A mathematical model for recurrent twinning

In an attempt to improve our understanding of the factors that affect human twinning, we further developed the models given by Hellin (1895) and Peller (1946). The connection between these models and our own model ("Fellman's law") were studied. These attempts have resulted in a more general model, which was then applied to data from Aland Islands (1750-1939), Nmes (1790-1875), Stuttgart (about 1790-1900) and Utah (1850-1900). The product of the mean sibship size and the total twinning rate can be considered as a crude estimate of the expected number of sets of twins in a sibship. The same can be said about the twinning parameter in our model. These estimates are in good agreement. If we consider twinning data only, we obtain the geometric distribution, and log (Nk), where Nk is the number of mothers with k twin maternities, is a linear function of the number of recurrences. Graphically, this property can easily be checked. For sibships containing three or more sets of twins, all four populations show higher values than expected, particularly the populations from Stuttgart and Utah, which data also show poor agreement according to a chi 2-test. A more exact model would demand more detailed demographic information, such as distribution of sibship sizes, age-specific twinning rates and temporal variations in twinning. The observed number of mothers in Aland with several recurrences of multiple maternities shows a considerable excess over the expected number as predicted by Peller's rule. The parameters in our model can be estimated by the maximum likelihood method and the obtained model fits the data better then Peller's model.