Bayesian Inference of Phylogenetic Distances: Revisiting the Eigenvalue Approach

Area of Science:

• Evolutionary biology
• Computational phylogenetics
• Molecular evolution

Background:

• Phylogenetics commonly uses Markov substitution models to infer evolutionary distances from genetic data, aiding in starting tree selection.
• Standard models like the general time reversible (GTR) model handle DNA data well but struggle with complex phenomena like heterotachy (lineage-specific rate variation).
• Existing advanced models for heterotachy lack analytical solutions, hindering likelihood calculations essential for Bayesian inference.

Purpose of the Study:

• To develop a novel hybrid Bayesian phylogenetic framework that integrates GTR-style modeling with rate variation and heterotachy.
• To create a method that is mathematically tractable for optimization and Bayesian inference.
• To investigate the evolutionary origins of the eukaryotic cell using this new approach within a universal tree of life context.

Main Methods:

• Developed a hierarchical Bayesian GTR-style framework incorporating gamma-distributed rate variation and heterotachy.
• Ensured the approach is differentiable, enabling optimization via stochastic gradient descent.
• Facilitated Bayesian inference using Hamiltonian Markov Chain Monte Carlo methods.

Main Results:

• The proposed hybrid method successfully models complex evolutionary rate variations and heterotachy.
• The framework is amenable to modern computational inference techniques like stochastic gradient descent and Hamiltonian Monte Carlo.
• Analysis of universal tree of life data provided evidence supporting a two-domain theory for eukaryotic cell origins.

Conclusions:

• The novel Bayesian framework offers a powerful tool for phylogenetic analysis incorporating complex evolutionary dynamics.
• This method advances the modeling of molecular evolution, particularly for lineage-specific rate variations.
• Findings lend support to the two-domain theory regarding the evolutionary emergence of eukaryotic cells.