Folding and unfolding phylogenetic trees and networks

Area of Science:

• Computational Biology
• Evolutionary Biology
• Graph Theory

Background:

• Phylogenetic networks model reticulate evolution using directed acyclic graphs.
• These networks have a close relationship with multi-labelled trees (MUL-trees).
• Operations like unfolding networks into MUL-trees (U) and folding MUL-trees into networks (F) are key.

Purpose of the Study:

• To investigate the properties of unfolding (U) and folding (F) operations.
• To introduce and characterize a new class of phylogenetic networks called "stable networks."
• To explore the relationship between displaying trees in networks and MUL-trees.

Main Methods:

• Defining and characterizing "stable networks" where F(U(N)) is isomorphic to N.
• Relating stable networks to the established class of tree-sibling networks.
• Developing a phylogenetic analogue of graph fibrations to study tree display within networks.

Main Results:

• Stable networks are formally defined and characterized.
• A connection is established between stable networks and tree-sibling networks.
• A novel framework analogous to graph fibrations is presented for phylogenetic networks.

Conclusions:

• The study provides a deeper understanding of the relationship between phylogenetic networks and MUL-trees.
• Stable networks offer a new perspective on representing evolutionary history.
• The developed fibration analogue facilitates reconciling phylogenetic trees with networks.