Evolutionary change of restriction sites under unequal rates of nucleotide substitution among the three positions of codons

Summary Under the assumption of unequal rates of nucleotide substitution among the three positions of codons, mathematical formulas are derived for the probability that a restriction site observed at time 0 in a DNA sequence will be present at time t, the probability that a new restriction site will emerge at a particular place in two descendant sequences, and the proportion of identical restriction sites between two such sequences. All three quantitites are shown to be larger for the case of unequal rates than for the case of equal rates. As a consequence, estimates of nucleotide divergence (2t) between two sequences based on restriction-site data tend to be lower than the actual values of the assumption of equal rates is made but actually does not hold. However, the degree of underestimation is slight if 2t is 0.10 or smaller. The underestimation can be serious when 2t becomes 0.20 or larger, particularly if the substitution rates at the three codon positions are very different or if transitional substitution occurs more frequently than transversional substitution. The underestimation is more serious for four-base enzymes than for sixbase enzymes.