Phylogenetic network models as graphical models

TL;DR

This paper shows how phylogenetic network models can be viewed as graphical models, enabling new insights into their structure, identifiability, and tensor rank conditions, with implications for evolutionary biology.

Contribution

It introduces a framework connecting phylogenetic networks to graphical models, developing local modifications and analyzing nonidentifiability issues.

Findings

Displayed tree models are submodels of DAG-based graphical models.

Identifiability issues are linked to reticulation edges and network stacking.

Rank conditions on probability tensor flattenings generalize classic phylogenetic results.

Abstract

The displayed tree phylogenetic network model is shown to sit as a natural submodel of the graphical model associated to a directed acyclic graph (DAG). This representation allows to derive a number of results about the displayed tree model. In particular, the concept of a local modification to a DAG model is developed and applied to the displayed tree model. As an application, some nonidentifiability issues related to the displayed tree models are highlighted as they relate to reticulation edges and stacked reticulations in the networks. We also derive rank conditions on flattenings of probability tensors for the displayed tree model, generalizing classic results for phylogenetic tree models.