Department of Biosystems Science & Engineering, Eidgenössische Technische Hochschule Zürich, Basel 4058, Switzerland; Swiss Institute of Bioinformatics (SIB), Switzerland.
Department of Biosystems Science & Engineering, Eidgenössische Technische Hochschule Zürich, Basel 4058, Switzerland; Swiss Institute of Bioinformatics (SIB), Switzerland.
J Theor Biol. 2018 Jun 14;447:41-55. doi: 10.1016/j.jtbi.2018.03.005. Epub 2018 Mar 14.
A birth-death-sampling model gives rise to phylogenetic trees with samples from the past and the present. Interpreting "birth" as branching speciation, "death" as extinction, and "sampling" as fossil preservation and recovery, this model - also referred to as the fossilized birth-death (FBD) model - gives rise to phylogenetic trees on extant and fossil samples. The model has been mathematically analyzed and successfully applied to a range of datasets on different taxonomic levels, such as penguins, plants, and insects. However, the current mathematical treatment of this model does not allow for a group of temporally distinct fossil specimens to be assigned to the same species. In this paper, we provide a general mathematical FBD modeling framework that explicitly takes "stratigraphic ranges" into account, with a stratigraphic range being defined as the lineage interval associated with a single species, ranging through time from the first to the last fossil appearance of the species. To assign a sequence of fossil samples in the phylogenetic tree to the same species, i.e., to specify a stratigraphic range, we need to define the mode of speciation. We provide expressions to account for three common speciation modes: budding (or asymmetric) speciation, bifurcating (or symmetric) speciation, and anagenetic speciation. Our equations allow for flexible joint Bayesian analysis of paleontological and neontological data. Furthermore, our framework is directly applicable to epidemiology, where a stratigraphic range is the observed duration of infection of a single patient, "birth" via budding is transmission, "death" is recovery, and "sampling" is sequencing the pathogen of a patient. Thus, we present a model that allows for incorporation of multiple observations through time from a single patient.
一个出生-死亡-抽样模型产生了过去和现在样本的系统发育树。将“出生”解释为分支物种形成，“死亡”解释为灭绝，“抽样”解释为化石保存和恢复，这个模型——也称为化石出生-死亡（FBD）模型——产生了现存和化石样本的系统发育树。该模型已经进行了数学分析，并成功应用于不同分类水平的一系列数据集，如企鹅、植物和昆虫。然而，目前该模型的数学处理方法不允许将一组时间上不同的化石标本分配到同一物种。在本文中，我们提供了一个通用的数学 FBD 建模框架，明确考虑了“地层范围”，地层范围定义为与单个物种相关的谱系间隔，从物种的第一个化石出现到最后一个化石出现，跨越时间。为了在系统发育树中将一系列化石样本分配给同一物种，即指定地层范围，我们需要定义物种形成的模式。我们提供了用于三种常见物种形成模式的表达式：芽殖（或不对称）物种形成、分支（或对称）物种形成和渐成物种形成。我们的方程允许灵活地联合贝叶斯分析古生物学和现代生物学数据。此外，我们的框架直接适用于流行病学，其中地层范围是单个患者感染的观察持续时间，芽殖的“出生”是传播，“死亡”是恢复，“抽样”是对患者病原体进行测序。因此，我们提出了一个允许从单个患者随时间多次纳入观察的模型。
