Diffusion processes and coalescent trees

Diffusion processes and coalescent trees
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扩散过程和聚结树

DOI：
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发表时间：
2010
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影响因子：
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通讯作者：
Dario Spanò
Dario Spanò
中科院分区：
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文献类型：
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作者：
R. Griffiths;Dario Spanò

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我们谨将本文献给约翰·金曼爵士 70 岁生日。 在现代数学群体遗传学中，祖先的历史 约翰·金曼（John Kingman）描述了过去的一组基因 合并树。经典和现代方法模拟基因频率 通过扩散过程。本文部分是综述，讨论了 分析中聚结过程如何与扩散过程对偶 和概率感。 Bochner (1954) 和 Gasper (1972) 对表征感兴趣 具有 Beta 平稳分布和雅可比多项式的过程 特征函数。我们讨论与赖特-费舍尔扩散的联系 以及这些过程的特征。隶属于赖特·费希尔 扩散属于这种类型。逆高斯从属函数在从属赖特-费希尔扩散中非常有趣且重要，并且是 与正交多项式理论中的雅可比泊松核相关。 金曼中非突变边缘的相关时间从属森林 聚结剂是新颖的。
We dedicate this paper to Sir John Kingman on his 70th Birthday. In modern mathematical population genetics the ancestral history of a population of genes back in time is described by John Kingman’s coalescent tree. Classical and modern approachesmodel gene frequencies by diffusion processes. This paper, which is partly a review, discusses how coalescent processes are dual to diffusion processes in an analytic and probabilistic sense. Bochner (1954) and Gasper (1972) were interested in characterizations of processes with Beta stationary distributions and Jacobi polynomial eigenfunctions. We discuss the connection with Wright-Fisher diffusions and the characterization of these processes. Subordinated Wright-Fisher diffusions are of this type. An Inverse Gaussian subordinator is interesting and important in subordinated Wright-Fisher diffusions and is related to the Jacobi Poisson Kernel in orthogonal polynomial theory. A related time-subordinated forest of non-mutant edges in the Kingman coalescent is novel.