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Phylogenetic Flexibility via Hall-Type Inequalities and Submodularity.

Katharina T Huber1, Vincent Moulton2, Mike Steel3

  • 1School of Computing Sciences, University of East Anglia, Norwich, UK. K.Huber@uea.ac.uk.

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|March 29, 2018
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Summary

Phylogenetic flexibility is determined by a

Keywords:
Bipartite graphHall’s marriage theoremPartial taxon coveragePhylogenetic treeSet systemsSubmodularity

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Graph Theory

Background:

  • Phylogenetic tree reconstruction is crucial for understanding evolutionary relationships.
  • Supertree methods require compatible input trees, posing challenges with diverse datasets.
  • The concept of phylogenetic flexibility addresses the compatibility of tree collections.

Purpose of the Study:

  • To define and characterize phylogenetic flexibility in collections of subsets.
  • To develop efficient algorithms for verifying flexibility conditions.
  • To connect flexibility to existing concepts like 'slim' and 'thin' sets.

Main Methods:

  • Utilizing Hall-type inequality conditions to define 'slimness'.
  • Employing submodularity arguments for algorithmic development.
  • Analyzing special cases for subsets of size 3 ('thin' sets) and size 2.

Main Results:

  • Phylogenetic flexibility is equivalent to the 'slim' condition.
  • A polynomial-time algorithm exists to determine 'slimness'.
  • 'Thin' sets (size 3 subsets) are linked to caterpillar trees and injective median functions.
  • Size 2 subsets are 'thin' if and only if an associated bipartite graph is a forest.

Conclusions:

  • Provides efficient and verifiable conditions for phylogenetic flexibility.
  • Enables broader application of supertree methods by ensuring input compatibility.
  • Establishes a clear link between set properties and phylogenetic tree construction.