HW 3: due Thursday, November 10th in class
For this assignment, all answers are to be submitted in hardcopy in class.
This problem compares different algorithms for tree inference. Note that
even though in this case, you will know the correct tree, in the case of real
data you would have only the distance matrix and not the tree available to
you.
1. Compute the distance matrix for the taxa V,W, X, Y, and Z from the
tree below:
2. Is the distance matrix additive? Is it an ultrametric? How do you
know?
3. Suppose you do not know the underlying tree. Working only from the
computed distance matrix in part 1, which taxa would the UPGMA
algorithm first select as neighbors? Show the first subtree connecting
these two taxa, with branch lengths, according to the UPGMA algo-
rithm.
4. Suppose again that you do not know the underlying tree. Working only
from the computed distance matrix in part 1, show the corrected dis-
tance matrix computed for the first step of the NJ algorithm. Which
taxa would the neighbor joining (NJ) algorithm first select as neigh-
bors? Show the subtree connecting these two taxa, with the branch
lengths as determined by the NJ algorithm.
5. Which algorithm is a better one for reconstructing this tree, and why?
zvw y x
5
2
10
1
2
210
5
