The time-dependent reconstructed evolutionary process with a key-role for mass-extinction events

Area of Science:

• Evolutionary Biology
• Phylogenetics
• Computational Biology

Background:

• Birth-death processes model species diversification, but often assume constant rates or ignore extinct lineages.
• Reconstructed phylogenies from molecular data are commonly used to infer evolutionary rates.
• Existing models may not adequately capture time-dependent diversification or mass-extinction events.

Purpose of the Study:

• To develop general probability density functions for reconstructed trees under homogeneous, time-dependent birth-death processes.
• To provide a unified mathematical framework for various birth-death models.
• To enable more accurate inference of diversification rates from phylogenetic data.

Main Methods:

• Developed general probability density functions for reconstructed trees under time-dependent birth-death processes.
• Adapted probability densities for conditions such as surviving lineages or a specific number of species.
• Transformed between tree probability densities and speciation time probability densities.
• Applied functions to birth-death-shift models with mass extinctions and special cases like pure-birth/death processes.

Main Results:

• Derived general time-dependent probability density functions for reconstructed phylogenies.
• Demonstrated adaptability for various conditioning events and transformations.
• Specified equations for common birth-death models within a unified framework.
• Provided a method to model mass-extinction events.

Conclusions:

• The developed framework unifies the analysis of various birth-death models for reconstructed phylogenies.
• This approach allows for more robust inference of speciation and extinction dynamics, including time-varying rates and mass extinctions.
• The generalized probability densities enhance the study of evolutionary processes using molecular phylogenetic data.