BNFO 602 Phylogenetics maximum parsimony Usman Roshan

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BNFO 602 Phylogenetics –maximum parsimony Usman Roshan BNFO 602 Phylogenetics –maximum parsimony Usman Roshan

Why phylogenetics? • Study of evolution – Origin and migration of humans – Origin Why phylogenetics? • Study of evolution – Origin and migration of humans – Origin and spead of disease • Many applications in comparative bioinformatics – Sequence alignment – Motif detection (phylogenetic motifs, evolutionary trace, phylogenetic footprinting) – Correlated mutation (useful for structural contact prediction) – Protein interaction – Gene networks – Vaccine devlopment – And many more…

Maximum Parsimony • Character based method • NP-hard (reduction to the Steiner tree problem) Maximum Parsimony • Character based method • NP-hard (reduction to the Steiner tree problem) • Widely-used in phylogenetics • Slower than NJ but more accurate • Faster than ML • Assumes i. i. d.

Maximum Parsimony • Input: Set S of n aligned sequences of length k • Maximum Parsimony • Input: Set S of n aligned sequences of length k • Output: A phylogenetic tree T – leaf-labeled by sequences in S – additional sequences of length k labeling the internal nodes of T such that is minimized.

Maximum parsimony (example) • Input: Four sequences – ACT – ACA – GTT – Maximum parsimony (example) • Input: Four sequences – ACT – ACA – GTT – GTA • Question: which of the three trees has the best MP scores?

Maximum Parsimony ACT GTA ACT GTT ACA GTT GTA ACA GTA ACT GTT Maximum Parsimony ACT GTA ACT GTT ACA GTT GTA ACA GTA ACT GTT

Maximum Parsimony ACT GTT 2 GTT GTA 1 2 GTA ACA GTT ACA ACT Maximum Parsimony ACT GTT 2 GTT GTA 1 2 GTA ACA GTT ACA ACT 1 3 3 MP score = 7 MP score = 5 ACA ACT GTA ACA GTA 2 1 1 MP score = 4 Optimal MP tree GTT ACT GTA

Maximum Parsimony: computational complexity Optimal labeling can be computed in linear time O(nk) ACA Maximum Parsimony: computational complexity Optimal labeling can be computed in linear time O(nk) ACA ACT GTA ACA 1 GTA 2 1 GTT MP score = 4 Finding the optimal MP tree is NP-hard

Local search strategies Local optimum Cost Global optimum Phylogenetic trees Local search strategies Local optimum Cost Global optimum Phylogenetic trees

Local search for MP • Determine a candidate solution s • While s is Local search for MP • Determine a candidate solution s • While s is not a local minimum – Find a neighbor s’ of s such that MP(s’)

Starting tree for MP • Random phylogeny---O(n) time • Greedy-MP Starting tree for MP • Random phylogeny---O(n) time • Greedy-MP

Greedy-MP takes O(n^2 k^2) time Greedy-MP takes O(n^2 k^2) time

Local moves for MP: NNI • For each edge we get two different topologies Local moves for MP: NNI • For each edge we get two different topologies • Neighborhood size is 2 n-6

Local moves for MP: SPR • Neighborhood size is quadratic in number of taxa Local moves for MP: SPR • Neighborhood size is quadratic in number of taxa • Computing the minimum number of SPR moves between two rooted phylogenies is NP-hard

Local moves for MP: TBR • Neighborhood size is cubic in number of taxa Local moves for MP: TBR • Neighborhood size is cubic in number of taxa • Computing the minimum number of TBR moves between two rooted phylogenies is NP-hard

Local optima is a problem Local optima is a problem

Iterated local search: escape local optima by perturbation Local search Local optimum Iterated local search: escape local optima by perturbation Local search Local optimum

Iterated local search: escape local optima by perturbation Local search Local optimum Perturbation Output Iterated local search: escape local optima by perturbation Local search Local optimum Perturbation Output of perturbation

Iterated local search: escape local optima by perturbation Local search Local optimum Perturbation Local Iterated local search: escape local optima by perturbation Local search Local optimum Perturbation Local search Output of perturbation

ILS for MP • Ratchet (Nixon 1999) • Iterative-DCM 3 (Roshan et. al. 2004) ILS for MP • Ratchet (Nixon 1999) • Iterative-DCM 3 (Roshan et. al. 2004) • TNT (Goloboff et. al. 1999)




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