Gernhard Tanja
Department of Mathematics, Kombinatorische Geometrie (M9), TU München, Bolzmannstr. 3, 85747 Garching, Germany.
Bull Math Biol. 2008 May;70(4):1082-97. doi: 10.1007/s11538-007-9291-0. Epub 2008 Jan 3.
In this paper, we investigate the standard Yule model, and a recently studied model of speciation and extinction, the "critical branching process." We develop an analytic way-as opposed to the common simulation approach-for calculating the speciation times in a reconstructed phylogenetic tree. Simple expressions for the density and the moments of the speciation times are obtained. Methods for dating a speciation event become valuable, if for the reconstructed phylogenetic trees, no time scale is available. A missing time scale could be due to supertree methods, morphological data, or molecular data which violates the molecular clock. Our analytic approach is, in particular, useful for the model with extinction, since simulations of birth-death processes which are conditioned on obtaining n extant species today are quite delicate. Further, simulations are very time consuming for big n under both models.
在本文中，我们研究了标准尤尔模型以及一种最近被研究的物种形成和灭绝模型——“临界分支过程”。我们开发了一种解析方法——与常见的模拟方法不同——用于计算重建系统发育树中的物种形成时间。得到了物种形成时间的密度和矩的简单表达式。如果对于重建的系统发育树没有时间尺度可用，那么确定物种形成事件时间的方法就变得很有价值。缺少时间尺度可能是由于超树方法、形态学数据或违反分子钟的分子数据。我们的解析方法对于有灭绝情况的模型尤其有用，因为以如今有n个现存物种为条件的生死过程模拟相当复杂。此外，对于这两种模型下的大n值，模拟非常耗时。
