Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics

Area of Science:

• Evolutionary Biology
• Computational Biology
• Mathematical Modeling

Background:

• Phylogenetic birth-death models are crucial for inferring evolutionary dynamics across various biological scales.
• Current models are limited by linearity assumptions, preventing the inclusion of individual interactions like carrying capacity or frequency-dependent selection.

Purpose of the Study:

• To develop a novel multi-type birth-death process that incorporates inter-individual interactions.
• To enable more realistic modeling of evolutionary dynamics by overcoming the limitations of current phylogenetic models.

Main Methods:

• Introduced a multi-type birth-death process interacting with an ensemble of replicas.
• Proved convergence of the interaction field to a deterministic trajectory in an infinite ensemble limit.
• Derived self-consistent interactions as nonlinearities in the infinitesimal generator.

Main Results:

• The ensemble limit results in decoupled replicas with self-consistent interactions appearing as nonlinearities.
• Developed a tractable special case modeling both carrying capacity and frequency-dependent selection.
• Achieved message-passing likelihoods within a phylogenetic birth-death framework.

Conclusions:

• The new model provides a more comprehensive framework for phylogenetic birth-death processes.
• It allows for the incorporation of crucial ecological interactions into evolutionary inference.
• This advancement has broad implications for understanding evolutionary dynamics from species to cellular levels.