  Phylogenetic networks provide a means of describing the evolutionary history
of sets of species believed to have undergone hybridization or gene flow during
their evolution. The mutation process for a set of such species can be modeled
as a Markov process on a phylogenetic network. Previous work has shown that a
site-pattern probability distributions from a Jukes-Cantor phylogenetic network
model must satisfy certain algebraic invariants. As a corollary, aspects of the
phylogenetic network are theoretically identifiable from site-pattern
frequencies. In practice, because of the probabilistic nature of sequence
evolution, the phylogenetic network invariants will rarely be satisfied, even
for data generated under the model. Thus, using network invariants for
inferring phylogenetic networks requires some means of interpreting the
residuals, or deviations from zero, when observed site-pattern frequencies are
substituted into the invariants. In this work, we propose a method of utilizing
invariant residuals and support vector machines to infer 4-leaf level-one
phylogenetic networks, from which larger networks can be reconstructed. Given
data for a set of species, the support vector machine is first trained on model
data to learn the patterns of residuals corresponding to different network
structures to classify the network that produced the data. We demonstrate the
performance of our method on simulated data from the specified model and
primate data.
