Hellin's law states that if the twinning rate is w, then the triplet rate is w2, the quadruplet rate is w3, and so forth. The opinion of today is that Hellin's law holds only approximately. In this study the inaccuracy of Hellin's law is studied and the discrepancies are explained mathematically. In our earlier studies we built linear models for the twinning rate. Because most of the mothers are younger than 40 years of age and because in this age interval the twinning rate depends linearly on age, linear regression methods have been applied. Hellin's law suggests using the square-root transformation of the triplet rate r. Statistical arguments speak in favor of using the arcsin square root of r transformation. We discuss both transformations. Despite the fact that Hellin's law is only approximate, the arcsin transformation proves valuable. The transformed triplet rate can be modeled in a way similar to the twinning rate. We consider secular data from Finland for 1881-1990 and from Sweden since 1751. Using Hellin's law, we compare the triplet rates and the twinning rates and study the time trends of the observed twinning and triplet rates. The data are standardized. Our theoretical results are applied to multiple maternity data for Finland. Using maternal age as the regressor, we build a linear model for the twinning rate and for the arcsin-transformed triplet rate. This analysis shows a decreasing linear time trend in the triplet series for the period 1881-1950 but not in the twinning series. The triplet rate has an increasing trend after 1960, which seems to be mainly caused by artificial induction of ovulation.
Pedigree data are analyzed in order to determine the factors responsible for the high frequencies of certain genetic disorders in an isolated Swedish-speaking population of Finland's A land archipelago. The founders of Sottunga are identified, and the genetic contributions of each founder to descending birth cohorts are estimated. Founders born before 1700 have far more descendants in the contemporary gene pool than do more recent founders. However, because of migration and depopulation since 1900, the expected genetic contributions of the early founders to the present-day population are similar to those of later founders. A descendant in the contemporary population has a 2% chance of having inherited a particular gene from the founder who makes the largest single contribution to the gene pool. This corresponds approximately to a 2% probability of inheriting an autosomal dominant disease gene from this founder. Given an average inbreeding coefficient of 0.0016, the probability of inheriting two recessive disease genes from this founder is 0.000032. The incidence of autosomal dominant von Willebrand disease in Sottunga is greater than 10% while that of autosomal recessive tapetoretinal disease is 1.5%. We conclude, therefore, that the high frequencies of these diseases are not due to the disproportionate genetic contribution of one or a few particular founders. It is more likely that these disease genes occurred in high frequency in the initial population or were introduced repeatedly through time.
A genetic analysis of marital migration in Kitee, Finland, is presented. The data are based on 9970 marriages which took place between 1750 and 1877. The results of this analysis are compared with those of previous studies of the population of the Aland Islands, Finland. Analysis of inter-subdivision genetic kinship matrices shows that genetic heterogeneity in Kitee is substantially less than in Aland. This is due primarily to higher rates of migration, both between subdivisions and from outside the population, in Kitee compared to Aland. These differences in migration rates can in turn be attributed to greater geographic isolation in Aland and the contrasting social structures of the two populations. Because of differences in geographic structure and population distribution, geographic distance between subdivisions is a better predictor of inter-subdivision genetic kinship in Kitee than in Aland. The Aland Islands are known to have high frequencies of several otherwise rare genetic diseases; in addition, these diseases are distributed very non-randomly among Aland's subdivisions. The genetic structure results presented here suggest that Kitee should have a less unique distribution of genetic diseases.
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.
Linear regression models are used to explain the variations in the twinning rates. Data sets from different countries are analysed and maternal age, parity and marital status are the main regressors. The model building technique is also used in order to study the secular decline in the twinning rate. Linear regression technique makes it possible to compare the effect of different factors but the method requires sufficiently disaggregated data.
Twinning rates were studied in Swedes, Aland Islanders, Finns, Germans, and Dutch during years of starvation when death rates were two to three times higher than average. In contrast to the situation among some animals, this study suggests that nutrition above a certain threshold is unimportant for human reproduction, including twinning. The twinning rates for these different populations display marked temporal differences, but low values in the twinning rate are not consistently associated with periods of epidemics, famine, or similar nutritional stress. After years of privation and/or separation of spouses, a rapid "catch-up effect" can often be seen in the twinning rates, as well as marriage and birth rates. Psychoendocrine factors and interparental immunological conditions that may be involved in this phenomenon are discussed.