TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI.
TRACTABLE DIFFUSION AND COALESCENT PROCESSES FOR WEAKLY CORRELATED LOCI.
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DOI：
10.1214/ejp.v20-3564
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发表时间：
2014-05
影响因子：
1.4
通讯作者：
P. A. Jenkins;P. Fearnhead;Yun S. Song
中科院分区：
文献类型：
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作者：
P. A. Jenkins;P. Fearnhead;Yun S. Song
遗传学中广泛使用的模型包括Wright-Fisher扩散及其时刻对偶，Kingman's coalescent。每一个都有一个多轨迹可拓，但在两个可拓下都没有封闭的抽样分布，计算非常困难。本文推导了两个新的多位点群体遗传模型，一个是扩散过程，另一个是凝聚过程，它们比标准模型简单得多，但却捕捉到了它们在大重组率下的关键特性。扩散模型基于密度相关总体过程的中心极限定理，我们证明了抽样分布是高斯分布的矩的线性组合，因此可以以封闭形式获得。合并过程是基于祖先重组图的概率耦合到一个更简单的家谱过程，它揭示了前者的主要动态。进一步证明，当我们把抽样分布看作复合参数的逆幂渐近展开式时，新模型的抽样分布直到前两阶都与标准模型一致。
Widely used models in genetics include the Wright-Fisher diffusion and its moment dual, Kingman's coalescent. Each has a multilocus extension but under neither extension is the sampling distribution available in closed-form, and their computation is extremely difficult. In this paper we derive two new multilocus population genetic models, one a diffusion and the other a coalescent process, which are much simpler than the standard models, but which capture their key properties for large recombination rates. The diffusion model is based on a central limit theorem for density dependent population processes, and we show that the sampling distribution is a linear combination of moments of Gaussian distributions and hence available in closed-form. The coalescent process is based on a probabilistic coupling of the ancestral recombination graph to a simpler genealogical process which exposes the leading dynamics of the former. We further demonstrate that when we consider the sampling distribution as an asymptotic expansion in inverse powers of the recombination parameter, the sampling distributions of the new models agree with the standard ones up to the first two orders.