A Space of Phylogenetic Networks

A classical problem in computational biology is constructing a phylogenetic tree given a set of distances between $n$ species. In many cases, a tree structure is too constraining. We consider a split network, which is 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 familiar space of phylogenetic trees. We explore properties of the space of networks and construct a natural embedding of the compactification of the real moduli space of curves within it.