Inhomogeneous continuous-time Markov chains to infer flexible time-varying evolutionary rates

2025-10-13

AI Summary

Modeling time-varying evolutionary rates remains a key challenge in phylogenetic inference and pathogen transmission studies. We propose the Multi-Epoch Clock model, which parameterizes the rate function of a non-homogeneous continuous-time Markov chain (ICTMC) as piecewise-constant across epochs, incorporates temporal smoothing via a Gaussian Markov random field (GMRF) prior, and introduces a differentiable gradient computation framework to enable efficient Hamiltonian Monte Carlo (HMC) sampling. Integrated within a Bayesian phylogenetic framework, our approach enables accurate and scalable inference of time-varying substitution rates. Simulation studies demonstrate robust recovery of diverse rate trajectories—including stepwise, linear, and unimodal dynamics. Applied to empirical data, the model successfully reconstructs the temporal evolution of substitution rates for West Nile virus, dengue virus, influenza A virus, and SARS-CoV-2 in Europe during early 2020, substantially enhancing the flexibility and statistical reliability of time-varying molecular clock modeling.

Technology Category

• Machine Learning: Evolutionary Learning
• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Graphical Models

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Reconstructing evolutionary histories and estimating the rate of evolution from molecular sequence data is of central importance in evolutionary biology and infectious disease research. We introduce a flexible Bayesian phylogenetic inference framework that accommodates changing evolutionary rates over time by modeling sequence character substitution processes as inhomogeneous continuous-time Markov chains (ICTMCs) acting along the unknown phylogeny, where the rate remains as an unknown, positive and integrable function of time. The integral of the rate function appears in the finite-time transition probabilities of the ICTMCs that must be efficiently computed for all branches of the phylogeny to evaluate the observed data likelihood. Circumventing computational challenges that arise from a fully nonparametric function, we successfully parameterize the rate function as piecewise constant with a large number of epochs that we call the polyepoch clock model. This makes the transition probability computation relatively inexpensive and continues to flexibly capture rate change over time. We employ a Gaussian Markov random field prior to achieve temporal smoothing of the estimated rate function. Hamiltonian Monte Carlo sampling enabled by scalable gradient evaluation under this model makes our framework computationally efficient. We assess the performance of the polyepoch clock model in recovering the true timescales and rates through simulations under two different evolutionary scenarios. We then apply the polyepoch clock model to examine the rates of West Nile virus, Dengue virus and influenza A/H3N2 evolution, and estimate the time-varying rate of SARS-CoV-2 spread in Europe in 2020.

Problem

• Modeling time-varying evolutionary rates using inhomogeneous Markov chains
• Estimating evolutionary histories from molecular sequence data efficiently
• Applying flexible Bayesian inference to viral evolution and spread

Innovation

• Inhomogeneous Markov chains model evolutionary rate changes
• Piecewise constant parameterization enables efficient likelihood computation
• Gaussian Markov random field prior smooths rate estimation