Inference rules for supernetwork construction - PowerPoint PPT Presentation

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  1. Inference rules for supernetwork construction Katharina Huber, School of Computing Sciences, University of East Anglia.

  2. gene2( ) gene1( ) gene2( ) gene1( ) gene2( ) gene1( ) gene2( ) gene1( ) gene2( ) gene1( ) An ultimate goal

  3. gene1( ) But, … ? gene1( ) gene2( ) gene1( ) gene1( ) gene2( ) gene2( ) gene2( )

  4. gene1( ) gene1( ) gene1( ) gene1( ) gene1( ) Or, even worse ? gene2( ) gene2( ) gene2( ) gene2( )

  5. gene1( ) gene1( ) gene1( ) gene1( ) gene1( ) We could, … ? gene2( ) gene2( ) gene2( ) gene2( )

  6. gene1( ) gene1( ) gene1( ) gene1( ) gene1( ) or, … ? gene2( ) gene2( ) gene2( ) gene2( )

  7. Not very satisfactory!

  8. So far, .. • Z-closure supernetwork (Huson et al, 2004) • Q-imputation (Holland et al, 2007), Attractive but produce many splits Filtering approaches

  9. Weak compatibility(Bandelt and Dress, 1992) A1 A1 A2 A2 A3 A3 One of intersections marked by a dot is empty!

  10. Weak compatibility(Bandelt and Dress, 1992) A1 A1 A2 A2 A3 A3

  11. Y- inference rule

  12. M - inference rule(Meacham, 1972)

  13. Repeat until inference process stabilizes apply inference rule and add (if underlying condition is violated stop) Collection of partial splits Collection of partial splits remove partial splits that can get extended A|B extends C|D if either A C and B D or A D and B C.

  14. Theorem (Gruenewald, Huber, Wu) Suppose  is an irreducible collection of partial splits and is either the Y- or M- or M/Y-rule. Then any two closures of   obtained via  are the same. Irreducible: no split in  extends another split in . Closure: if the underlying condition(s) is (are) never violated, the set of partial splits generated when inference process stabilizes, and  otherwise.

  15. S1 7 1 S2 6 2 5 S3 3 4 Circular collections of partial splits S1=123|4567 S2=23|45671 S3=345|6712 A collection  of partial split is said to be displayed by a cycle if every split in  can get extended to a full split such that the resulting split system is circular.

  16. Theorem (Gruenewald, Huber, Wu) Suppose  is an irreducible collection of partial splits. Then  is displayed by a cycle C if and only if the closure of  via M/Y is displayed by C. In that case the closure of  via Y and the closure of  via M is also displayed by C.

  17. Rivera et al’s ring of lifeRivera et al, 2004 5 most probable phylogenetic trees from a study of 10 bacterial genomes from Rivera et al, 2004  in its early stages life was more like a network than a tree. How much does this result depend on the fact that trees were all on the same taxa set?

  18. Z-closure supernetwork The ring of lifeRivera et al, 2004 M/Y-inference rules