These mutations have included single base insertions and deletions, splice phase mutations, missense mutations, and other more complex patterns. Each of these mutations alters the genes protein product (i.e., the enzyme), sometimes severely inhibiting its function. In recent years, population studies and pedigree analysis have shown how such mutations arise and spread within small founder populations. Initial research focused on several such founder populations:

Ashkenazi Jews. A four base pair insertion in exon 11 (1278insTATC) results in an altered reading frame for the HEXA gene. This mutation is the most prevalent mutation in the Ashkenazi Jewish population, and leads to the infantile form of Tay–Sachs disease. Cajuns. The same 1278insTATC mutation found among Ashkenazi Jews occurs in the Cajun population of southern Louisiana. Researchers have traced the ancestry of carriers from Louisiana families back to a single founder couple – not known to be Jewish – who lived in France in the 18th century. French Canadians. Two mutations, unrelated to the Ashkenazi/Cajun mutation, are absent in France but common among certain French-Canadian communities living in southeastern Quebec and Acadians from the Province of New Brunswick. Pedigree analysis suggests the mutations were uncommon before the late 17th century.In the 1960s and early 1970s, when the biochemical basis of Tay–Sachs disease was first becoming known, no mutations had been sequenced directly for genetic diseases. Researchers of that era did not yet know how common polymorphisms would prove to be.
Studies of Tay–Sachs mutations using new molecular techniques such as linkage disequilibrium and coalescence analysis have brought an emerging consensus among researchers supporting the founder effect theory. History
Waren Tay and Bernard Sachs were two physicians. They described the diseases progression and provided differential diagnostic criteria to distinguish it from other neurological disorders with similar symptoms.Both Tay and Sachs reported their first cases among Ashkenazi Jewish families. Tay reported his observations in 1881 in the first volume of the proceedings of the British Ophthalmological Society, of which he was a founding member. By 1884, he had seen three cases in a single family. Years later, Bernard Sachs, an American neurologist, reported similar findings when he reported a case of "arrested cerebral development" to other New York Neurological Society members.Sachs, who recognized that the disease had a familial basis, proposed that the disease should be called amaurotic familial idiocy. However, its genetic basis was still poorly understood. Although Gregor Mendel had published his article on the genetics of peas in 1865, Mendels paper was largely forgotten for more than a generation – not rediscovered by other scientists until 1899. Thus, the Mendelian model for explaining Tay–Sachs was unavailable to scientists and doctors of the time. The first edition of the Jewish Encyclopedia, published in 12 volumes between 1901 and 1906, described what was then known about the disease:
It is a curious fact that amaurotic family idiocy, a rare and fatal disease of children, occurs mostly among Jews.