Feldman M W, Bergman A, Pollock D D, Goldstein D B
Department of Biological Sciences, Stanford University, California 94305, USA.
Genetics. 1997 Jan;145(1):207-16. doi: 10.1093/genetics/145.1.207.
Statistical properties of the symmetric stepwise-mutation model for microsatellite evolution are studied under the assumption that the number of repeats is strictly bounded above and below. An exact analytic expression is found for the expected products of the frequencies of alleles separated by k repeats. This permits characterization of the asymptotic behavior of our distances D1 and (delta mu)2 under range constraints. Based on this characterization we develop transformations that partially restore linearity when allele size is restricted. We show that the appropriate transformation cannot be applied in the case of varying mutation rates (beta) and range constraints (R) because of statistical difficulties. In the special case of no variation in beta and R across loci, however, the transformation simplifies to a usable form and results in a distance much more linear with time than distances developed for an infinite range. Although analytically incorrect in the case of variation in beta and R, the simpler transformation is surprisingly insensitive to variation in these parameters, suggesting that it may have considerable utility in phylogenetic studies.
在重复数严格有上下界的假设下，研究了微卫星进化的对称逐步突变模型的统计特性。找到了由k个重复分隔的等位基因频率的期望乘积的精确解析表达式。这使得我们能够刻画在范围限制下距离D1和（δμ）2的渐近行为。基于此刻画，我们开发了一些变换，当等位基因大小受到限制时，这些变换能部分恢复线性。我们表明，由于统计上的困难，在突变率（β）和范围限制（R）变化的情况下，无法应用适当的变换。然而，在β和R在不同基因座间无变化的特殊情况下，该变换简化为一种可用形式，并且得到的距离随时间的线性程度比为无限范围开发的距离高得多。尽管在β和R变化的情况下分析上不正确，但这个更简单的变换对这些参数的变化出人意料地不敏感，这表明它在系统发育研究中可能有相当大的用途。
