分子进化中取代数方差的一个简单而普遍的结果
A simple, general result for the variance of substitution number in molecular evolution
摘要：
取代（核苷酸、氨基酸、.）在序列进化过程中发生的变化是分子进化领域中具有根本重要性的随机变量。虽然在一个序列的分子进化过程中的平均取代数可以估计为一个给定的替代模型，没有简单的解决方案存在的方差这个随机变量。在这篇文章中，我们表明，方差的计算是一样简单的，无论是短时间和长时间的替代的平均数。除了它的基本重要性，这个结果可以用来研究分散指数R，即方差与平均取代数的比值，这在分子进化的中性学说〈动〉<动>中是最重要的。通过调查大类的替代模型，我们证明，虽然R \ge 1，以获得R显着大于单位需要在一般情况下额外的假设结构的替代模型。
英文摘要：
The number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random variable. We show in this article that the computation of the variance is as simple as that of the mean number of substitutions for both short and long times. Apart from its fundamental importance, this result can be used to investigate the dispersion index R , i.e. the ratio of the variance to the mean substitution number, which is of prime importance in the neutral theory of molecular evolution. By investigating large classes of substitution models, we demonstrate that although R\ge1 , to obtain R significantly larger than unity necessitates in general additional hypotheses on the structure of the substitution model.
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