then the output tree is one of the “parent trees”. There is no supertree method that can satisfy P1-P3 when the input trees are unrooted; however, for rooted trees an extension of BUILD satisfies P1-P3.

  11. Rooted subtrees (BUILD)(Aho et al 1981) • Input: Set of rooted trees • Output: Tree that contains

  12. BUILD (2) - Definitions • Cluster: Set of taxa in a rooted subtree • A different representation of rooted phylogenetic trees • Let C(T) be the clusters of tree T. In this example C(T) = {{1,2}, {3,4}, {1,2,3,4},{1,2,3,4,5}} • We write (IJ)K in T, if I,J are in some cluster of T which doesn’t contain J; e.g. (12)3, (34)5 are in T

  13. BUILD (3) - Algorithm • Initialize C as set of input taxa • If |C|=1 return C, else compute graph • Let C’ be the sets of taxa in the connected components of G. If |C’| = 1 then is incompatible, else set C = C C’, and repeat step (2) on each new cluster in C’.

  14. BUILD (4) - Algorithm

  15. BUILD (5) - Algorithm

  16. BUILD (6) - Algorithm

  17. BUILD (7) - Algorithm

  18. Compatible source trees • For compatible source trees, MRP or BUILD can be used; however, the strict consensus of MRP trees (or the strict consensus supertree) may not be compatible with the input. • BUILD has been extended to output all parent trees; also shown that source trees have a unique parent tree iff BUILD constructs a binary tree.

  19. Incompatible source trees (1) For incompatible source trees two strategies: • Resolve incompatibilities by using quartet methods or removing troublesome taxa. • Use an appropriate algorithm such as MRP or MinCutSupertrees; the latter is an extension of BUILD so that it always outputs a tree.

  20. Incompatible source trees (2) Desirable property • P1: If at least one tree contains (IJ)K and no source tree contains (IK)J or (JK)L, then the output tree must contain (IJ)K No method can satisfy P1; however, the condition: if all source trees contain (IJ)K then output must contain (IJ)K can be satisfied.

  21. Supertree criticism • Do not take biomolecular sequences into account • Dataset non-independence • MRP: Favors larger source trees because they contribute more characters; may also favor unbalanced source trees • Direct methods: Cannot incorporate support values in the source trees (except for MinCutSupertrees), and cannot compute support values in the supertree (unlike MRP)

  22. Applications of supertrees • Systematics – MRP is the standard method used by biologists • Evolutionary models • Rates of cladogenesis • Evolutionary patterns • Biodiversity and conservation

  23. Bright future for supertree construction • Despite increase in phylogenetic data, species are poorly characterizes at the molecular level; thus, giving rise to problems from taxon sampling (non-random sampling), long branch attraction, and missing data • ML analysis: Genes evolve under different models • Non-molecular data

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