Tree-based networks: characterisations, metrics, and support trees.

Area of Science:

• Evolutionary Biology
• Computational Biology
• Graph Theory

Background:

• Phylogenetic trees model evolutionary history but struggle with reticulate events like hybridization.
• Phylogenetic networks generalize trees to represent complex evolutionary histories.
• Tree-based networks are a significant class of phylogenetic networks.

Purpose of the Study:

• To generalize existing tree-based characterizations and proximity measures for binary phylogenetic networks to arbitrary phylogenetic networks.
• To characterize support trees (tree-based embeddings) of arbitrary tree-based networks.
• To derive an explicit formula for the number of support trees in binary tree-based networks.

Main Methods:

• Generalizing characterizations based on matchings in bipartite graphs, path partitions, and antichains.
• Developing novel approaches for non-binary phylogenetic networks.
• Characterizing support trees using network structure and graph theory.

Main Results:

• Successful generalization of tree-based characterizations to arbitrary phylogenetic networks.
• New characterization of support trees for arbitrary tree-based networks.
• An explicit formula for counting support trees in binary tree-based networks based on bipartite graph components.

Conclusions:

• The study provides a unified framework for analyzing tree-based phylogenetic networks.
• The findings advance the representation and analysis of complex evolutionary histories.
• The derived formula offers a computational tool for phylogenetic network research.