1. Building Phylogenies
Parsimony 2

2. Methods
Distance-based
Parsimony
Maximum likelihood

3. Searching for an MP tree
Exhaustive search (exact)
Branch-and-bound search (exact)
Heuristic search methods
Stepwise addition
Branch swapping
Star decomposition

4. Exhaustive Enumeration
Order the taxa: s1, s2, , sn
Build (unique) unrooted tree for s1, s2, s3
Try all possible places to add s4, and score each tree
Try all places to add s5 to previous trees and score again . . .

5. Adding the 4th taxon
[S05]

6. Adding the 5th taxon
[S05]

7. [S05]

8. Branch and bound Similar to exhaustive search, except that we maintain
Score of best tree obtained so far
A lower bound on score of best tree that can be obtained from this point forward.
If score of current tree exceeds the current best score, backtrack and takes the next available path.
When a tip of the search tree is reached the tree is either optimal (and hence retained) or suboptimal (and rejected).
When all paths leading from the initial 3-taxon tree have been explored, the algorithm terminates, and all most-parsimonious trees will have been identified.

10. Branch Swapping Local search approach:
Define a “neighborhood” for a tree
Neighbors are obtained by rearranging branches: cut and paste
Instead of exhaustive exploration of tree space, just try neighbors.

11. Branch Swapping Nearest-Neighbor Interchange (NNI)
Subtree Pruning and Regrafting (SPR)
Tree Bisection and Reconnection (TBR)

12. Nearest-Neighbor Interchange

13. All 15 5-taxon trees, connected by NNIs

14. Subtree Pruning and Regrafting

15. Tree Bisection and Reconnection

16. Stepwise Addition A greedy method Start with 3-taxon tree
Add taxa one at a time.
Keep only the best tree found so far
No guarantee of optimality, but may provide good starting point for search

17. A problem with parsimony: Long branch attraction
Convergent evolution along long branches can confuse parsimony G A     G A    
Incorrect!

18. Compatibility
A set of characters is compatible if there exixts a tree where each character state emerges exactly once. a 1 A B C D c e f b
a, b

19. Consistency index
Homoplasy: Multiple emergence of the same state in a phylogeny
Perfect fit (= compatible characters)  no homoplasy
Let mi = min #(steps possible for site i) and si = min #(steps for site i given the tree)
The consistency index is CI = mi / si (0  CI  1)
CI measures amount of homoplasy in tree

20. The bootstrap
A bootstrap sample is obtained by sampling sites randomly with replacement
Obtain a data matrix with same number of taxa and number of characters as original one
Construct phylogenies for samples
For each branch in original tree, compute fraction of bootstrap samples in which that branch appears
Assigns a bootstrap support value to each branch.
Idea: If a grouping has a lot of support, it will be supported by at least some positions in most of the bootstrap samples
Can be applied to other methods of phylogenetic reconstruction