Estimation of evolutionary distances between homologous nucleotide sequences.

By using two models of evolutionary base substitutions--"three-substitution-type" and "two-frequency-class" models--some formulae are derived which permit a simple estimation of the evolutionary distances (and also the evolutionary rates when the divergence times are known) through comparative studies of DNA (and RNA) sequences. These formulae are applied to estimate the base substitution rates at the first, second, and third positions of codons in genes for presomatotropins, preproinsulins, and alpha- and beta-globins (using comparisons involving mammals). Also, formulae for estimating the synonymous component (at the third codon position) and the standard errors are obtained. It is pointed out that the rates of synonymous base substitutions not only are very high but also are roughly equal to each other between genes even when amino acid-altering substitution rates are quite different and that this is consistent with the neutral mutation-random drift hypothesis of molecular evolution.