Dimensions of Level-1 Group-Based Phylogenetic Networks

TL;DR

This paper derives a formula for the dimension of algebraic varieties associated with triangle-free level-1 group-based phylogenetic networks, aiding in understanding their algebraic and identifiability properties.

Contribution

It provides a new dimension formula for these phylogenetic network models and explores applications to their identifiability.

Findings

Dimension formula for the variety of triangle-free level-1 networks

Dimension formula for codimension zero toric fiber products

Applications to network identifiability

Abstract

Phylogenetic networks represent evolutionary histories of sets of taxa where horizontal evolution or hybridization has occurred. Placing a Markov model of evolution on a phylogenetic network gives a model that is particularly amenable to algebraic study by representing it as an algebraic variety. In this paper, we give a formula for the dimension of the variety corresponding to a triangle-free level-1 phylogenetic network under a group-based evolutionary model. On our way to this, we give a dimension formula for codimension zero toric fiber products. We conclude by illustrating applications to identifiability.