  Phylogenetic inference-the derivation of a hypothesis for the common
evolutionary history of a group of species- is an active area of research at
the intersection of biology, computer science, mathematics, and statistics. One
assumes the data contains a phylogenetic signal that will be recovered with
varying accuracy due to the quality of the method used, and the quality of the
data.
  The input for distance-based inference methods is an element of a Euclidean
space with coordinates indexed by the pairs of organisms. For several
algorithms there exists a subdivision of this space into polyhedral cones such
that inputs in the same cone return the same tree topology. The geometry of
these cones has been used to analyze the inference algorithms. In this chapter,
we model how input data points drawn from DNA sequences are distributed
throughout Euclidean space in relation to the space of tree metrics, which in
turn can also be described as a collection of polyhedral cones.
