A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences

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.