Johan Fellman

Weinberg's Differential Rule Reconsidered

ABSTRACT A central problem in research on twins is the estimation of the rates of monozygotic and dizygotic twin maternities. The estimation usually follows Weinbergs differential rule. According to this rule, the rate of dizygotic twinning is twice the rate of twin maternities in which the twins are of opposite sex. The monozygotic twinning rate is the difference between the rates of same-sex and opposite-sex twin sets. Weinbergs differential rule is implicitly based on the assumptions that the probability of a male equals the probability of a female and that the sexes in a dizygotic twin set are independent. Although Weinbergs differential rule has been the target of continuing discussions, the reliability of these assumptions has never been conclusively verified or rejected. In this study we present new variance formulas for the monozygotic and dizygotic twinning rates obtained using Weinbergs differential rule and stress that these new formulas have to be used. We analyze the accuracy of Weinbergs differential rule by considering alternative attempts. Especially, we build a general likelihood function and show that the maximum-likelihood estimates differ only slightly from the rates obtained using Weinbergs differential rule. In addition, our methods are applied to twinning data from Finland and Sweden. We compare our results with findings in the literature. In conclusion, our findings indicate that Weinbergs differential rule is rather robust and that despite its simplicity, it gives reliable results when official birth registers are analyzed.

Demographic Analysis of the Variation in the Rates of Multiple Maternities in Sweden Since 1751

To elucidate the causes and mechanisms of twinning and higher multifetal maternities, we have taken advantage of the statistical sources of Sweden, where continuous statistics for the whole population are the oldest available. We found strong secular and regional fluctuations. The rates of multiple maternities were the highest during the last three decades of the 18th century, when the twinning rate was more than 17 per 1,000, the triplet rate was more than 3 per 10,000, and the quadruplet rate was almost 7 per 1 million maternities. During 1849-1873 the twinning rate in Sweden was 14.2 per 1,000, but this rate showed great regional differences, being 18.0 per 1,000 on the island of Gotland and 12.6 per 1,000 in the county of Älvsborg. During this period the twinning rate in the countryside in the county of Stockholm was 20.4, but in the city of Stockholm it was only 14.1 per 1,000. In Sweden after the 1930s there was a marked decrease in the twinning rate, which by the 1960s had fallen to only about half of what it had been two centuries earlier. The corresponding reductions for triplet and quadruplet rates were about 75%. The aim of this paper was to study the temporal and regional variations in multiple maternities in Sweden from 1751 to 1960 based on demographic and some socioeconomic data for the counties. We confirmed our earlier studies that maternal age and parity cannot satisfactorily explain the secular and regional differences in the twinning rates. In contrast to studies in France (1901-1968), we found no unequivocal association between the twinning rates and the crude birth rates. The correlation coefficients between the twinning rate and the crude birth rate showed statistically significant regional and temporal variations. After eliminating the temporal trends, regional differences in the correlation coefficients remained. The twinning rates for the counties seem to converge toward a common low level, 10-12 per 1,000. The observed convergence toward relatively similar levels may be caused by the increased matrimonial migration distances and decreased endogamy of the citizens as a consequence of better communications. The increased urbanization and industrialization that started in the last decades of the 19th century broke up the old static agrarian isolates and caused Sweden, within 2-3 generations, to develop from a poor nation to one of the most prosperous in the world. A more urban and affluent lifestyle, a better diet, and increased stress and sedentary occupations may have reduced the physical capacity of mothers to carry gestations with multiple embryos or fetuses to completion.

Stillbirth rates in singletons, twins and triplets in Sweden, 1869 to 2001.

The temporal variation in the stillbirth rates (SBR), measured as the number of stillborn per 1000 total births, among singletons, twins and triplets was studied on Swedish birth data for the period 1869 to 2001 and comparisons with data from other populations were made. Among both single and multiple births there were marked, almost monotonously decreasing trends in the stillbirth rates. Among singletons the stillbirth rate decreased from 29.5 per 1000 in the period 1869 to 1878 to 3.4 in the period 1991 to 2001. Among twins the stillbirth rate decreased from 94 per 1000 in 1869 to 1878 to a minimum of 8.2 in 1991 to 2001 and among triplets from 166 per 1000 to a minimum of 19.8. The relative declining pattern in the SBRs was almost the same, being 88% among singletons, 91% among twins and 88% among triplets. In the 1980s and 1990s the definition of the stillbirth rate was changed in many countries, including Finland, but no changes in the definition of stillbirths have been made in Sweden. The effect of the artificial reproduction techniques, including in vitro fertilization, on the rates of multiple maternities is also discussed. It was noted especially that they had a more marked effect on the triplet than on the twinning rate.

Changes of the eye caused by the climate in Rwanda, Africa.

Rwanda is a small but densely populated country, situated at the watershed between East and West Africa, close to the equator. The mean elevation is around 1500 m. We studied 114 males (mean age 28.42 years) and 111 females (mean age 29.84 years) at the ophthalmological outpatient department of the Centre Hospitalier in Kigali. Changes to the eye caused by the climate were fewer than expected. Only 10 patients (5 males, 5 females) with pterygium (mean age 33.0 years), and four males and two females with climatic droplet keratopathy (mean age 47.5 years) were observed. However, the size of the pinguecula was marked. Corneal thickness, measured with Haag-Streits device, averaged 0.524 mm in 38 males and 0.521 mm in 38 females. The Rwandans showed a normal chamber depth, a mean of 2.98 mm being noted in 107 males and a mean of 2.80 mm in 106 females.

Temporal differences in the regional twinning rates in Sweden after 1750.

When twinning rates are studied, maternal age and parity should be considered. Data on parity are seldom available. We studied information about the mean parity, using the gross reproduction rate, the total fertility rate and the crude birth rate. These are strongly correlated with the mean parity. The crude birth rate is more readily available than the gross reproduction rate or the total fertility rate. Earlier studies have shown that it is difficult to model variations in the twinning rate with data for the macrolevel. In this study these findings are explained by theoretical analyses and illustrated by empirical data. Sweden, having the oldest continuous population statistics and high twinning rates, offers excellent possibilities for analyses of the twinning rate. We considered data for the counties of Gotland, Alvsborg and Stockholm and the city of Stockholm from 1749 to 1960 and for Sweden until 1996. For Alvsborg, the twinning rate was low for the whole period, showing no statistically significant decreasing trend. It is mainly about 11-14 per thousand, which is only 50-60% of the twinning rate in Gotland in the 18th century. In Gotland, in the county of Stockholm, in the city of Stockholm and in Sweden as a whole, the decreasing trends in the twinning rate were statistically significant. The decreasing twinning rates converge towards the low twinning rate of Alvsborg. After standardization of the twinning rate, the differences remained and the low rate in Alvsborg could not be explained by maternal age.

Temporal trends in the secondary sex ratio in Nordic countries.

Attempts have been made to identify factors influencing the number of males per 100 females at birth, also called the secondary sex ratio. It has been proposed to vary inversely with the frequency of prenatal losses, but available data lend at best only weak support for this hypothesis. Statistical analyses have shown that comparisons between secondary sex ratios demand large data sets. Variations in the secondary sex ratio that have been reliably identified in family data have mostly been slight and without a notable influence on national birth registers. For Sweden, 1751–1950, the secondary sex ratio among all births and live births revealed increasing trends. The Swedish results are compared with available findings for live births in Finland, Norway, Denmark, and the small Icelandic population. For Norway and Denmark, the secondary sex ratio increased during 1801–1950. A similar, but stronger pattern was observed for Finland (1751–1950) and Iceland (1838–1950). During the latter half of the twentieth century, marked decreases were observed in all countries. Attempts to identify reliable associations between secondary sex ratios and stillbirth rates have been made, but no consistent results have emerged.

Variations in the maternal age effect on twinning rates: the Nordic experience.

Maternal age is the most important nongenetic factor influencing the twinning rate. Every study of the effect of other factors should consider the age distribution of the mothers. Besides standardizing techniques, the age-specific twinning rates are analyzed. Especially, the slope of the regression line is considered when the age-specific twinning rates are regressed against maternal age. How well the maximum age-specific twinning rate measures the variation in the maternal age effect is also studied. The two measures, which are strongly correlated, give consistent results. The proposed methods are applied to data from Finland (1866 to 2003) and Denmark (1855 to 2000). Comparisons with Sweden (1861 to 2000) and Norway (1855 to 2003) are also made. In general, marked decreasing trends in the twinning rates are discernible up to the middle of the 20th century. In Sweden the decline starts around the beginning of the 20th century and is stronger than in Denmark and Norway. The decrease in the twinning rate for Finland, which up to World War II was rather isolated, sets in around the middle of the 20th century and is not as strong as in other Nordic countries. After the minima around 1980, strong increasing trends are noted. This is mainly caused by the influence of the artificial reproduction technologies and particularly the use of fertility-enhancing drugs on the commonly noted dependence between maternal age and the twinning rate. Similar temporal trends can be observed in the slopes of the regression line and in the maximum age-specific twinning rates.

Population structure of the Aland Islands, Finland.

The total description of population structure, as so well discussed by Harrison and Boyce,44 requires the integration of biological, social, and demographic data set in an ecological framework. This, by itself, is understood to be an unobtainable and unapproachable goal. Moreover, we recognize that a major aim of population research is to describe and understand the complex evolution of the population structure as well as to describe it at a single point in time. Unfortunately, process as such can never be inferred from structure and thus longitudinal perspectives are obligate. The time span underlying a processual problem varies according to the focus of the research, itself partially limited by human factors and the kinds of data which can be obtained (historical, archeological, demographic, biological, etc.). The study of population structure therefore involves both studies with a short time span, such as analyses of pathological or normal biological development or recent sociohistoric changes, and a long-term perspective on the macroevolutionary history antecedent to the contemporary biological and social structure.

Secondary sex ratio in multiple births.

Attempts have been made to identify factors influencing the sex ratio at birth (number of males per 100 females). Statistical analyses have shown that comparisons between sex ratios demand large data sets. The secondary sex ratio has been believed to vary inversely with the frequency of prenatal losses. This hypothesis suggests that the ratio is highest among singletons, medium among twins and lowest among triplets. Birth data in Sweden for the period 1869-2004 showed that among live births the secondary sex ratio was on average 105.9 among singletons, 103.2 among twins and 99.1 among triplets. The secondary sex ratio among stillbirths for both singletons and twins started at a high level, around 130, in the 1860s, but approached live birth values in the 1990s. This trend is associated with the decrease and convergence of stillbirth rates among males and females. For detailed studies, we considered data for Sweden in 1869-1878 and in 1901-1967. Marital status or place of residence (urban or rural) had no marked influence on the secondary sex ratio among twins. For triplets, the sex ratio showed large random fluctuations and was on average low. During the period 1901-1967, 20 quadruplet, two quintuplet and one sextuplet set were registered. The sex ratio was low, around 92.0.

Association Between the Rates of Multiple Maternities

We analyze the association between the rates of multiple maternities. Correlation analysis is suitable if there are at least monotonic relationships between the variables. A decreasing tendency can be observed in the rates of multiple maternities in Sweden and in its 25 counties for the period 1751-1960 and the effect of external variables can be assumed to be monotonic. After 1960, the rates of multiple maternities show marked increases, mainly caused by ovulation stimulants and the introduction of other artificial reproduction techniques. We transformed the triplet and quadruplet rates according to Hellins law in order to obtain rates on the same scale as the twinning rate. The time trends for the multiple maternities in Sweden as a whole were quite similar. The regional differences in the twinning rates could not be satisfactorily explained by maternal age. Alternative attempts to eliminate the effect of other time-dependent factors were to study partial correlation coefficients when the time was kept fixed and the correlation coefficients based on cross-sectional regional data. Both the ordinary and the partial correlation coefficients showed strong regional variation. Cross-sectional analyses gave correlation coefficients similar to the partial correlation coefficients for Sweden as a whole. The variations in the correlation coefficients between the twinning and the triplet rates seem to be caused by other time-dependent factors and the effects of these factors show strong regional variation. After elimination of such factors, the correlation between the twinning and the triplet rates is moderate.