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Identifiability of two-tree mixtures for group-based models.

Elizabeth S Allman1, Sonja Petrović, John A Rhodes

  • 1Department of Mathematics and Statistics, University of Alaska Fairbanks, PO Box 756660, Fairbanks, AK 99775-6660, USA. e.allman@alaska.edu

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Summary

Phylogenetic mixture models can be identifiable, unlike previous findings. This study shows tree topologies and substitution parameters are identifiable for DNA sequence data, challenging earlier assumptions.

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Area of Science:

  • Phylogenetics
  • Computational Biology
  • Molecular Evolution

Background:

  • Phylogenetic data can arise from mixtures of different tree topologies or substitution processes.
  • Previous studies indicated non-identifiable parameters for 2-state symmetric models, hindering topology determination.
  • This limitation posed challenges for understanding complex evolutionary histories.

Purpose of the Study:

  • To investigate the identifiability of parameters in two-tree mixtures of 4-state group-based phylogenetic models.
  • To determine if phylogenetic signal is preserved in mixtures relevant to DNA sequence data.
  • To assess the applicability of previous findings on 2-state models to more complex scenarios.

Main Methods:

  • Utilized algebraic techniques to analyze identifiability of model parameters.
  • Focused on 4-state group-based models, including JC, K2P, and K3P.
  • Examined identifiability for both tree topologies and substitution parameters.

Main Results:

  • Tree parameters are identifiable for the Jones-Chorpenning (JC) and Kimura 2-Parameter (K2P) models.
  • Generic substitution parameters are identifiable for JC mixture models.
  • Generic identifiability results were obtained for K2P and K3P models with mixtures on the same tree.

Conclusions:

  • The identifiability of parameters in phylogenetic mixture models is possible for relevant DNA sequence models.
  • Results challenge the generalizability of non-identifiability findings from simpler models.
  • Phylogenetic signal is largely retained in these mixture models, providing a more accurate evolutionary inference.