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

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

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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

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

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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

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Wayne Maddison’s Observation “What is needed is a method that counts the minimal number of branch moves needed to convert one tree into another, where branch moves are restricted so as not to violate a linear order.” Syst. Biol., 46(3): , 1997.

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Species Networks ABCDE

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Gene Tree I in Species Networks ABCDE ABCDE

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Gene Tree II in Species Networks ABCDE ABCDEABCDE

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The SPR Operation SPR: Subtree Prune and Regraft Prune a subtree in tree T1 and regraft to another edge (by the same root), thus obtaining another tree T2 The SPR-Distance between two trees T1 and T2 is the minimum number of SPR moves required to transfer T1 to T2

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SPR Distances Among Gene Trees ABCDE ABCDEABCDE SPR Distance 1

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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

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Challenges (1) Computational –Computing SPR distances is of unknown computational complexity (probably hard)

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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

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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.)

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Solving the Systematic Challenge: Our Method SpNet 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

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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

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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

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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?

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

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Detection Quality of SpNet Model Phylogeny: 20-taxon Tree

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Detection Quality of SpNet Model Phylogeny: 20-taxon 1-hybrid network

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Detection Quality of SpNet Model Phylogeny: 20-taxon 2-hybrid network

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Reconstruction Quality Model Phylogeny: 20-taxon tree

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Reconstruction Quality Model Phylogeny: 20-taxon 1-hybrid network

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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

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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

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