Exact coalescent for the Wright-Fisher model
Exact coalescent for the Wright-Fisher model
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DOI：
10.1016/j.tpb.2005.11.005
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发表时间：
2006-06-01
影响因子：
1.4
通讯作者：
Fu, Yun-Xin
中科院分区：
文献类型：
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作者：
Fu, Yun-Xin
金曼聚结模型是赖特-费舍尔 (WF) 模型的近似模型，已成为广泛的理论和实证研究的基础。该近似很大程度上依赖于总体规模较大且样本量远小于总体规模的假设。在应用基于金曼合并的统计方法时，在实践中很少有人质疑样本量与总体规模相比是否太大。由于 WF 模型是最广泛使用的繁殖群体遗传学模型，因此需要为 WF 模型开发一个合并框架，只要担心金曼合并作为近似值的准确性，就可以使用该框架。本文描述了 WF 模型的精确聚结理论，并开发了一种模拟算法，然后将其与分析方法一起用于研究精确聚结的特性及其与 Kingman 聚结的差异。我们证明金曼聚结与精确聚结的不同之处在于：（1）连续聚结事件之间的等待时间较短； (2)观察样本中序列之间的拓扑关系的概率不同； (3)大样本谱系中的树长稍小。另一方面，样本的最近共同祖先（MRCA）的年龄几乎没有差异。精确的合并通过同时进行多个合并来弥补连续合并事件之间较长的等待时间。所检查的聚结剂的各种汇总统计数据中最显着的差异是外部分支的长度之和，精确聚结剂的长度总和可能比金曼聚结剂的长度大10%以上。总体而言，金曼合并是对样本和总体规模的精确合并的非常准确的近似，在最初预期的区域之外大大失败。 (c) 2005 Elsevier Inc. 保留所有权利。
The Kingman coalescent, which has become the foundation for a wide range of theoretical as well as empirical studies, was derived as an approximation of the Wright-Fisher (WF) model. The approximation heavily relies on the assumption that population size is large and sample size is much smaller than the population size. Whether the sample size is too large compared to the population size is rarely questioned in practice when applying statistical methods based on the Kingman coalescent. Since WF model is the most widely used population genetics model for reproduction, it is desirable to develop a coalescent framework for the WF model, which can be used whenever there are concerns about the accuracy of the Kingman coalescent as an approximation. This paper described the exact coalescent theory for the WF model and develops a simulation algorithm, which is then used, together with an analytical approach, to study the properties of the exact coalescent as well as its differences to the Kingman coalescent. We show that the Kingman coalescent differs from the exact coalescent by: (1) shorter waiting time between successive coalescent events; (2) different probability of observing a topological relationship among sequences in a sample; and (3) slightly smaller tree length in the genealogy of a large sample. On the other hand, there is little difference in the age of the most recent common ancestor (MRCA) of the sample. The exact coalescent makes up the longer waiting time between successive coalescent events by having multiple coalescence at the same time. The most significant difference among various summary statistics of a coalescent examined is the sum of lengths of external branches, which can be more than 10% larger for exact coalescent than that for the Kingman coalescent. As a whole, the Kingman coalescent is a remarkably accurate approximation to the exact coalescent for sample and population sizes failing considerably outside the region that was originally anticipated. (c) 2005 Elsevier Inc. All rights reserved.