A new universal system of tree shape indices.

Area of Science:

• Computational Biology
• Phylogenetics
• Data Science

Background:

• Current tree shape indices have limitations in scope and interpretation.
• Existing methods struggle with non-ultrametric trees, variable branch lengths, and node sizes.

Purpose of the Study:

• Introduce a new, comprehensive system of indices for quantifying tree shape.
• Address shortcomings of existing tree comparison and categorization methods.
• Enable robust and interpretable analysis of tree structures across disciplines.

Main Methods:

• Developed a novel system of indices accounting for node sizes and branch lengths.
• Ensured indices are robust to small variations in tree attributes.
• Defined indices to be interpretable for all rooted trees and comparable across any pair.

Main Results:

• New indices provide interpretable values for all rooted trees, enabling meaningful comparisons.
• The system unifies measures of diversity, richness, balance, symmetry, height, outdegree, and branch count.
• Demonstrated practical advantages in quantifying diversity, assessing balance, and comparing trees with varying characteristics.

Conclusions:

• The new tree indices offer a coherent, multidimensional quantification of tree shape.
• This system is robust to sampling and inferential errors, with broad applications.
• The indices facilitate comparisons of evolutionary trees (HIV, Uralic languages) and computational models.