Recent European fertility patterns: Fitting curves to ‘distorted’ distributions

Recent patterns of fertility in Europe show marked differences between countries. Recent United Kingdom and Irish fertility curves show ‘distortions’ in terms of a ‘bulge’ in early age fertility, distinct from the smoother curves of other European countries. These patterns may not be adequately described by mathematical functions used by previous studies to model fertility curves. A mixture model with two component distributions may be more appropriate. The suitability of the simple and mixture Hadwiger functions is examined in relation to the fertility curves of a number of European countries. While the simple Hadwiger model fits recent period age-specific fertility distributions for some countries, others which display a ‘bulge’ in early age fertility require a mixture Hadwiger model. Some of the parameters of the Hadwiger models appear to be related to familiar demographic indices. The simple and mixture Hadwiger models appear useful in describing and comparing fertility patterns across European countries.     

The trend of intelligence in certain districts of England

An estimate of the change in intelligence in ten English education authorities during the past 10 years has been made by comparing the scores of complete year groups of 11-year-old children in 1947 with scores made by similar groups in the same test on an earlier occasion. The first test was taken by 31,728 children and the second by 28,505 children, boys and girls in approximately equal numbers.

For boys and girls together there was a fall of 0.0034 point of intelligence quotient per year, which was far from significant. In seven districts where we had separate scores for boys and girls on both occasions there was a significant fall in intelligence quotient of 0.0921 point per year amongst boys and a significant rise of 0.0921 point per year amongst girls.

The adventitious influences which might invalidate a comparison of the two sets of scores have been considered; they probably tend to depress the score at the second test.

A study of sex differences in attainment tests at 11 years and in intelligence tests at 13 years and later suggests that the scores of the boys in 1947 are underestimates of their ability, and that a truer measure of the trend of intelligence amongst the population is represented by the change in the girls' scores.

By assuming a certain parallelism between the present survey and that of the Scottish children, the rise in intelligence quotient of the latter is estimated at 0.0543 point per year.

A significant increase in the dispersion of intelligence test score of both boys and girls during the past 10 years has been recorded.     

The impact of mortality development on the number of centenarians in England and wales

The world is ageing both at an individual and a population level, and population ageing is truly a global phenomenon. Life expectancies at birth have increased at the global level from 47 years in the mid-20th century to around 70 years today, and are expected to rise to 76 years by the mid-21st century. The proportion of the world’s population aged 60 years and over has increased from 8 % in the mid-20th century to 12 %, and by 2050 it is expected to reach 21 %. The emergence of large numbers of centenarians has accompanied this development. This paper outlines this emergence historically and the likely growth in the number of centenarians in the 21st century, in particular in England and Wales, analysing mortality trends since 1840 and the rise in the number of centenarians in the 20th and 21st centuries. The number of centenarians in England and Wales increased from around 160 in 1922 to almost 12,500 by 2012, but if mortality at all ages had remained constant from 1912 to 2012, then by 2012 the number of centenarians would only have been around 720. By 2100, the number of centenarians is expected to reach around 1.4 million, but if future mortality at all ages were to remain constant, then by 2100 the number of centenarians would be around 78,000. However, if predicted mortality for those aged 55 years and over was to decrease by an additional 5 % every 5 years until 2100, then the number of centenarians in England and Wales would reach around 1.8 million by the end of the century.     

Tribal affiliation and fertility: A note

This not extends T. L. F. Devis's recent investigation of the relationship between tribal affiliation and fertility in Sierra Leone. Controls are introduced for age structure and economic variables. The findings suggest that tribal affiliation does not have much independent influence on fertility after these factors are allowed for.     

Comment on ‘Facts and Artifacts in the Study of Intra-Uterine Mortality: A Reconsideration from Pregnancy Histories’ by Henri Léridon1

Extract

I have suggested that at a given birth order the probability of having a further pregnancy is greater when the last pregnancy had been spontaneously aborted than when it resulted in a birth.² Léridon,³in the course of a valuable paper on foetal wastage, presents data which, according to him, impugn my suggestion. I would like to question his claim.     

The estimation of fertility rates from ratios of total to first births

In a previous paper a formula was derived from which the total fertility rate of a group of women could be estimated from the average number of live births to women in the reproductive period. In the present paper the argument is carried further and a method is given by which the total fertility rate may be estimated from the average number of children born to fertile women during the reproductive period. The method given in this paper may, under certain circumstances, have considerable advantages over the previous method suggested.     

A life table for a West Indian slave population

This note comments briefly on the system of slave registration set up in the British colonies, and deals in particular with the data tabulated for the British Guiana slave population in the Parliamentary Papers, 1833. From the age distributions given there a life table has been constructed by a census differencing method. This life table shows the extremely high mortality then being experienced by slave populations in the West Indies.     

“As a Shepherd Divideth his Sheep from the Goats”: Does the Daily Spiritual Experiences Scale Encapsulate Separable Theistic and Civility Components?

Numerous studies suggest spirituality and subjective well-being (SWB) are positively associated. However, critics argue that popular spirituality instruments—including the Daily Spiritual Experiences Scale (DSES)—contain items that conflate religiosity/spirituality (R/S), prosociality and SWB. Advocates of the DSES retort that, despite this concern, the available evidence confirms a single underlying factor. The current paper evaluates the DSES’s development, factor structure, reliability and convergent and predictive validity using a community sample. Despite the full DSES scale’s excellent internal reliability, two related factors—theism and civility—are identified. Both scales are reliable and converge meaningfully with related R/S measures. As expected, given previous findings, the full DSES scale predicts higher SWB yet the two subscales display divergent associations. This finding offers new insights into the DSES and raises questions about the claimed belief-as-benefit effect.     

Pre‐procreative ages in population stability and cyclicity

Age‐specific models of population renewal (with and without feedback) which imply convergence to a stable state for some levels of fertility or feedback may imply the presence of long‐term cycling around a constant or exponentially changing equilibrium for other levels of fertility or feedback. The switch from one regime to the other is a “bifurcation.”; The conditions for bifurcation involve the roots of an analogue of Lotka's Equation.

Typically bifurcation is induced by raising the strength of feedback or the level of fertility. It has been known since the early 1980s, however, that this is sometimes impossible. It is sometimes impossible even with the linear renewal equation itself and with the most basic of non‐linear models, Lee's cohort feedback model.

Here it is proved that this typical route to bifurcation does not fail for these basic models in the presence of a condition which always holds for realistic applications with higher organisms: the existence of a span of ages before the onset of fertility.

Specifically, a strictly positive lower bound on ages of procreation is proved to be sufficient to guarantee the existence of a rescaling of Lotka's Equation for which the real part of some complex root vanishes. This result holds for absolutely Lebesgue‐integrable (signed) net maternity functions on the positive real line and for absolutely summable (signed) net maternities on the positive integers.

It follows that Coale's rescaling device for the analysis of approach to stability in stable population theory can be implemented for all realistic human net maternity schedules. It also follows that the many special cases of the cohort feedback model throughout population biology will all generate persistent cycling instead of stability if feedback is sufficiently strong.