Exact phylodynamic likelihood via structured Markov genealogy processes

TL;DR

This paper develops a general framework for calculating exact likelihoods of genealogies in Markovian population models, enabling more efficient phylodynamic inference beyond traditional methods.

Contribution

It introduces a novel genealogy process and filter equations that generalize existing models, facilitating likelihood computation for a broader class of population models.

Findings

Derived exact likelihood expressions for genealogies

Unified existing phylodynamic models as special cases

Proposed algorithms for numerical likelihood computation

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 is currently possible.