A Separate Analysis Approach to the Reconstruction of Phylogenetic Networks

1. A Separate Analysis Approach to the Reconstruction of Phylogenetic Networks Luay Nakhleh Department of Computer Sciences UT Austin

2. Who’s Involved • UT CS: Tandy Warnow, Luay Nakhleh • UT BIO: Randy Linder • UNM CS: Bernard Moret

3. Why Networks? • Lateral gene transfer (LGT) • Ochman estimated that 755 of 4,288 ORF’s in E.coli were from at least 234 LGT events • Hybridization • Estimates that as many as 30% of all plant lineages are the products of hybridization • Fish • Some frogs

4. Phylogenetic Networks • Rooted, directed, acyclic graphs that actually model the evolutionary process • “tree” nodes and “network” nodes • Time constraints

5. Separate Analysis • Analyze individual genes separately • Reconcile the resulting phylogenies • As opposed to combined analysis in which the datasets are combined (via concatenation) and the combined dataset is then analyzed

6. SPR Distances Among Gene Trees A B C D E SPR Distance 1 A B C D E A B C D E

7. Maddison’s Method Given two gene datasets • Construct two gene trees T1 and T2 • If SPR(T1,T2)=0 • Return a tree • If SPR(T1,T2)=1 • Return a network with one reticulation event Open problem: extend to reconstructing a network with m reticulation events

8. Challenges (1) Computational • Computing SPR distances is of unknown computational complexity (probably hard)

9. Solving the Computational Challenge • Galled-networks: reticulation events are independent • For two gene trees T1 and T2 on n leaves we can • Decide whether SPR(T1,T2)=m in O(mn) time, and • Construct network N from T1 and T2 in O(mn) time

10. Challenges (2) Systematic • Obtaining the correct gene trees in practice is very hard (due to missing data, inaccuracy of tree reconstruction methods, wrong assumptions, etc.)

11. Solving the Systematic Challenge: Our MethodSpNet Given the sequences of two genes I & II on a set of species • Run MP or ML on gene I and obtain a set U1 of trees, represented by its consensus tree t1 • Run MP or ML on gene II and obtain a set U2 of trees, represented by its consensus tree t2 • Find binary trees T1 and T2, that refine t1 and t2, respectively, and such that SPR(T1,T2)=1 • Build network N from T1 and T2

12. SpNet: Running Time • We have a linear-time algorithm for the single hybrid case (implementation and experimental results are available as well) • We are working on the general case of arbitrary number of reticulation events

13. Experimental Study • Generated random networks on 10 and 20 taxa, with 0, 1, and 2 hybrids • Evolved sequences under the GTR+Gamma model of evolution with invariant sites • We studies the topological accuracy based on the splits defined by the model and inferred network

14. Evaluation Criteria • Detection Quality • How often did the method infer the correct number of hybrids in the model phylogeny? • Reconstruction Quality • What is the topological accuracy of the inferred phylogeny?

15. Methods • SpNet(i): Our method where we contract i edges • NNet: The method of Bryant and Moulton • NJ

16. Detection Quality of SpNetModel Phylogeny: 20-taxon Tree

17. Detection Quality of SpNetModel Phylogeny: 20-taxon 1-hybrid network

18. Detection Quality of SpNetModel Phylogeny: 20-taxon 2-hybrid network

19. Reconstruction QualityModel Phylogeny: 20-taxon tree

20. Reconstruction QualityModel Phylogeny: 20-taxon 1-hybrid network

21. Reconstruction QualityModel Phylogeny: 20-taxon 1-hybrid network

22. Conclusions • Considering a set of “good” trees rather than a single optimal tree is advantageous in network reconstruction • Separate analysis approaches outperform combined analysis approaches

23. Ongoing research • Using other techniques for obtaining unresolved trees (e.g., Bayesian analyses, bootstrapping, etc.) • Detection vs. reconstruction – visualization and clustering techniques may also be useful (collaboration with St John) • Refining unresolved networks • DCM-like network reconstruction