How often are polymorphic restriction sites due to a single mutation?

An approximate expression is obtained for the probability that a restriction site, which is polymorphic in a random sample, is a site at which two or more mutations have occurred in the descent to the sample from the most recent common ancestor of the sample. The analysis is based on the assumption that the population from which the sample is obtained is at equilibrium under a selectively neutral Wright-Fisher model. Monte Carlo simulations show that the approximation is quite accurate. For commonly observed levels of genetic variation in humans and in natural populations of Drosophila, it is found that multiple mutations would occur at 5 to 10 percent of polymorphic restriction sites assuming that six-cutter enzymes are used on samples of size 50 to 100. Simulations are also used to investigate the bias and mean square error of four estimators of 4Nu, where N is the population size and u is the neutral mutation rate per nucleotide site. Two of the estimators are biased by approximately 20 percent when levels of variation are similar to those which have been observed in natural populations of Drosophila.