Stephens M
Department of Statistics, University of Oxford, Oxford, United Kingdom.
Theor Popul Biol. 2000 Mar;57(2):109-19. doi: 10.1006/tpbi.1999.1442.
In this paper we consider the genealogy of a random sample of n chromosomes from a panmictic population which has evolved with constant size N over many generations. We address two related problems. First we describe how genealogical information may be usefully partitioned into information on the events (mutations and coalescences) which occur in the genealogy, and the times between these events. We show that the distribution of the times given information on the events is particularly simple and describe how this can considerably reduce the computational burden when performing inference for these times. Second we investigate the effect on the genealogy of conditioning on a single mutation having occurred during the ancestry of the sample. In particular we use results from the first part of the paper to derive explicit formulae for the density of the age of a mutant allele, conditional on its frequency in either a sample or the population.
在本文中，我们考虑从一个随机交配群体中抽取的n条染色体的随机样本的系谱，该群体在许多代中以恒定大小N进化。我们解决两个相关问题。首先，我们描述系谱信息如何有效地划分为关于系谱中发生的事件（突变和合并）的信息，以及这些事件之间的时间。我们表明，给定事件信息时时间的分布特别简单，并描述了在对这些时间进行推断时这如何能大大减轻计算负担。其次，我们研究在样本祖先期间发生单个突变的条件对系谱的影响。特别是，我们利用本文第一部分的结果推导出突变等位基因年龄密度的显式公式，条件是其在样本或群体中的频率。
