The Fossilized Birth-Death Model Is Identifiable.

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.