2. This question is about phylogenetic tree reconstruction. You are given the following distance
matrix among 5 sequences:
$\begin{array}{|c|c|c|c|c|c|}
\hline
& s_1 & s_2 & s_3 & s_4 & s_5 \\
\hline
s_1 & 0 & 8 & 6 & 8 & 2 \\
s_2 & 8 & 0 & 2 & 6 & 8 \\
s_3 & 6 & 2 & 0 & 10 & 6 \\
s_4 & 8 & 6 & 10 & 0 & 6 \\
s_5 & 2 & 8 & 6 & 6 & 0 \\
\hline
\end{array}$
(a) Use the UPGMA algorithm to reconstruct a phylogenetic tree among the five sequences. You
need to show the distance matrix and tree topology after every step (as in the lecture note),
but do not need to show branch lengths.
During the reconstruction process, if multiple pairs of clusters have the same smallest
distance, use the following rule to break ties. First, get the indices of all the sequences in the
two clusters and sort them in ascending order. Then treat the resulting string as a signature of
the pair and merge the one ordered first lexicographically. For example, if the pairs ($s_1, s_3$)
and ($s_2, s_5$), ($s_1, s_3$) and ($s_4$) and ($s_2, s_5$) and ($s_4$) all have the same smallest distance,
the pair ($s_1, s_3$) and ($s_2, s_5$) is merged because its signature is 1235, which is
lexicographically smaller than both 134 and 245.
(15%)
(b) Then, use the Neighbor-Joining algorithm to reconstruct the phylogenetic tree among the
five sequences. Show the tree, distance matrix, u vector and Q matrix after every step. Break
ties using the same rules as in Part (a).
(15%)
(c) Actually, there are some webtools available to conduct phylogenetic tree reconstruction. Use
the following provided webtool and the distance matrix of this question as input to
reconstruct the phylogenetic tree. Record the details of all steps. Give the final tree both in a
graphical form and in Newick format.
