Distinguishing Level-2 Phylogenetic Networks Using Phylogenetic Invariants

TL;DR

This paper investigates the distinguishability of level-2 phylogenetic networks using algebraic methods, extending previous work on simpler networks to more complex models, which aids in understanding their identifiability.

Contribution

It introduces an algebraic approach using discrete Fourier transformation to analyze the distinguishability of level-2 phylogenetic networks, generalizing prior results for level-1 networks.

Findings

Results on distinguishability of some level-2 networks

Comparison of varieties for semisimple level-2 and cycle networks

Extension of algebraic methods to complex network models

Abstract

In phylogenetics, it is important for the phylogenetic network model parameters to be identifiable so that the evolutionary histories of a group of species can be consistently inferred. However, as the complexity of the phylogenetic network models grows, the identifiability of network models becomes increasingly difficult to analyze. As an attempt to analyze the identifiability of network models, we check whether two networks are distinguishable. In this paper, we specifically study the distinguishability of phylogenetic network models associated with level-2 networks. Using an algebraic approach, namely using discrete Fourier transformation, we present some results on the distinguishability of some level-2 networks, which generalize earlier work on the distinguishability of level-1 networks. In particular, we study simple and semisimple level-2 networks. Simple and semisimple level-2 networks can be thought as generalizations of level-1 sunlet and cycle networks, respectively. Moreover, we also compare the varieties associated with semisimple level-2 and cycle networks.