Aspects of the History of Twin Research: Statistical Congresses in the 19th Century and Hellin's Law

In the 19th century, a series of international statistical congresses began that were important for population studies, including twin research. The introduction of common rules for the national demographic registers enabled scientists to contribute to the genesis of statistical research. The congress in St. Petersburg in 1872, in particular, focused on the movements of the population, and how they should be registered. Among the facts to be recorded were in multiple births, the sex and number of children born alive or still-born, whether legitimate or illegitimate, and the age of the mother at the date of the births. During the history of twin research, Hellin's law has played a central role because it is an approximately correct association between the rates of multiple maternities. It has been mathematically proven that Hellin's law does not hold as a general rule. Analyses show divergences from the law that are difficult to explain and/or eliminate. Varying improvements of this law have been proposed. The majority of all studies of Hellin's law are based on empirical rates of multiple maternities, ignoring random errors. Such studies can never confirm the law, but only identify errors with respect to Hellin's law that are too large to be characterized as random. It is of particular interest to note and explain why the rates of higher multiple maternities are sometimes too high or too low when Hellin's law is used as a benchmark. Studies have shown that there were investigators before Hellin who have contributed substantially to Hellin's law. In this article, we re-examine some old data sets and contributions in which Hellin's law has been evaluated and also analyze recent data.