Birth–death stochastic processes are the foundations of many phylogenetic models and are widely used to make inferences about epidemiological and macroevolutionary dynamics. There are a large number of birth–death model variants that have been developed; these impose different assumptions about the temporal dynamics of the parameters and about the sampling process. As each of these variants was individually derived, it has been difficult to understand the relationships between them as well as their precise biological and mathematical assumptions. Without a common mathematical foundation, deriving new models is nontrivial. Here, we unify these models into a single framework, prove that many previously developed epidemiological and macroevolutionary models are all special cases of a more general model, and illustrate the connections between these variants. This unification includes both models where the process is the same for all lineages and those in which it varies across types. We also outline a straightforward procedure for deriving likelihood functions for arbitrarily complex birth–death(-sampling) models that will hopefully allow researchers to explore a wider array of scenarios than was previously possible. By rederiving existing single-type birth–death sampling models, we clarify and synthesize the range of explicit and implicit assumptions made by these models. [Birth–death processes; epidemiology; macroevolution; phylogenetics; statistical inference.]

中文翻译：

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统一流行病学和宏观进化中的系统发育生死模型

出生-死亡随机过程是许多系统发育模型的基础，并被广泛用于推断流行病学和宏观进化动力学。已经开发了大量的生死模型变体；这些对参数的时间动态和采样过程施加了不同的假设。由于这些变体中的每一个都是单独衍生的，因此很难理解它们之间的关系以及它们精确的生物学和数学假设。如果没有共同的数学基础，推导出新模型并非易事。在这里，我们将这些模型统一到一个框架中，证明许多先前开发的流行病学和宏观进化模型都是更一般模型的特例，并说明这些变体之间的联系。这种统一包括所有血统的过程都相同的模型和不同类型的过程不同的模型。我们还概述了一个简单的程序，用于为任意复杂的生死（-采样）模型推导似然函数，这有望使研究人员能够探索比以前更广泛的场景。通过重新推导现有的单一类型生死抽样模型，我们阐明并综合了这些模型做出的显式和隐式假设的范围。[出生-死亡过程；流行病学；宏观进化；系统发育学；统计推断。] 我们还概述了一个简单的程序，用于为任意复杂的生死（-采样）模型推导似然函数，这有望使研究人员能够探索比以前更广泛的场景。通过重新推导现有的单一类型生死抽样模型，我们阐明并综合了这些模型做出的显式和隐式假设的范围。[出生-死亡过程；流行病学；宏观进化；系统发育学；统计推断。] 我们还概述了一个简单的程序，用于为任意复杂的生死（-采样）模型推导似然函数，这有望使研究人员能够探索比以前更广泛的场景。通过重新推导现有的单一类型生死抽样模型，我们阐明并综合了这些模型做出的显式和隐式假设的范围。[出生-死亡过程；流行病学；宏观进化；系统发育学；统计推断。] 流行病学；宏观进化；系统发育学；统计推断。] 流行病学；宏观进化；系统发育学；统计推断。]