1. Why Models of Sequence Evolution Matter
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.
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.

2. Models of sequence evolution expect 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.

3. Branch-length Information
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.
Increase # replicates – keeps happening.
Increase # bp – happens with certainty.

4. Branch-length Information
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 B C D A B C D

5. Branch-length Information
Optimum tree is the true tree.
We’re getting pretty lousy estimates of branch lengths – under these conditions,
branch-length estimates would converge on true values with more data.
So 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

6. Long-branch attraction
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) 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.

7. Long-branch attraction1 2
If X1 ≠ X2 , the site is uninformative. If X1 = X2 , the site is misleading.
4) There could be substitutions to X1 and X2 along both long branches.
X1 X2
C C
C G
C T
X1 X2
G C
G G
G T
X1 X2
T C
T G
T T
So 1/3 of all possibilities results in a convergence.

8. The Importance of Branch Lengths
Fitch Optimization :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 a, no change along b and change to G along g.
G at node 2, transition to A along short branch a, no change along g, and change to C along b.
A at node 2, no change along short branch a, a change to C along b, and change to G along g.

9. The Importance of Branch Lengths
{A,C,G}
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.
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.