Wright-Fisher diffusion bridges
Wright-Fisher diffusion bridges
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DOI：
10.1016/j.tpb.2017.09.005
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发表时间：
2018-07-01
影响因子：
1.4
通讯作者：
Spano, Dario
中科院分区：
文献类型：
--
作者：
Griffiths, Robert C.;Jenkins, Paul A.;Spano, Dario
从时间0的x开始并且已知在时间T具有频率z的等位基因的频率的轨迹可以通过赖特-费舍尔扩散的桥过程来建模。当x = z = 0时的桥是特别有趣的，因为它们模拟了等位基因频率的轨迹，该等位基因在某个时间出现，然后在时间T之后由于随机漂移或突变而丢失。中性Wright-Fisher扩散过程中种群的合并系谱是很好理解的。本文给出了当t是（0，T）的元素时桥上种群的聚合谱系的新解释。在时间0和T时等位基因频率为0的桥中，聚结结构是群体在从t到0和t到T的两个方向上聚结，使得在时间0和T时仅存在一个所考虑的等位基因谱系。带有选择的Wright-Fisher扩散桥中的谱系比中性模型中的更复杂，但仍然具有从时间t开始在两个方向上分支和合并的种群的属性是（0，T）的元素。等位基因在时间t的频率密度以显示在两个方向上的合并的方式表示。本文提出了一种精确模拟中立型赖特-费希尔电桥的新算法。这是根据知道桥中的频率密度和来自Wright-Fisher扩散的精确模拟得出的。中性赖特-费舍尔桥的谱系也通过分支波利亚瓮来建模，扩展了赖特-费舍尔扩散中的表示。这是一个新的非常有趣的表示，将赖特-费舍尔桥与贝叶斯环境中的经典瓮模型联系起来。(C)2017爱思唯尔公司All rights reserved.
The trajectory of the frequency of an allele which begins at x at time 0 and is known to have frequency z at time T can be modelled by the bridge process of the Wright-Fisher diffusion. Bridges when x = z = 0 are particularly interesting because they model the trajectory of the frequency of an allele which appears at a time, then is lost by random drift or mutation after a time T. The coalescent genealogy back in time of a population in a neutral Wright-Fisher diffusion process is well understood. In this paper we obtain a new interpretation of the coalescent genealogy of the population in a bridge from a time t is an element of (0, T). In a bridge with allele frequencies of 0 at times 0 and T the coalescence structure is that the population coalesces in two directions from t to 0 and t to T such that there is just one lineage of the allele under consideration at times 0 and T. The genealogy in Wright-Fisher diffusion bridges with selection is more complex than in the neutral model, but still with the property of the population branching and coalescing in two directions from time t is an element of (0, T). The density of the frequency of an allele at time t is expressed in a way that shows coalescence in the two directions. A new algorithm for exact simulation of a neutral Wright-Fisher bridge is derived. This follows from knowing the density of the frequency in a bridge and exact simulation from the Wright-Fisher diffusion. The genealogy of the neutral Wright-Fisher bridge is also modelled by branching Polya urns, extending a representation in a Wright-Fisher diffusion. This is a new very interesting representation that relates Wright-Fisher bridges to classical urn models in a Bayesian setting. (C) 2017 Elsevier Inc. All rights reserved.