Association Between the Rates of Multiple Maternities

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Theorems, proofs, laws and rules are commonly named according to the presumed investigator, but often earlier investigators have contributed substantially to the findings. One example of this is Hellin's law, which was named after Hellin, although he was not the first to discover it. In research on twinning and higher multiple maternities, the law has played a central role because it is approximately correct, despite showing discrepancies that are difficult to explain or eliminate. Several improvements to this law have been proposed. In this study, we re-examine some old papers to provide an overview of the scientists who have contributed to the genesis and the improvements of this law. In addition, we consider more recent contributions in which Hellin's law has been discussed and evaluated. It has been mathematically proven that Hellin's law does not hold as a general rule. However, most studies are based on empirical rates of multiple maternities, ignoring random errors. Such studies can never confirm the law, but only serve to identify errors too large to be characterized as random.

mentioning

confidence: 99%

mentioning

confidence: 99%

On the History of Hellin's Law

Fellman¹,

Eriksson

2009

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“…Fellman and Eriksson (2004) considered the correlation between the TWR and the square root of the TRR in Sweden. After elimination of influential temporal factors, they found that the correlation was positive, but not very strong.…”

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confidence: 99%

Statistical Analyses of Hellin's Law

Fellman

Eriksson²

2009

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During the history of research on multiple maternities, Hellin's law has played a central role as a rule of thumb. It is mathematically simple and approximately correct, but shows discrepancies that are difficult to explain or to eliminate. It has been mathematically proven that Hellin's law does not hold as a general rule. Varying improvements to this law have been proposed. In this paper, we consider how Hellin's law can be used and tested in statistical analyses of the rates of multiple maternities. Such studies can never confirm the law, but only identify errors too large to be characterized as random. It is of particular interest to determine why the rates of higher multiple maternities are sometimes too high or too low when Hellin's law is used as a benchmark. Excesses of triplet and quadruplet maternities are particularly unexpected and challenging. Our analyses of triplet and quadruplet rates indicated that triplet rates are closer to Hellin's law than quadruplet rates. According to our analyses of the twinning rate and the transformed triplet rate and quadruplet rate for Sweden , both triplet and quadruplet rates showed excesses after the 1960s. This is mainly caused by artificial fertility-enhancing reproduction technologies. Regression analyses of twinning and triplet rates yield rather good fits, but deficiencies in the triplet rates are commonly present. We introduced measures of concordance between triplet rates with Hellin's law. According to these measures, historic data showed deficiencies in triplet rates, but recent data revealed excesses, especially found among older mothers. The excesses obtained are in good agreement with other studies of recent data.

“…Fellman and Eriksson (2004) stressed that in population studies the Hellin-transformed triplet rate can be compared with the twinning rate. We now evaluate how this holds in sibship studies.…”

Section: Twin Research and Human Geneticsmentioning

confidence: 99%

Repeated Multiple Maternities in Triplet Families

Fellman

Eriksson

2014

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In earlier studies, scientists have attempted to identify genetic and environmental factors affecting the rate of multiple maternities among humans. We contribute to these studies by analysing the frequencies of multiple maternities in sibships containing triplets. Use of the Hellin transformation is included in evaluation of the triplet rate. Our results indicate greater frequencies of repeated multiple maternities in the sibships than expected, based on population frequencies. The excesses obtained are more marked in triplet maternities than in twin maternities. The transformed triplet rate shows results similar to the twinning rate. The findings also indicate that in families, the influence of maternal factors on the frequencies of multiple maternities is stronger than the influence of paternal factors.Key words: Hellin's law, maximum likelihood, probability models, parameter transformationsStudies have been performed to identify genetic and environmental factors affecting the rate of multiple maternities among humans (e.g., Bulmer, 1970;Weinberg, 1902). Fellman and Eriksson (1990) developed models previously presented by Hellin (1895), Peller (1946), andEriksson et al. (1973). They presented the probability model:where P st is the probability that a sibship contains s twin pairs and t triplet sets, w is the probability of a twin set and r is the probability of a triplet set. However, they had no information about sibships without twin pairs and triplet sets. Fellman and Eriksson (1990) stressed that a sibship could be included in their study only if it contained multiple maternities. Consequently, their data sets resulted in the distribution being truncated and they had to cope with the conditional probabilityThis truncation complicated the parameter estimation. They needed to apply iterative numerical processes in order to obtain maximum likelihood estimates .In this study, we modify the Fellman-Eriksson model so that it can be applied to sibships that contain triplet sets. Material and Methods MaterialOur data consist of sibships containing triplets initially presented by Miettinen (1954). We have studied these data in different contexts (Eriksson & Fellman, 1986;Eriksson et al., 1990Eriksson et al., , 2007Fellman & Eriksson, 2014). The family data set comprises triplets born in Finland from 1905 to 1959. During this period, 723 triplet sets were registered in the official Finnish birth records. Using genealogical studies, sibships of the triplets and of their parents were collected. The genealogical investigations, initiated by Miettinen (1954) and continued by our group, resulted in birth information for 642 sibships of triplets containing 650 triplet sets and 125 twin pairs. Consequently, almost 90% of all officially registered triplet sets were included in our family series. Our data are presented in Table 1.For sake of comparison, we include in this study the distributions of multiple maternities in sibships of the triplet mothers and triplet fathers. There are 587 sibships of mothers containing 3 tri...