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A Third Strike Against Perfect Phylogeny.

Leo Van Iersel1, Mark Jones1, Steven Kelk2

  • 1Delft Institute of Applied Mathematics, Delft University of Technology, Van Mourik Broekmanweg 6, 2628 XE, Delft, The Netherlands.

Systematic Biology
|March 14, 2019
PubMed
Summary
This summary is machine-generated.

The conjecture that checking small subsets of evolutionary traits is sufficient to determine perfect phylogenies is false. This study demonstrates that even when all small subsets have perfect phylogenies, the entire dataset may not, refuting a long-standing hypothesis in evolutionary biology.

Keywords:
Four gamete conditionlocal obstructions conjecturemaximum parsimonyperfect phylogenyphylogenetic tree

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Evolutionary Biology

Background:

  • Perfect phylogenies represent evolutionary histories where traits arise only once, adhering to Occam's Razor for parsimony.
  • Previous work established that 2-state and 3-state characters have perfect phylogenies if and only if their subsets of size 2 and 3, respectively, do.

Purpose of the Study:

  • To investigate the long-standing conjecture that a constant bound exists for subset size to determine perfect phylogenies for any number of states.
  • To determine if checking fixed-size subsets of characters is sufficient for inferring perfect phylogenies, regardless of the total number of characters.

Main Methods:

  • Constructed a set of 8-state characters.
  • Demonstrated that this set lacks a perfect phylogeny.
  • Proved that all subsets of this set, up to a specified constant size 't', do possess a perfect phylogeny.

Main Results:

  • The conjecture is proven false: a constant bound for subset size does not exist for determining perfect phylogenies.
  • A dataset of 8-state characters was shown to have no perfect phylogeny, yet all its subsets of size 't' do.
  • Even ignoring a single character is insufficient to guarantee a perfect phylogeny for the remaining set.

Conclusions:

  • This 'third strike' refutes the possibility of efficient algorithms relying on fixed-size subset checks for perfect phylogeny inference.
  • While closing certain algorithmic avenues, the findings do not preclude other methods for developing efficient algorithms in phylogenetics.
  • The study highlights the complexity of perfect phylogeny inference, particularly with multi-state characters.