A distance metric for unlabeled phylogenetic networks

Music City Center 

In the field of phylogenetics, researchers traditionally model evolutionary relationships represented by a phylogenetic tree. However, due to the complex nature of evolution, phylogenetic networks offer a robust alternative by describing reticulate processes accurately. Among many tasks relevant to phylogenetic network inference, quantifying distances among networks is a crucial, yet understudied task. One successful approach to improving distance functions on trees is to map trees onto matrix spaces. Any ranked tree of n leaves can be encoded as an integer-valued lower triangular matrix that we call F-matrix. In this talk, we extend the definition of F-matrix to the case of phylogenetic networks and prove the bijection between network space and matrix space subject to certain constraints. We propose a metric on the space of rooted, ranked and unlabeled phylogenetic network distributions. Once phylogenetic networks are bijectively mapped onto a matrix space, we can calculate distances using Frobenius norm, which makes it possible to conduct statistical analysis of ranked network shapes. We show the utility of our metrics via simulations and an application in infectious diseases.

phylogenetic network

distance metric

ranked genealogy

ranked network shape 

Biometrics Section