  A classic problem in computational biology is constructing a phylogenetic
tree given a set of distances between n species. In most cases, a tree
structure is too constraining. We consider a circular split network, a
generalization of a tree in which multiple parallel edges signify divergence. A
geometric space of such networks is introduced, forming a natural extension of
the work by Billera, Holmes, and Vogtmann on tree space. We explore properties
of this space, and show a natural embedding of the compactification of the real
moduli space of curves within it.
