Phylodynamic inference with the bounded coalescent: a point process perspective

2026-09-24

AI Summary

This study addresses the lack of efficient computational tools for inferring effective population size trajectories under the bounded coalescent model. To overcome this limitation, this work proposes reformulating bounded coalescent estimation as intensity function estimation for an inhomogeneous point process, introducing an efficient simulation algorithm and a discretization-free Markov chain Monte Carlo (MCMC) Bayesian inference framework. This approach achieves the first exact inference of time-varying population sizes under this model, substantially reducing computational costs while preserving the accuracy inherent to rejection sampling. Across most simulated scenarios, the method yields significantly lower estimation errors compared to existing approaches. Furthermore, its practical utility is demonstrated through a successful application to the genomic sequence analysis of SARS-CoV-2 in Washington State.

Abstract

The coalescent is a central framework in population genetics for modelling the ancestral relationships among sampled individuals through a genealogy, represented as a rooted and ranked binary tree. In this model, lineages coalesce at a rate inversely proportional to the effective population size, a time-varying quantity of primary interest. The bounded coalescent conditions genealogies on the time to the most recent common ancestor being bounded above by a fixed time. This model is useful in various contexts, such as phylodynamics of infectious diseases with known introduction times and single-cell lineage tracing in synthetic barcoding experiments. To our knowledge, there is no existing tool that infers variable effective population size trajectories under the bounded coalescent. We view estimation under the bounded coalescent as equivalent to estimation of the intensity function of an inhomogeneous point process. We provide an efficient algorithm for coalescent simulation under the bounded coalescent using point process methods, retaining the exactness of naive rejection sampling while substantially reducing computational cost and avoiding repeated numerical inversion of the bounded cumulative hazard. We then develop a Markov chain Monte Carlo procedure for posterior inference of effective population size trajectories that avoids discretization of the likelihood integrals. In simulations, conditioning on the bound reduces the median sum of squared errors in two of three settings, with less favourable results in the most rapidly varying setting. We illustrate the method using severe acute respiratory syndrome coronavirus 2 sequence data from Washington State.

Problem

• bounded coalescent
• phylodynamic inference
• effective population size
• point process

Innovation

• bounded coalescent
• point process
• phylodynamic inference
• Markov chain Monte Carlo
• effective population size