BNFO 602 Phylogenetics Usman Roshan

Summary of last time Models of evolution Distance based tree reconstruction Neighbor joining UPGMA

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) 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 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 GTA Question: which of the three trees has the best MP scores?

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

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

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

Local search strategies Phylogenetic trees Cost Global optimum Local optimum

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’)<MP(s) If found set s=s’ Else return s and exit Time complexity: unknown---could take forever or end quickly depending on starting tree and local move Need to specify how to construct starting tree and local move

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

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

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

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 Computing the minimum number of TBR moves between two rooted phylogenies is NP-hard

Local optima is a problem

Iterated local search: escape local optima by perturbation Local optimum

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

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

ILS for MP Ratchet (Nixon 1999) Iterative-DCM3 (Roshan et. al. 2004) TNT (Goloboff et. al. 1999)

Maximum Likelihood Find the tree that has the highest likelihood. Problems: What is the likelihood of a tree with branch lengths and internal nodes? What if no internal nodes are given? Felsenstein’s algorithm What if no branch lengths are given?

Maximum Likelihood NP-hard like Maximum Parsimony (MP) Similar local search heuristics as MP