Exact Phylodynamic Likelihood via Structured Markov Genealogy Processes

August 11, 2026 · View on GitHub

Theoretical Population Biology 171: 79–105, 2026.

Authors

Static Badge   Static Badge   Static Badge

Abstract

We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed genealogy in terms of a filter equation, the structure of which is completely determined by the population model. We show that existing phylodynamic methods based on the coalescent and linear birth-death processes are special cases. We derive some properties of filter equations and describe a class of algorithms that can be used to numerically solve them. Importantly, because these algorithms rely only on simulation of the population model, they retain the plug-and-play property upon which simulation-based inference depends. Our results open the door to statistically efficient likelihood-based phylodynamic inference for a much wider class of models than has been possible.

Archives

A version is available on the arXiv:

The codes needed to generate the text and figures are archived on Zenodo:

Software

The figures and numerical results in the paper were prepared using the R package phylopomp:

Contents

  • ms.pdf: manuscript document.
  • ms.Rnw: main manuscript file.
  • Makefile, rules.mk: for use with GNU make. Running make will build the manuscript document de novo. To run all computations de novo delete or move the results/ directory.
  • defs.tex: LaTeX macro definitions.
  • ms_header.tex: LaTeX header file.
  • ms.R: R code contained in ms.Rnw.
  • ms.Rout: output of running ms.R.
  • setup.R: needed R definitions.
  • phylopomp_0.19.4.2.tar.gz: source tarball of phylopomp package used in the computations.
  • preprint.bst: BibTeX style file.
  • figures/: directory containing LaTeX code for diagrams.
  • results/: directory containing the results of some of the computations. By default, these will be read rather than recomputed. Move or delete these files to force re-computation.
  • PhyloPOMP.jl
  • pomp
      
  • A. A. King, Q-Y. Lin, and E. L. Ionides, Markov genealogy processes. Theoretical Population Biology 143: 77–91, 2022.
  • A. A. King, Q-Y. Lin, and E. L. Ionides, The sampled Moran genealogy process. arXiv 2002.11184, 2020.