1. BNFO 602 Phylogenetics
Usman Roshan

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

3. 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…

4. 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.

5. 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.

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

7. Maximum Parsimony
ACT
GTA
ACA
ACT
GTT
ACA
GTT
GTA
GTA
ACA
ACT
GTT

8. 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

9. 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)

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

11. 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

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

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

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

15. 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

16. 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

17. Local optima is a problem

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

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

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

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

22. 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?

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