Department of Integrative Biology, University of California Berkeley, 3060 Valley Life Sciences Bldg #3140, Berkeley, CA 94720-3140, USA.
J Theor Biol. 2012 May 7;300:265-76. doi: 10.1016/j.jtbi.2012.01.041. Epub 2012 Feb 5.
Much recent research has investigated the effect that different time variable birth-death processes have on the distribution of branching times in phylogenies of extant taxa. Previous work has shown how to calculate the distributions of number of lineages and branching times for a reconstructed constant rate birth-death process that started with one or two reconstructed lineages at some time in the past or ended with some number of lineages in the present. Here I expand that work to include any time variable birth-death process that starts with any number of reconstructed lineages and/or ends with any number of reconstructed lineages at any time, and I calculate a number of distributions under that process. I also explore the discrete time birth-death process which operates as an efficient and accurate numerical solution to any time-variable birth-death process and allows for the analytical incorporation of sampling and mass extinctions. I describe how these distributions can be used to compare different time variable models using maximum likelihood analysis, and I show how to simulate random trees under any of these models. I also introduce two visual methods for evaluating different time variable birth-death processes; these methods illustrate the shape of distributions for the number of lineages and waiting times by plotting them over time.
近期有大量研究调查了不同的时变生死过程对现存分类单元系统发育分支时间分布的影响。先前的研究已经展示了如何计算重建的恒定速率生死过程的分支时间和谱系分支数量的分布，该过程从过去某个时间的一个或两个重建谱系开始，或者在现在结束时有一定数量的谱系。在这里，我将该工作扩展到包括任何时变生死过程，该过程从任何数量的重建谱系开始和/或在任何时间结束有任何数量的重建谱系，并计算了该过程下的许多分布。我还探索了离散时间生死过程，它作为任何时变生死过程的有效且准确的数值解决方案，并且允许对采样和大规模灭绝进行分析合并。我描述了如何使用最大似然分析来比较不同的时变模型，并展示了如何在这些模型中的任何一个下模拟随机树。我还引入了两种用于评估不同时变生死过程的可视化方法；这些方法通过随时间绘制谱系分支数量和等待时间的分布来展示它们的形状。
