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Jeanne Lemant1,2,3, Cécile Le Sueur1, Veselin Manojlović4

  • 1Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse 26, 4058 Basel, Switzerland.

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New tree balance indices offer a universal and robust method for comparing evolutionary trees, overcoming limitations of existing measures. These generalized indices unify and extend popular metrics like the Colless and Sackin indices.

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Area of Science:

  • Phylogenetics and Evolutionary Biology
  • Computational Biology
  • Data Science

Background:

  • Existing tree balance indices, used for comparing evolutionary processes and algorithms, have limitations.
  • These limitations include undefined values for certain rooted trees, unreliability for trees with varying leaf numbers, and sensitivity to rare data.
  • Popular indices like the Colless index and Sackin index lack universality and robustness.

Purpose of the Study:

  • To introduce a new class of universal and robust tree balance indices.
  • To address the shortcomings of existing indices in defining balance for all rooted trees and comparing trees with different numbers of leaves.
  • To unify and generalize the Colless and Sackin indices.

Main Methods:

  • Definition of a new class of Colless-like tree balance indices.
  • Demonstration of equivalence between a generalized Colless-like index and the normalized reciprocal of Sackin's index for specific cladogram types.
  • Development of intrinsically normalized indices computable in linear time.

Main Results:

  • A new class of universal tree balance indices is defined, applicable to trees with any degree distribution.
  • These indices can account for population sizes and enable meaningful comparisons of trees with different numbers of leaves.
  • For bifurcating and full m-ary cladograms, a novel index unifies and generalizes the Colless and Sackin indices.

Conclusions:

  • The newly developed tree balance indices are more robust and universally applicable than existing measures.
  • These indices offer a unified and generalized approach, superseding the limitations of the Colless and Sackin indices.
  • The computational efficiency (linear time) and intrinsic normalization make these indices highly practical for diverse applications in phylogenetics and computational biology.