Expectation-Maximization enables Phylogenetic Dating under a Categorical Rate Model

Area of Science:

• Computational Biology
• Phylogenetics
• Evolutionary Biology

Background:

• Phylogenetic tree dating is essential for evolutionary studies but faces challenges in accurately inferring substitution rates across branches.
• Existing methods often rely on rigid, parametric rate distributions, leading to inaccuracies when these assumptions are violated (model misspecification).
• Optimization problems arise from integrating over continuous rate domains in maximum likelihood dating.

Purpose of the Study:

• To develop a novel method for molecular dating that is robust to misspecified rate distributions.
• To address the computational challenges associated with likelihood-based dating methods.
• To improve the accuracy of phylogenetic tree dating, especially for complex rate variations.

Main Methods:

• Introduced Molecular Dating using Categorical-models (MD-Cat), a non-parametric approach discretizing rate distributions into k categories.
• Employed the Expectation-Maximization algorithm for co-estimation of rate categories and branch lengths.
• Validated the method on simulated datasets and real-world data (Angiosperms, HIV) across diverse rate distributions.

Main Results:

• MD-Cat demonstrated higher accuracy compared to existing methods, particularly with exponential or multimodal rate distributions.
• The categorical model effectively approximates a wide range of rate distributions, reducing the impact of model misspecification.
• Co-estimation via Expectation-Maximization proved effective for inferring both rates and divergence times.

Conclusions:

• MD-Cat offers a more flexible and accurate approach to molecular dating than traditional parametric methods.
• The method is particularly advantageous when evolutionary rates vary significantly or exhibit complex patterns.
• MD-Cat provides a robust framework for inferring divergence times in phylogenetic analyses.