Abstract：
We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios.
摘要：
我们使用扩散近似建立了一个通用框架，以模拟随时间变化的状态依赖物种灭绝（ClaSSE）模型的时间向前状态计数或频率。我们将该框架应用于各种两区域和三区域地理状态物种灭绝（GeoSSE）模型。我们表明，在基于树的过程和基于扩散的过程下模拟的物种范围状态动力学是可比的。我们推导了一种方法来推断与给定观察到的稳态频率兼容的速率参数，并获得分析结果以计算给定速率参数集的稳态频率。我们还描述了使用基于扩散的方法找到到达ClaSSE模型固定频率的时间的过程，我们使用两区域GeoSSE模型的工作示例进行了演示。最后,我们讨论了在状态依赖的多样化情景下，如何应用扩散框架来形式化进化模式和过程之间的关系。
