Université Joseph Fourier Grenoble 1, Institut Fourier UMR 5582 UJF-CNRS, 100 rue des Maths, BP 74, 38402 Saint Martin d'Hères, France.
Math Biosci. 2010 Apr;224(2):101-8. doi: 10.1016/j.mbs.2009.12.010. Epub 2010 Jan 11.
We consider models of nucleotidic substitution processes where the rate of substitution at a given site depends on the state of the neighbours of the site. We first estimate the time elapsed between an ancestral sequence at stationarity and a present sequence. Second, assuming that two sequences are issued from a common ancestral sequence at stationarity, we estimate the time since divergence. In the simplest non-trivial case of a Jukes-Cantor model with CpG influence, we provide and justify mathematically consistent estimators in these two settings. We also provide asymptotic confidence intervals, valid for nucleotidic sequences of finite length, and we compute explicit formulas for the estimators and for their confidence intervals. In the general case of an RN model with YpR influence, we extend these results under a proviso, namely that the equation defining the estimator has a unique solution.
我们考虑核苷酸替换过程的模型，其中给定位置的替换率取决于该位置的邻居的状态。我们首先估计从稳定状态的祖先序列到现在序列所经过的时间。其次，假设两个序列来自稳定状态的共同祖先序列，我们估计分歧时间。在最简单的非平凡情况下，即具有 CpG 影响的 Jukes-Cantor 模型，我们在这两种情况下提供并证明了数学上一致的估计量。我们还为有限长度的核苷酸序列提供了渐近置信区间，并为估计量及其置信区间计算了显式公式。在具有 YpR 影响的 RN 模型的一般情况下，我们在一个假定下扩展了这些结果，即定义估计量的方程有唯一解。
