Building Phylogenies Distance-Based Methods

Methods Distance-based Parsimony Maximum likelihood

Distance Matrices a0 b60 c730 d abcd a b c d Distance matrix is additive if there is a tree that fits it exactly

Ultrametric Matrices a0 b20 c660 d abcd a b c d Additive + molecular clock assumption

Methods Fitch - Margoliash UPGMA Neighbor-joining Many others

Least squares trees Minimize over all trees Choice of weights w ij : –Uniform: w ij  1 –Fitch-Margoliash: w ij  1/D ij 2 –Others...

Sarich's (1969) immunological distances

Least squares tree for Sarich’s data

Clustering Methods E.g., UPGMA and Neighbor-Joining A cluster is a set of taxa Interspecies distances translate into intercluster distances Clusters are repeatedly merged –“Closest” clusters merged first –Distances are recomputed after merging

UPGMA Unweighted pair group method using arithmetic averages The distance between clusters C i and C j is After merging C i and C j to create cluster C k define distance from k to every other cluster r as

UPGMA: Initialization 1.Assign each sequence i to its own cluster C i 2.Define one leaf (tip) of tree for each sequence and place it at height 0

UPGMA: Iteration 1.Choose the two clusters i and j with smallest D ij 2.Create a new cluster k, where C k = C i  C j 3.Compute D kr for all r. 4.Define a new node k with children i and j, and place it at height D ij /2. 5.Add k to the current clusters and delete i and j Let i and j be the remaining clusters. Place root at height D ij /2 Repeat until only two clusters remain:

UPGMA Example

UPGMA tree for Sarich’s data

A pitfall of UPGMA The algorithm produces an ultrametric tree: the distance from the root to any leaf is the same UPGMA assumes a constant molecular clock: all species accumulate mutations (evolve) at the same rate.

UPGMA fails when molecular clock assumption doesn’t hold

Neighbor Joining Saitou and Nei, Molecular Biology and Evolution 4 (1987) Idea: Find a pair of leaves that are close to each other but far from other leaves –Implicitly finds a pair of neighboring leaves Advantages: –Works well for additive and other nonadditive matrices –Does not have the molecular clock assumption

Long branches must be handled carefully!      and  are closer to each other than to  or .  Obvious approach produces incorrect clusters!

Compensating for long edges Introduce “correction terms” “Corrected” distances: Distances are reduced for pairs that are far away from all other species: They may be close to each other. Average dist. to other taxa

Neighbor-joining 1.Choose i, j such that D ij  u i  u j is minimum 2.Define a new leaf k whose distances to i and j are 3.Compute the distance from k to every other leaf r 4.Delete i and j Repeat the following until only two leaves remain: Connect the 2 remaining leaves by a branch of length D ij

NJ tree for Sarich’s data

Computing distance matrices Based on sequence alignment Various possibilities: –Distance = average number of differences –Try different PAM matrices; distance = index of matrix that gives highest score –Feng and Doolitle: Based on alignment scores – roughly ratio to max possible score (see text) Read, e.g., PHYLIP documentation: on.edu/phylip/general.html on.edu/phylip/general.html

Distance correction The amount of evolutionary change is not linearly related to time Over a long period of time, a series of substitutions may bring us back to where we started Percentage difference may underestimate evolutionary time

Jukes-Cantor Model

Correcting for multiple substitutions in the JC model

Many other models!