Phylogenetic networks that are their own fold-ups

TL;DR

This paper explores the structural properties of stable phylogenetic networks, especially those that are their own fold-ups, providing new characterizations using properties like tree-basedness, reticulation-visible, and tree-child.

Contribution

It introduces novel characterizations of stable phylogenetic networks that are their own fold-ups, linking combinatorial properties with biological relevance.

Findings

Characterizations for when stable networks are tree-based, reticulation-visible, or tree-child.

Insights into the structural complexity of stable phylogenetic networks.

Connections between fold-up operations and network properties.

Abstract

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted directed acyclic graphs whose leaves are labelled by, for example, species. A number of mathematically interesting classes of phylogenetic networks are known. These include the biologically relevant class of stable phylogenetic networks whose members are defined via certain "fold-up" and "un-fold" operations that link them with concepts arising within the theory of, for example, graph fibrations. Despite this exciting link, the structural complexity of stable phylogenetic networks is still relatively poorly understood. Employing the popular tree-based, reticulation-visible, and tree-child properties which allow one to gauge this complexity in one way or another, we provide novel characterizations for when a stable phylogenetic network satisfies either one of these three properties.