Griffiths R C, Tavaré S
Department of Mathematics, Monash University, Clayton, Australia.
Math Biosci. 1995 May;127(1):77-98. doi: 10.1016/0025-5564(94)00044-z.
The infinitely-many-sites process is often used to model the sequence variability observed in samples of DNA sequences. Despite its popularity, the sampling theory of the process is rather poorly understood. We describe the tree structure underlying the model and show how this may be used to compute the probability of a sample of sequences. We show how to produce the unrooted genealogy from a set of sites in which the ancestral labeling is unknown and from this the corresponding rooted genealogies. We derive recursions for the probability of the configuration of sequences (equivalently, of trees) in both the rooted and unrooted cases. We give a computational method based on Monte Carlo recursion that provides approximates to sampling probabilities for samples of any size. Among several applications, this algorithm may be used to find maximum likelihood estimators of the substitution rate, both when the ancestral labeling of sites is known and when it is unknown.
无限位点过程常被用于对DNA序列样本中观察到的序列变异性进行建模。尽管它很受欢迎，但该过程的抽样理论却相当难以理解。我们描述了该模型背后的树结构，并展示了如何用它来计算序列样本的概率。我们展示了如何从一组祖先标记未知的位点生成无根谱系，并由此得到相应的有根谱系。我们推导了有根和无根情况下序列（等同于树）配置概率的递归公式。我们给出了一种基于蒙特卡罗递归的计算方法，它能为任意大小的样本提供抽样概率的近似值。在多个应用中，该算法可用于在已知和未知位点祖先标记的情况下找到替换率的最大似然估计值。
