Hellin's law

Hellin's law, also called Hellin-Zeleny's law, is an empirical observation in demography that the approximate rate of multiple births is one n-tuple birth per 89^n-1 singleton births: twin births occur about once per 89 singleton births, triplets about once per 89², quadruplets about once per 89³, and so on.

Origin

Throughout the 1800s demographics registers were becoming more common in Europe, which generated data sets in different administrative regions. There was interest in twin research, and many demographers began studying patterns in birth rates. Analysis by Veit in 1855 of a Prussian data set covering 1826 to 1849 showed the numbers of twin, triplet, and quadruplet maternities were respectively one for every 89, 7910, and 371126 single maternities. Paul Strassmann analyzed the same data in 1889 and noted the rates of twin and triplet maternities were approximately one per 89 and 89², and in 1895 Hellin gave the law a general form. In 1921, Charles Zeleny further analyzed the data and posited that since the rates of multiple maternities can simply be multiplied together, then they were the result of independent processes that occurred with equal frequencies.

References

• Fellman, Johan; Eriksson Aldur W (Apr 2009). "Statistical analyses of Hellin's law". Twin Research and Human Genetics. 12 (2). Australia: 191–200. doi:10.1375/twin.12.2.191. ISSN 1832-4274. PMID 19335191.
• Fellman, Johan; Eriksson Aldur W (Apr 2009). "On the history of Hellin's law". Twin Research and Human Genetics. 12 (2). Australia: 183–90. doi:10.1375/twin.12.2.183. ISSN 1832-4274. PMID 19335190.
• Fellman, John (Dec 2017). "Aspects of the History of Twin Research: Statistical Congresses in the 19th Century and Hellin's Law". Twin Research and Human Genetics. 21 (1): 57–66. doi:10.1017/thg.2017.68. PMID 29258629.
• Hellin, D. (1895). Die Ursache der Multiparität der uniparen Tiere überhaupt und der Zwillingsschwangerschaft beim Menschen insbesondere. München: Seitz und Schauer. p. 25. Während man sagen kann, dass beim Menschen durchschnittlich eine Zwillingsgeburt auf etwa 89 einfache Geburten vorkommt tritt eine Drillingsgeburt auf (89)² einfache Geburten auf, eine Vierlingsgeburt auf (89)³; überhaupt, soweit dies in Grenzen der Möglichkeit liegt, erscheint eine x fache Geburt auf (89)^x–1 einfache Geburten.
• Zeleny, Charles (Mar 1921). "The Relative Numbers of Twins and Triplets". Science. 53 (1368): 262–263. Bibcode:1921Sci....53..262Z. doi:10.1126/science.53.1368.262. PMID 17794418.