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.

翻译：我们证明，在广义马尔可夫群体模型类别中，每个模型都会在谱系空间上诱导一个唯一随机过程。通过构建该谱系过程，我们推导出观测谱系似然性的精确表达式，该表达式基于滤波器方程，其结构完全由群体模型决定。研究显示，现有基于溯祖模型和线性出生-死亡过程的系统发育动力学方法均为本文框架的特例。我们推导了滤波器方程的一些性质，并描述了一类可用于数值求解该方程的算法。重要的是，由于这些算法仅依赖群体模型的模拟过程，因此保留了模拟推理所需的即插即用特性。本研究结果为比当前可行范围更广的模型类别，打开了实现统计高效的基于似然的系统发育动力学推理之门。