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 A     G A     Incorrect!

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

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