Abstract
We consider the problem of distance estimation under the TKF91 model of sequence evolution by insertions, deletions and substitutions on a phylogeny. In an asymptotic regime where the expected sequence lengths tend to infinity, we show that no consistent distance estimation is possible from sequence lengths alone. More formally, we establish that the distributions of pairs of sequence lengths at different distances cannot be distinguished with probability going to one.
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Acknowledgements
SR was supported by NSF grants DMS-1614242, CCF-1740707 (TRIPODS), DMS-1902892, and DMS-1916378, as well as a Simons Fellowship and a Vilas Associates Award. BL was supported by DMS-1614242, CCF-1740707 (TRIPODS), DMS-1902892 (to SR). WTF was supported by NSF grants DMS-1614242 (to SR) and DMS-1855417, and ONR-TCRI N00014-20-1-2411.
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Fan, WT.L., Legried, B. & Roch, S. Impossibility of Consistent Distance Estimation from Sequence Lengths Under the TKF91 Model. Bull Math Biol 82, 123 (2020). https://doi.org/10.1007/s11538-020-00801-3
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DOI: https://doi.org/10.1007/s11538-020-00801-3