Two demographic scenarios are considered: two populations with migration and two populations that have been completely isolated from each other for some period of time. The variance of the number of differences between pairs of sequences in a single sample is studied and forms the basis of a test of the isolation model. The migration model is one possible alternative to isolation. The isolation model is rejected when the proposed test statistic, which involves the variances of pairwise difference within and between populations, is larger than some critical value. The power and realized significance of the test are investigated using simulations, and an example using mitochondrial DNA illustrates its application.