Advances in Computational Methods for Phylogenetic Networks in the Presence of Hybridization R. A. Leo Elworth, Huw A. Ogilvie, Jiafan Zhu, and Luay Nakhleh Abstract Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parame- ters, such as divergence times and population sizes, they form a generative process of molecular sequence evolution. Early work on computational methods for phylo- genetic network inference focused exclusively on reticulations and sought networks with the fewest number of reticulations to fit the data. As processes such as incom- plete lineage sorting (ILS) could be at play concurrently with hybridization, work in the last decade has shifted to computational approaches for phylogenetic net- work inference in the presence of ILS. In such a short period, significant advances have been made on developing and implementing such computational approaches. In particular, parsimony, likelihood, and Bayesian methods have been devised for estimating phylogenetic networks and associated parameters using estimated gene trees as data. Use of those inference methods has been augmented with statistical tests for specific hypotheses of hybridization, like the D-statistic. Most recently, Bayesian approaches for inferring phylogenetic networks directly from sequence data were developed and implemented. In this chapter, we survey such advances and discuss model assumptions as well as methods’ strengths and limitations. We also discuss parallel efforts in the population genetics community aimed at inferring similar structures. Finally, we highlight major directions for future research in this area. R. A. Leo Elworth Rice University e-mail:
[email protected] Huw A.