BNFO 602 Phylogenetics

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