Extending Tree Models to Split Networks

In this chapter we take statistical models designed for trees and adapt them for split networks, a more general class of mathematical structures. The models we propose provide natural swing-bridges between trees, filling in gaps in the probability simplex. There are many reasons why we might want to do this. Firstly, the split networks provide a graphical representation of phylogenetic uncertainty. Data that is close to tree-like produces a network that is close to a tree, while noisy or badly modeled data produce complex networks. Secondly, models that incorporate several trees open up possibilities for new tests to assess the relative support for different trees, in both likelihood and Bayesian frameworks. Thirdly, by searching through network space rather than tree space we may well be able to avoid some of the combinatorial headaches that make searching for trees so difficult.