# Distinguishing Phylogenetic Networks

## TL;DR

This paper explores the mathematical properties of Markov models on large-cycle phylogenetic networks, demonstrating that their topology can be generically identified using algebraic geometry tools.

## Contribution

It introduces a novel analysis of large-cycle networks, proving generic identifiability of their semi-directed topology with algebraic geometry methods.

## Key findings

- Semi-directed network topology is generically identifiable.
- Uses computational algebraic geometry to analyze phylogenetic models.
- Focuses on large-cycle networks with cycles of length at least four.

## Abstract

Phylogenetic networks are becoming increasingly popular in phylogenetics since they have the ability to describe a wider range of evolutionary events than their tree counterparts. In this paper, we study Markov models on phylogenetic networks and their associated geometry. We restrict our attention to large-cycle networks, networks with a single undirected cycle of length at least four. Using tools from computational algebraic geometry, we show that the semi-directed network topology is generically identifiable for Jukes-Cantor large-cycle network models.