AI Insight
This paper establishes a mathematical framework showing that a broad class of Markovian population models each generate a unique stochastic process over genealogies, allowing the derivation of exact likelihood expressions for observed genealogies through filter equations. The authors demonstrate that established phylodynamic approaches, including coalescent-based and linear birth-death process methods, are special cases of this more general framework. They also describe a class of numerical algorithms to solve these filter equations that rely on simulation of the population model, preserving computational flexibility.
Why it matters
This framework substantially expands the range of population models amenable to statistically rigorous, likelihood-based phylodynamic inference, with potential applications in epidemiology, evolutionary biology, and ecology where understanding population dynamics from genetic data is critical.
arXiv:2405.17032v4 Announce Type: replace
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.
Source: Exact phylodynamic likelihood via structured Markov genealogy processes