Kimura M
J Mol Evol. 1980 Dec;16(2):111-20. doi: 10.1007/BF01731581.
Some simple formulae were obtained which enable us to estimate evolutionary distances in terms of the number of nucleotide substitutions (and, also, the evolutionary rates when the divergence times are known). In comparing a pair of nucleotide sequences, we distinguish two types of differences; if homologous sites are occupied by different nucleotide bases but both are purines or both pyrimidines, the difference is called type I (or "transition" type), while, if one of the two is a purine and the other is a pyrimidine, the difference is called type II (or "transversion" type). Letting P and Q be respectively the fractions of nucleotide sites showing type I and type II differences between two sequences compared, then the evolutionary distance per site is K = -(1/2) ln [(1-2P-Q) square root of 1-2Q]. The evolutionary rate per year is then given by k = K/(2T), where T is the time since the divergence of the two sequences. If only the third codon positions are compared, the synonymous component of the evolutionary base substitutions per site is estimated by K'S = -(1/2) ln (1-2P-Q). Also, formulae for standard errors were obtained. Some examples were worked out using reported globin sequences to show that synonymous substitutions occur at much higher rates than amino acid-altering substitutions in evolution.
我们得到了一些简单的公式，这些公式能让我们根据核苷酸替换的数量来估计进化距离（当分歧时间已知时，还能估计进化速率）。在比较一对核苷酸序列时，我们区分两种类型的差异；如果同源位点被不同的核苷酸碱基占据，但两者都是嘌呤或都是嘧啶，这种差异就称为I型（或“转换”型），而如果两者之一是嘌呤，另一个是嘧啶，这种差异就称为II型（或“颠换”型）。设P和Q分别为所比较的两个序列之间显示I型和II型差异的核苷酸位点的比例，那么每个位点的进化距离为K = -(1/2) ln [(1 - 2P - Q) √(1 - 2Q)]。每年的进化速率则由k = K/(2T)给出，其中T是两个序列分歧以来的时间。如果只比较第三个密码子位置，每个位点进化碱基替换的同义成分由K'S = -(1/2) ln (1 - 2P - Q)估计。此外，还得到了标准误差的公式。利用已报道的珠蛋白序列给出了一些例子，以表明在进化过程中同义替换的发生速率比改变氨基酸的替换要高得多。
