Calculations for multi-type age-dependent binary branching processes.

Area of Science:

• Mathematical Biology
• Computational Biology
• Evolutionary Biology

Background:

• Branching processes are fundamental in modeling population dynamics.
• Existing models often simplify particle behavior and lifespans.
• A need exists for more flexible models in macroevolution and phylogenetic analysis.

Purpose of the Study:

• To develop a method for calculating the joint probability density of tree topology and node times from multi-type age-dependent binary branching processes.
• To generalize the constant rate birth-death process by incorporating multiple particle types and arbitrary lifetime distributions.
• To provide a more realistic and robust prior distribution over trees for Bayesian phylogenetic analysis.

Main Methods:

• Derivation of the joint probability density for tree topology and node times.
• Modeling of multi-type age-dependent binary branching processes with arbitrary lifetime distributions.
• Application of the method to macroevolutionary models and Bayesian phylogenetic analysis.

Main Results:

• A method for calculating joint probability densities for complex branching processes.
• Comparison of 1-type and 2-type models in macroevolution.
• Demonstration of improved prior distributions for phylogenetic trees.

Conclusions:

• The developed method offers a more realistic framework for studying population dynamics.
• The approach enhances macroevolutionary modeling and Bayesian phylogenetic inference.
• The models are applicable to diverse fields like macroevolution and cell proliferation studies.