arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1806.01416q-bio.PEq-bio.QMstat.CO
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群体遗传学中的相型分布

Phase-type distributions in population genetics

Asger Hobolth, Arno Siri-Jégousse, Mogens Bladt

摘要:

DNA序列进化的概率模型已经建立,并为理解来自一个或多个种群的个体样本之间的遗传变异提供了丰富的框架。我们表明,无论是经典的和最近的聚结模型(有或没有重组)可以描述在所谓的相型理论,其中复杂和繁琐的计算是规避使用矩阵。相型理论的应用包括通过适当地建立状态空间并计算相应的强度和奖励矩阵来将随机模型描述为马尔可夫模型。感兴趣的公式,然后表示在这些上述矩阵。我们说明了这几个例子计算的平均值,方差,甚至更高阶的时刻的网站频谱在多个合并模型,并通过分析的平均值和方差的分离位点的数量为多个样品中的两个位点的祖先重组图。我们相信,相型理论作为分析群体遗传学中概率模型的工具具有很大的潜力。紧凑的矩阵符号是有用的澄清目前的模型,特别是他们的正式操作(计算),但也为进一步的发展或扩展。

英文摘要:

Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We show that both classical and more recent models for coalescence (with or without recombination) can be described in terms of the so-called phase-type theory, where complicated and tedious calculations are circumvented by the use of matrices. The application of phase-type theory consists of describing the stochastic model as a Markov model by appropriately setting up a state space and calculating the corresponding intensity and reward matrices. Formulae of interest are then expressed in terms of these aforementioned matrices. We illustrate this by a few examples calculating the mean, variance and even higher order moments of the site frequency spectrum in the multiple merger coalescent models, and by analysing the mean and variance for the number of segregating sites for multiple samples in the two-locus ancestral recombination graph. We believe that phase-type theory has great potential as a tool for analysing probability models in population genetics. The compact matrix notation is useful for clarification of current models, in particular their formal manipulation (calculation), but also for further development or extensions.

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