A founder effect can account for the presence of an allele at an unusually high frequency in an isolated population if the allele is selectively neutral and if all copies are identical by descent with a copy that either was carried by a founder individual or arose by mutation later. Here, a statistical test of both aspects of the founder-effect hypothesis is developed. The test is performed by a modified version of a program that implements the Slatkin-Bertorelle test of neutrality. The test is applied to several disease-associated alleles found predominantly in Ashkenazi Jews. Despite considerable uncertainty about the demographic history of Ashkenazi Jews and their ancestors, available genetic data are consistent with a founder effect resulting from a severe bottleneck in population size between a.d. 1100 and a.d. 1400 and an earlier bottleneck in a.d. 75, at the beginning of the Jewish Diaspora. The relatively high frequency of alleles causing four different lysosomal storage disorders, including Tay-Sachs disease and Gaucher disease, can be accounted for if the disease-associated alleles are recessive in their effects on reproductive fitness.