Building Phylogenies

Parsimony 2

Methods

• Distance-based• Parsimony• Maximum likelihood

Searching for an MP tree

• Exhaustive search (exact)• Branch-and-bound search (exact)• Heuristic search methods

– Stepwise addition– Branch swapping– Star decomposition

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 . . .

Adding the 4th taxon

[S05]

Adding the 5th taxon

[S05]

[S05]

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.

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.

Branch Swapping

• Nearest-Neighbor Interchange (NNI)

• Subtree Pruning and Regrafting (SPR)

• Tree Bisection and Reconnection (TBR)

Nearest-Neighbor Interchange

All 15 5-taxon trees, connected by NNIs

Subtree Pruning and Regrafting

Tree Bisection and Reconnection

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

A problem with parsimony: Long branch attraction

Convergent evolution along long branches can confuse parsimony

G G

A A

G

G

A

A

Incorrect!

Compatibility

a0111

ABCD

c0011

e0001

f1000

b0111

A B C D

f

a, b

c

e

A set of characters is compatible if there exixts a tree where each character state emerges exactly once.

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

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