Analyzing Phylogenetic Trees with a Tree Lattice Coordinate System and a Graph Polynomial.

Area of Science:

• Phylogenetics and evolutionary biology
• Computational biology and bioinformatics
• Epidemiology and medical research

Background:

• Phylogenetic trees are essential for visualizing evolutionary relationships among species, genes, and individuals.
• Extracting evolutionary and epidemiological information from tree shapes and branch lengths is challenging due to variations in tree display and unlabeled structures.
• Existing methods for comparing phylogenetic trees often struggle with unlabeled tree shapes and varying branch length representations.

Purpose of the Study:

• To introduce novel representation and comparison methods for rooted unlabeled phylogenetic trees.
• To develop distance-based likelihood-free inference techniques for phylogenetic analysis.
• To apply these methods for analyzing phylogenies reconstructed from virus sequences.

Main Methods:

• Utilized a tree lattice as a coordinate system for rooted binary trees with branch lengths.
• Employed a graph polynomial to fully characterize phylogenetic tree shapes.
• Developed new tree metrics for comparing phylogenetic trees based on their lattice representation.

Main Results:

• The introduced tree representations and metrics enable effective distance-based likelihood-free methods.
• Demonstrated the utility of these methods for tree clustering, parameter estimation, and model selection.
• Successfully applied the methods to analyze phylogenies derived from virus sequence data.

Conclusions:

• The novel tree lattice and graph polynomial-based methods provide a robust framework for analyzing phylogenetic trees.
• These likelihood-free approaches offer powerful tools for evolutionary and epidemiological studies.
• The methods facilitate deeper insights into evolutionary patterns and disease transmission dynamics.