Abstract: Phylodynamics is the project of extracting information on the drivers of an epidemic from genomic data. A key unsolved mathematical problem is the probabilistic linkage of a genealogy with the stochastic process that generates it. In this talk, I introduce phylodynamics, and show how any member of a broad class of stochastic processes generates a Markov process on the space of genealogies. I then present new results giving the exact likelihood of a given genealogy in terms of a filtering equation, which can be integrated using Monte Carlo methods. These results unify and extend existing approaches and greatly broaden the scope of phylodynamic methods. The proofs rely on constructions that are both novel and more natural than the reverse-time constructions used in the more limited existing theories.

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