Refined Buneman Trees

efined Buneman therefore suffers a great penalty as as the number of species
goes up. Mathematically, when the number of species approaches infinity,
n − 3
n 4 → 0
This would indicate that the method is not very useful for large data sets,
since it suffers a great disadvantage. It would be interesting to see the performance
of a quartet based method that considers a fixed percentage of quartets
per split, e.g. 5–10%, which would not suffer from the same problems with scalability
as the refined Buneman method. The problem becomes finding the 5–10%
of least scoring quartets for every split in an efficient manner, while ensuring the
set of splits produced is still a compatible set of splits — or tree. The Q ∗ method
[BG00] tackles the problem of going from favorable quartets to a compatible set
of splits, at the cost of performance compared to the refined Buneman method.
One experiment which would be interesting to perform, but which the author
has not undertaken, is to measure the quality of splits from the Neighbor-Joining
method that are either accepted or rejected by the Buneman method. The
authors expectation is that the splits accepted by the refined Buneman method
would get a high confidence, as that method relies on much more evidence
then the Neighbor-Joining method does. Such an investigation could be done
by inspecting the PFAM data and interpreting their biological meaning, by
using bootstrap tests, or by using simulated data where one would know the
evolutionary history. Is it the case that the splits in RB(δ) are more trustworthy
than splits in NJ(δ) \ RB(δ) In the cases where the NJ method infers a fully
resolved binary tree, and the RB method infers no splits at all, which one
tells the truth Some datasets might be completely random, and an NJ tree
based on such a set is completely useless — on the other hand, tests show that
the refined Buneman method produces very few splits or non at all on input
distance matrices with random entries. So when the RB method tells us that
the dataset does not warrant any splits, is that because the RB method has
good biological properties This question is beyond the scope of this thesis, but
certainly deserves further investigation.
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