Phylogenetic Networks

Phylogenetic networks can model more complicated evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. Using the same Markov processes used on trees, these models can be extended to networks. In particular, we will look at the Cavendar-Farris-Neyman (CFN) model. A discrete Fourier transform can be applied to the CFN model which greatly simplifies the parametrization. In this talk, we will review how to find phylogenetic invariants for trees, and then we will give a description of all quadratic invariants for level-1 networks.