Phylogenetic Tree Reconstruction: Geometric Approaches - Mathematical Concepts and Methods in Modern Biology - page 302

CHAPTER

10

Phylogenetic Tree
Reconstruction: Geometric
Approaches

David Haws ∗ , Terrell L. Hodge † and Ruriko Yoshida ‡
∗ IBM T. J. Watson Research Center, Yorktown Heights, NY, USA
† Department of Mathematics and College of Arts and Sciences Dean's Office,
Western Michigan University, Kalamazoo, MI, USA
‡ Department of Statistics, University of Kentucky, Lexington, KY, USA

10.1 INTRODUCTION
In this section, we give a brief, high-level overview that encompasses the main topics
to be covered in this chapter, and the relationships between them. As will be seen,
phylogenetic tree reconstruction is a multi-layered process, and covering all aspects of
it would take far more than a single chapter. In the next section, we begin in earnest our
investigations into a subcollection of the concepts raised in the Introduction that we
intend to treat in more detail (and from scratch, with definitions). For comprehensive
mathematical treatments of terms, methods, and details that we do not cover, see, e.g.,
[ 1 , 2 ] for graph-theoretical/combinatorial approaches; see also [ 3 ] for an algebraic
geometry and statistics perspective on many of these topics. For a less mathematical,
more biologically oriented text, see, e.g., [ 4 ].
Through the ages, the diversity of species on earth and the sources of that diversity
have always featured prominently in human thought, as evidenced by Aurignacian
cave paintings, religious scriptures, and modern science. A prevailing biological con-
cept is that the diversification of life forms is related to the separation of gene pools.
If geographical or other barriers separate gene pools, the process of gene flow can
be insufficient to counteract genetic drift, and genetic or behavioral barriers emerge
against future gene flow (even after the removal of physical barriers) [ 5 ]. Of course,
genetic isolation alone is insufficient to explain diversity, which further requires the
raw material of genetic mutation, inevitably acted upon by natural selection.
A phylogenetic tree (or phylogeny ) is a diagram/graph which represents relations
of evolutionary descent of different species, organisms, or genes from a common
ancestor. A phylogenetic tree is a useful tool to understand and organize information
on biological diversity, structuring classifications, and providing insight into events
that occurred during evolution. An excellent preliminary guide to the biological per-
spective, upon which we build a more mathematical approach in this chapter, is [ 6 ];
see http://www.nature.com/scitable/topicpage/reading-a-
phylogenetic-tree-the-meaning-of-41956 .