Markov genealogy processes

Aaron A King; Qianying Lin; Edward L Ionides

doi:10.1016/j.tpb.2021.11.003

Markov genealogy processes

Theor Popul Biol. 2022 Feb:143:77-91. doi: 10.1016/j.tpb.2021.11.003. Epub 2021 Dec 9.

Authors

Aaron A King¹, Qianying Lin², Edward L Ionides³

Affiliations

¹ Department of Ecology & Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109, USA; Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48109, USA; Center for Computational Medicine & Biology, University of Michigan, Ann Arbor, MI 48109, USA; Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI 48109, USA. Electronic address: [email protected].
² Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI 48109, USA.
³ Department of Statistics, University of Michigan, Ann Arbor, MI 48109, USA; Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI 48109, USA.

Abstract

We construct a family of genealogy-valued Markov processes that are induced by a continuous-time Markov population process. We derive exact expressions for the likelihood of a given genealogy conditional on the history of the underlying population process. These lead to a nonlinear filtering equation which can be used to design efficient Monte Carlo inference algorithms. We demonstrate these calculations with several examples. Existing full-information approaches for phylodynamic inference are special cases of the theory.

Keywords: Hidden Markov model; Molecular epidemiology; Partially observed Markov process; Phylodynamics; Phylogeny; Statistical inference.

Markov genealogy processes

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