Phylogenetic Tree Reconstruction: Geometric Approaches - Mathematical Concepts and Methods in Modern Biology - page 335

likelihood methods and Bayesian approaches, the latter of which produce not just a
single tree, but a distribution of possible trees.
Still, there remain good reasons for using distance-based methods. We have, quite
misleadingly used trees with small examples of leaves in this chapter in order to
make the underlying ideas accessible, and because much of the underlying math-
ematical theory can be reduced to small trees, like quartets. However, in the “real
world” of biology, the most obvious reason for continuing interest in distance-based
methods is due to their effectiveness via good polynomial time algorithms in the
face of combinatorial explosion and computational complexity when the number of
leaves is large. Even n

20 can overwhelm many other methods, but we have (also
rather scandalously), with the exclusion of consistency, not gone into details in this
chapter about comparing the success, via additional factors such as efficiency, robust-
ness, power, and falsifiability, of distance-based algorithms and their competitors.
(See [ 4 , Section 6.1.4] for a brief but comprehensive treatment, up to its publication
date.)
The link between the NJ Algorithm and the BME method described above, but
not as well known as it might be, also addresses some issues which have perhaps
mistakenly led biologists to pull back from using the NJ Algorithm or its variants.
A very recent paper [ 13 ] also provides some thought-provoking arguments against
another commonly voiced concern among biologists, that in providing only infor-
mation between leaves, distance-based methods may lose (too much) information
(e.g., see [ 4 , Section 6.2.4] for a sample of such concerns in a biology-friendly text).
Looking at covariances in the dissimilarity maps reveals more information that has
commonly disregarded, given calculations like that for the Q-criterion which explic-
itly use only the values d

>

for an input dissimilarity map D . Still, we hope this
chapter's treatment will open the doors to these questions and issues, and to further
readings in the articles and topics referenced herein.

( i , j )

References
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[3] Pachter L, Sturmfels, B, editors. Algebraic statistics for computational biology.
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[4] Page RDM, Holmes EC. Molecular evolution: a phylogenetic approach.
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[5] Turelli M, Barton NH, Coyne JA. Theory and speciation. Trends Ecol Evol
2001;16:330-43.
[6] Baum D. Reading a phylogenetic tree: the meaning of monophyletic groups.
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