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.