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The Fossilized Birth-Death Model Is Identifiable.

Kate Truman1,2, Timothy G Vaughan3,4, Alex Gavryushkin1,2

  • 1Biological Data Science Laboratory, School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand.

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|October 22, 2024
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Summary
This summary is machine-generated.

Time-dependent birth-death sampling models can be unidentifiable. However, the widely used fossilized birth-death (FBD) model is identifiable, justifying its use for inferring evolutionary and epidemiological dynamics from phylogenetic trees.

Keywords:
Birth–death sampling modelsextinctionfossilsphylogeneticsspeciation

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Area of Science:

  • Evolutionary biology
  • Epidemiology
  • Phylogenetics
  • Computational biology

Background:

  • Time-dependent birth-death sampling models are crucial for inferring evolutionary and epidemiological dynamics from phylogenetic trees.
  • Some birth-death sampling models suffer from non-identifiability, where different rate sets produce identical tree distributions, hindering parameter estimation.
  • The fossilized birth-death (FBD) model offers a more realistic framework, accounting for fossilization and sampling processes in evolutionary and disease dynamics.

Purpose of the Study:

  • To determine the identifiability of time-dependent fossilized birth-death (FBD) models, a widely used class of phylogenetic models.
  • To assess whether the parameters of the time-dependent FBD model can be uniquely inferred from reconstructed phylogenetic trees.
  • To investigate the identifiability of an extended FBD model incorporating a 'removal after sampling' probability.

Main Methods:

  • Theoretical analysis of branching processes and their associated likelihood functions.
  • Mathematical formulation and evaluation of identifiability conditions for time-dependent birth-death and FBD models.
  • Comparison of parameter identifiability between standard FBD models and an extended FBD model with post-sampling removal.

Main Results:

  • The study demonstrates that widely used time-dependent fossilized birth-death (FBD) models are identifiable.
  • Identifiability of the FBD model validates the statistical inference of temporal diversification and epidemiological dynamics using this framework.
  • An extended time-dependent FBD model with a 'removal after sampling' probability is shown to be unidentifiable.

Conclusions:

  • The time-dependent FBD model is identifiable, supporting its application for robust inference of evolutionary and epidemiological processes from phylogenetic data.
  • The identifiability of the FBD model justifies the use of statistical methods relying on it for reconstructing past biological dynamics.
  • In scenarios with unknown post-sampling lineage behavior, inferring the 'removal after sampling' probability alongside other rates remains challenging using only tree data.