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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 - PowerPoint PPT Presentation
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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. ∑∈ )(),(
),(TEji
jiH
Maximum parsimony (example)
• Input: Four sequences– ACT– ACA– GTT– GTA
• Question: which of the three trees has the best MP scores?
Maximum Parsimony
ACT
GTT ACA
GTA ACA ACT
GTAGTT
ACT
ACA
GTT
GTA
Maximum Parsimony
ACT
GTT
GTT GTA
ACA
GTA
12
2
MP score = 5
ACA ACT
GTAGTT
ACA ACT
3 1 3
MP score = 7
ACT
ACA
GTT
GTAACA GTA
1 2 1
MP score = 4
Optimal MP tree
Maximum Parsimony: computational complexity
ACT
ACA
GTT
GTAACA GTA
1 2 1
MP score = 4
Finding the optimal MP tree is NP-hard
Optimal labeling can becomputed 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
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1 48 96 144 192 240 288 336
TNT
Iterated local search: escape local optima by perturbation
Local optimumLocal search
Iterated local search: escape local optima by perturbation
Local optimum
Output of perturbation
Perturbation
Local search
Iterated local search: escape local optima by perturbation
Local optimum
Output of perturbation
Perturbation
Local search
Local search
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