Refined Buneman Trees

worst case time and space complexity. However, with respect to performance
in terms of reconstructing accurate phylogenetic trees, the refined Buneman
method might demonstrate unknown strengths.
16.1 Test setup
In the following section we will test the refined Buneman tree algorithm against
two other known algorithms, the Buneman method ([Bun71]) and the Neighbor-
Joining ([SN87]) method. All experiments have been run on test data from the
PFAM database of protein sequence families. The data consists of distance
matrices with sizes ranging from 10–50 (30), 100–200 (50) and 500–700 (50),
for a total of 130 test matrices. Matrices with larger sizes are available, but
they will be disregarded due to time constraints. Distance data is given in the
common Phylip format.
16.2 Buneman and refined Buneman
The implementation of the refined Buneman tree algorithm can easily be adapted
to mark those splits which are both in B(δ) andinRB(δ). Since we have the
n − 3 least scoring quartets used to calculate the refined Buneman index for a
split, it is easy to find the least scoring quartet among them. If that quartet
has positive Buneman score, we can mark the split as belonging in B(δ).
This first experiment consists of running the (modified) refined Buneman
tree algorithm on examples from the set of PFAM distance matrices, counting
for each one the number of splits in B(δ) andinRB(δ). The results from the
experiment are given in Figure 16.1, sorted according to increasing distance
matrix size and plotted in percentage (the size of RB(δ) is 100%).
Figure 16.1 shows that the size of B(δ) fluctuates quite a bit, especially
when the size of the distance matrix increases, where more and more datasets
do not infer any Buneman splits at all. The refined Buneman method is clearly
much less restrictive then the Buneman method, as expected. Regarding the
quality of the splits that are in RB(δ) but not in B(δ), further studies would
need to be undertaken — one could study either the specific dataset for which
the Buneman method produces few splits, or use simulated data which would
provide a key to which splits are well-supported and which are unsupported.
16.3 Refined Buneman and Neighbor-Joining
To test the refined Buneman tree method against the Neighbor-Joining method,
the author has run the implementation of the refined Buneman tree algorithm
described in this paper, against the Quick-Join algorithm described in [BFM + 03].
The Quick-Join software is available from this website:
http://www.birc.dk/Software/QuickJoin/
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