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Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model.

Wai-Tong Louis Fan1,2, Brandon Legried3, Sebastien Roch4

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Estimating evolutionary distances using sequence lengths alone is impossible under the TKF91 model, even with infinitely long sequences. The distributions of sequence lengths at varying evolutionary distances are indistinguishable.

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Area of Science:

  • Computational Biology
  • Phylogenetics
  • Evolutionary Genetics

Background:

  • The TKF91 model describes sequence evolution via insertions, deletions, and substitutions along a phylogenetic tree.
  • Accurate distance estimation is crucial for reconstructing evolutionary relationships.

Purpose of the Study:

  • To investigate the feasibility of estimating evolutionary distances solely from sequence lengths under the TKF91 model.
  • To determine if sequence length distributions can uniquely identify evolutionary distances.

Main Methods:

  • Analysis of the TKF91 model in an asymptotic regime.
  • Mathematical derivation of sequence length distributions.
  • Information-theoretic analysis of distinguishability between distributions.

Main Results:

  • Demonstrated that consistent distance estimation is not possible using only sequence lengths.
  • Proved that sequence length distributions at different evolutionary distances are statistically indistinguishable.
  • Showed that the probability of distinguishing between different distances does not converge to one.

Conclusions:

  • Sequence length alone provides insufficient information for reliable evolutionary distance estimation under the TKF91 model.
  • The asymptotic behavior of sequence evolution under TKF91 leads to inherent ambiguity in distance estimation.
  • Future research may need to incorporate additional data beyond sequence lengths for accurate phylogenetic inference.