Relaxed Random Walks at Scale

Area of Science:

• Evolutionary Biology
• Computational Biology
• Phylogenetics

Background:

• Relaxed random walk (RRW) models enhance Brownian diffusion models for trait evolution by incorporating branch-specific rate multipliers.
• These models better capture overdispersed biological data but face computational challenges with increased taxonomic sampling due to a growing number of parameters.
• Existing inference methods struggle with scalability as the number of taxa increases.

Purpose of the Study:

• To present a scalable Bayesian method for efficiently fitting RRW models and inferring branch-specific variation in trait evolution.
• To address the computational challenges posed by large phylogenetic trees in RRW analyses.
• To improve the efficiency and applicability of RRW models in phylogenetics.

Main Methods:

• Developed a novel Hamiltonian Monte Carlo (HMC) sampler to approximate the high-dimensional posterior distribution.
• Implemented a closed-form gradient calculation for trait data log-likelihood with respect to all branch-rate multipliers simultaneously.
• Achieved linear computational complexity with respect to the number of taxa.

Main Results:

• The HMC sampler demonstrated at least a 6-fold speed increase compared to the standard univariable Metropolis-Hastings approach.
• Successfully applied the RRW method to study the spatial emergence of West Nile virus in North America.
• Demonstrated scalability by analyzing mammalian life history traits across a phylogeny with 3650 tips.

Conclusions:

• The new HMC-based Bayesian method offers a significant computational advantage for fitting RRW models.
• This approach enhances the scalability and efficiency of phylogenetic trait evolution analyses, particularly for large datasets.
• The method provides a robust framework for inferring evolutionary dynamics and correlations across diverse biological systems.