Continuous and tractable models for the variation of evolutionary rates

Area of Science:

• Evolutionary biology
• Phylogenetics
• Computational biology

Background:

• Existing models often assume constant evolutionary rates or simplified rate variation.
• The gamma distribution model is widely used but has limitations in capturing complex rate dynamics.
• Understanding evolutionary rate variation is crucial for accurate phylogenetic inference.

Purpose of the Study:

• To develop a novel continuous model for evolutionary rate variation across sites and along phylogenetic lineages.
• To incorporate the Cox-Ingersoll-Ross (CIR) process for modeling rate changes over time.
• To provide a flexible framework that extends existing models and enhances phylogenetic analyses.

Main Methods:

• Developed a continuous-time model for evolutionary rate variation.
• Utilized the Cox-Ingersoll-Ross (CIR) diffusion process to model rate changes.
• Derived exact transition probabilities for substitutions under the proposed model.
• Formulated an exact likelihood for three-taxon trees and proposed Monte Carlo methods for larger trees.

Main Results:

• The proposed model directly extends the gamma distributed rates across site model.
• Introduced an additional parameter to capture rate variation down the tree.
• Demonstrated that model parameters can be estimated from the index of dispersion and gamma shape parameter.
• Provided an exact likelihood formula for three-taxon trees.

Conclusions:

• The CIR process offers a powerful and flexible approach to model evolutionary rate variation.
• The new model enhances the accuracy of phylogenetic inference by accounting for dynamic rate changes.
• The model's parameters are empirically estimable, facilitating its practical application in evolutionary studies.