Importance of Sequence Evolution Models

Why Models of Sequence Evolution Matter Number of differences between each pair of taxa vs. genetic distance between those two taxa. The x-axis is a proxy for time since divergence between the two taxa. Differences accumulate linearly with time for only a very shot time after two taxa diverge. 2 pairs taxa that have different divergence times, may have a similar number of differences between them saturation.

Multiple Hits. 3 So even though there have been 4 substitutions, when we compare these two lineages, we only can detect 3 differences. Models of sequence evolution expect multiple hits.

Why Models Matter Let s assume a true tree. A ATCGAGCAGCCTGGGAGAGAGACTTATTTGACAAACGTAA B ATTGGGGAGTAGCGTAAACACTCTTATTTGACGAAATTAT C ATCGTGGGTTAGAGTAGAGACTCTCATTTGACGAAATTAT D AACGTGGCGAATAGTAGTCAAAAAATGTGTACCAGATTAC This tree is 37 steps, and the true tree is 38 steps.

Why Models Matter Let s assume a true tree. Support for Wrong Tree 100 90 80 70 60 50 0 100 200 300 400 500 600 700 Increase # replicates keeps happening. Increase # bp happens with certainty.

Why Models Matter Now let s subject the sequences to an ME search. First, we need to convert the character by taxon matrix to a matrix of pairwise distances: above diagonal are p-distances, below are JC distances. A ------- 0.572 0.572 1.091 B 0.400 -------- 0.232 0.903 C D 0.400 0.200 ------- 0.752 A B C D 0.575 0.525 0.475 -------

Why Models Matter Optimum tree is the true tree. We re getting pretty lousy estimates of branch lengths but, under these conditions, branch-length estimates would converge on true values with more data. Thus, in the simulation, the methods that are agnostic with respect to multiple hits (MP and ME using p-distances) incorrectly unite the long-branch taxa (A & D). ML can avoid long-branch attraction

Long-branch attraction 1 2 1 2 Let s assume that there is an A in both the short-branch taxa. There are four possibilities for states at the other two terminals. 1) The long-branch taxa could have A 2 & 3) One of the long-branch taxa has a substitution to nucleotide X ( = G, C, or T)

Long-branch attraction 1 2 1 2 4) There could be substitutions to X1 and X2 along both long branches. If X1 X2 , the site is uninformative. If X1 = X2 , the site is misleading. X1 X2 X1 X2 X1 X2 C C C C G T G G G C G T T T T C G T So, 1/3 of all possibilities result in a convergence.

Look at Original Data A ATCGAGCAGCCTGGGAGAGAGACTTATTTGACAAACGTAA B ATTGGGGAGTAGCGTAAACACTCTTATTTGACGAAATTAT C ATCGTGGGTTAGAGTAGAGACTCTCATTTGACGAAATTAT D AACGTGGCGAATAGTAGTCAAAAAATGTGTACCAGATTAC 2 sites that distinguish among topologies under parsimony are misleading and favor the LBA tree. Remember, these data were simulated on a known tree that is not the tree that the characters support under parsimony.

The Importance of Branch Lengths Fitch Optimization {A} :0 {A C G}:1 Large # of terminals with A, this is a slowly evolving site. C at node 2, transversion to A along short branch , no change along and change to G along . G at node 2, transition to A along short branch , no change along and change to C along . A at node 2, no change along short branch , a change to C along and change to G along .

The Importance of Branch Lengths {A} {A} All reconstructions are permitted and accounted for, but the reconstruction with A at node 2 (& node 1) contributes the most to the single-site likelihood. ML can voice a preference here, where parsimony can t. This is because ML accounts for branch lengths in calculating reconstruction probabilities. No change along a short branch and changes along both long branches is more likely than a change along the short branch coupled with no change along one of the long branches.