Spaces of ranked tree-child networks.

Area of Science:

• Evolutionary biology
• Computational phylogenetics
• Network theory

Background:

• Ranked tree-child networks represent ordered evolutionary events over time.
• Comparing phylogenetic trees and networks is crucial but challenging.
• Existing distance metrics are limited to ranked binary phylogenetic trees.

Purpose of the Study:

• To develop a novel approach for comparing binary ranked tree-child networks.
• To define new mathematical spaces for these networks.
• To enable efficient computation of distances between networks.

Main Methods:

• Encoding ranked tree-child networks using partially ordered sets.
• Defining two new spaces for ranked binary tree-child networks.
• Characterizing one space as a CAT(0)-orthant space.

Main Results:

• A new encoding for ranked tree-child networks is presented.
• Two novel spaces of ranked binary tree-child networks are defined.
• The continuous space generalizes ultrametric trees and is a CAT(0)-orthant space, allowing efficient distance computation.

Conclusions:

• The proposed encoding and spaces offer a robust framework for comparing ranked tree-child networks.
• Efficient distance computation is now possible for equidistant tree-child networks.
• This work advances the field of phylogenetic network comparison and analysis.