Intrinsic Growth Rates and Net Reproduction Rates in the Presence of Migration

Conventional measures of long‐term population growth such as the intrinsic growth rate and the net reproduction rate assume migration rates to be zero. We develop expressions for analogous measures that register the impact of net migration rates, and we develop a simple method of estimating their values. Applying these new measures to data for developed countries shows that allowance for migration raises net reproduction rates by 0.2‐0.3 in areas of overseas European settlement and by approximately half as much in Northern and Western Europe. The newly defined intrinsic growth rates in Eastern Europe are exceptionally low at ‐1.7 percent to ‐2.4 percent per annum. In contrast, the migration‐adjusted intrinsic growth rate of the United States exceeds those of Asia and Latin America. The formulas and estimation procedures described should allow a more precise understanding of the implications of current migration patterns for long‐term growth prospects.     

从稳定人口与人口再生产认识总和生育率真实涵义

文章阐述了总和生育率的来源、内涵及其理论基础,论述了人口粗、净再生产率表征更替生育水平与用总和生育率来表征更替生育水平的差异与不同;阐述了稳定与非稳定人口的差异和稳定人口理论的不足之处。文章指出,总和生育率属于稳定人口的指标,在度量非稳定人口的生育水平时,总和生育率是一个假定性条件极强的指标,必然要与实际非稳定人口生育水平存在差异。因此正确认识以总和生育率的真实涵义颇具现实意义。     

Growth of U.S. population, 1940–1971, in the light of an interactive two-sex model

Since it is logically impossible to hold constant both male and female age-specific fertility rates, the intrinsic growth rates or the net reproduction rates for males and females, based on that assumption, are internally inconsistent. The interactive two-sex model presented in this paper holds constant a set of bivariate age-specific fertility rates by age of men and women and allows the male and female age-specific fertility rates to adjust themselves to achieve stability. The model gives the same intrinsic growth rate for both sexes and generates intrinsic age-specific fertility rates and intrinsic net reproduction rates for males and females which are consistent and can operate simultaneously on a population. The model is applied to the U.S. data for 1940–1971, and the results are compared with those obtained from the one-sex models.     

中国人口增长之探讨

利用1990年人口普查数据,在1989年生育表基础上,分别以不同的方式改变妇女产次别平均生育年龄和产次别生育率水平这两个变量,仿真推算其变化与平均世代间隔、总和生育率、净再生产率、真实人口增长率及总和递进生育率等指标间的关系,并对中国人口未来发展趋势和政策做了深入的分析探讨。     

Population decline induced by gonorrhoea and tuberculosis transmission: Micronesia during the Japanese occupation, 1919–45

The islands of Yap in Micronesia survived a period of severe depopulation during the Japanese occupation from 1919 to 1945. Using data from historical documents, supplemented by ethnographic evidence, we calibrate a simulation model that accounts for this phenomenon. Our model tracks the reproduction histories of a synthetic cohort of women in Yap, including effects of infertility due to gonorrhoea as well as tuberculosis mortality, and predicts the net reproduction rate (NRR). In this particular case and throughout history, human migrations and associated social and cultural interactions have frequently been accompanied by dramatic changes in patterns of disease transmission and substantial demographic consequences. Despite the broad emphasis on mortality as a measure of demographic consequences in the historical and contemporary literature, there are important instances where life expectancy at birth, fertility rates, and total population size are important demographic consequences. We find that gonorrhoea may have significantly contributed to depopulation during the Japanese occupation of Micronesia, due to repeated infections and high risk of sterility. Results of our model suggest that gonorrhoea alone could have reduced the net reproduction rate by 82%, whereas deaths from tuberculosis may have contributed to a 17% decline.     

Two-Patch Transmission of Tuberculosis

For a two-patch transmission of tuberculosis (TB), the disease-free equilibrium and the basic reproduction rate ?₀ are computed. The disease-free equilibrium is globally asymptotically stable when the basic reproduction rate is less than one. The model can have one or more endemic equilibria. The increased progression rate from latent to active TB in one population may play a significant role in the rising prevalence of TB in the other population. The increased migration from the first to the second population increases the prevalence level of TB in the second population and decreases the TB prevalence in the first population.     

Reproduction and replacement

This paper presents net reproduction rates of the Swedish population for each year between 1750 ahd 1950. An attempt is made to include migration in the study of reproduction and replacement and to calculate cohort reproduction rates.     

Conditions determining the local stability of populations

The conditions that determine the local stability classification of an equilibrium population configuration are analyzed. The population investigated is age-structured and density-dependent, where density is determined by an age-weighted population size. 2 demographic parameters are introduced: the marginal birth rate and the marginal death rate, which describe the marginal density-dependence of the birth and death rates of the equilibrium population. Certain necessary and/or sufficient conditions determining stability are developed, most of them involving the net reproduction rate of the population, and examples illustrating these conditions are presented.     

A tentative discussion on the reproduction of population in China]

Population reproduction is a physiological phenomenon necessary to continue the human race, replacing the older generation with a new one. Population reproduction is also closely related to material production. Both are mutually restricted and supportive of each other. Population reproduction can be divided into 2 types: 1) short life span and rapid generation replacement or high birth rate and high mortality rate, and 2) long life span and slow generation replacement or low birth rate and low mortality rate. Since 1949 China has significantly reduced the mortality rate because of the improvement of our health system and working conditions and the increased living standard. The birth rate, however, still remains high because we are a developing country and our levels of education, science, and technology are quite low. This intermediate stage of low mortality rate but high birth rate also existed in most developed countries for several decades. China's large population and high population growth rate severely inhibit the development of social production and the achievement of the "Four Modernizations." The only way to resolve this contradiction of population reproduction and development of productivity is to control the population growth. Family planning and advocation of 1 child per couple are important strategic tasks in realizing the "Four Modernizations."     

Conditions determining the local stability of populations

The conditions that determine the local stability classification of an equilibrium population configuration are analyzed. The population investigated is age‐structured and density‐dependent, where density is determined by an age‐weighted population size. Two demographic parameters are introduced: the marginal birth rate and marginal death rate, which describe the marginal density‐dependence of the birth and death rates of the equilibrium population. Certain necessary and/or sufficient conditions determining stability are developed, most of them involving the net reproduction rate of the population, and examples illustrating these conditions are presented.     

Momentum and the growth-free segment of a population

In the scenario of a sudden drop in fertility to replacement level. Preston (1986) argued that the population segment under age T, the length of generation, remained growth-free. Here we first present a new relationship for the momentum of any observed population as the ratio of 1) the proportion of the observed population under the mean age at childbearing to 2) the proportion of its life table population under that mean age. We then use that relationship to demonstrate Preston's approximation. Growth factors for other population segments are also presented. When the initial population is stable, momentum can be approximated as a function of the net reproduction rate alone.     

Child mortality and fertility decline: Does the Barro-Becker model fit the facts?

I compare the predictions of three variants of the altruistic parent model of Barro and Becker for the relationship between child mortality and fertility. In the baseline model fertility choice is continuous, and there is no uncertainty over the number of surviving children. The baseline model is contrasted to an extension with discrete fertility choice and stochastic mortality and a setup with sequential fertility choice. The quantitative predictions of the models are remarkably similar. While in each model the total fertility rate falls as child mortality declines, the number of surviving children increases. The results suggest that factors other than declining infant and child mortality are responsible for the large decline in net reproduction rates observed in industrialized countries over the last century. Financial support by the National Science Foundation (grant SES-0217051) and the UCLA Academic Senate is gratefully acknowledged. I thank Sebnem Kalemli-Oczan, Rodrigo Soares, and two anonymous referees for comments that helped to substantially improve the paper. Olesya Baker and Ilya Berger provided excellent research assistance. Responsible editor: Junsen Zhang.     

Nuptiality and fertility of birth cohorts

The impact of changes in age patterns of nuptiality on the net reproduction rate is examined using life table techniques and assuming that age-specific fertility within marriage and fertility outside of marriage are fixed. In the second section, a standardization technique is used to investigate the impact of changes in nuptiality on age-cumulative measures of marital fertility. Examples using data for selected generations of Australian women demonstrate the extent to which recent changes in average completed family size in Australia were affected by changing nuptiality patterns.     

Nuptiality,fertility and reproduction in Norway

The vital and census statistics of Norway for the last 25 years are analysed in order to compute the average family size of different marriage cohorts, and to assess the extent to which the Norwegian population is replacing itself. Methods are devised to overcome the gaps in some of the statistics caused by the war. The conclusion is reached that replacement level has been reached in the post-war years, though the conventional net reproduction rate overestimated the replacement index by 16%.     

Theoretical consideration of effect of fishing mortality on growth and reproduction of fish populations

Summary An increase in fish mortality due to fishing can theoretically change the growth and reproduction of fish populations from the viewpoint of adaptation. We address the issue of how an iteroparous fish should convert surplus energy into somatic growth and reproduction at each age under given conditions of mortality. A model of life history, which maximizes the net reproductive rate using the discrete maximum principle, is improved employing a new relationship between body weight and surplus energy which we have recently proposed. The model is applied to the North Sea plaicePleuronectes platessa, for which it has been reported that the average length of young fish had increased whereas that of old ones had decreased for some decades. Although the model cannot directly explain the former phenomenon, the two phenomena can be interpreted as a change in the optimal life history due mainly to an increase in mortality.     

Postmetamorphic growth, survival, and age at first reproduction of the salamander,hynobius nebulosus tokyoensis Tago in relation to a consideration on the optimal timing of first reproduction

Summary The postmetamorphic growth and survival of the salamanderHynobius nebulosus tokyoentis Tago were surveyed in the study site located in Habu village of Hinodemachi, a suburb of Tokyo City, during 1975–1981. A laboratory experiment on the growth rate of juveniles was conducted in parallel with the field survey. The result indicated that this salamander grew at the rate of 8,mm in s.v.l. per year during the juvenile stage, but its growth rate decreased markedly as low as 1.8 mm for males and 1.1 mm for females, once it had attained sexual maturity. According to the “capture-recapture” procedure the annual survival rate after metamorphosis was found to be quite high; that is, approximately 0.7. By using the growth rate of juveniles and the difference between the sizes at metamorphosis and sexual maturity, the age at first reproduction was estimated to be 4 year for males and 5 year for females. From the data obtained in this study, the intrinsic rates of increase (r) were calculated for various values of age at first reproduction under different survival schedules, and the relationship between the age at first reproduction and fitness as measured byr was examined. The result indicated that an optimal age maximizing fitness always existed under respective survival schedules, and the observed age at first reproduction of this salamandei was found to coincide well with the predicted optimal age.     

Empirical analysis of the contribution of age composition to population growth

The method of decomposition is applied to rates of natural increase in order to elucidate the role played by age composition in the growth of populations. A population’s age distribution and fertility schedule are contrasted to those in a "stationary" population having the same mortality rates and having a fertility schedule equal to that of the observed population divided by its net reproduction rate. In this manner it is shown that about one-quarter to one-third of the growth of most current high-growth populations can be attributed to non-stationarity of their age distributions. This fraction will rise, as it has in most industrialized countries, if fertility is reduced and age distributions become middle-heavy. In projections of the 1963 Venezuelan female population with fertility rates declining by 20/0 and 1% annually, more than half of the growth (in numbers) that occurs prior to zero-growth attainment is contributed by non-stationarity of its intervening age distributions.

     

Immigration and the stable population model

This paper reports on work aimed at extending stable population theory to include immigration. Its central finding is that, as long as fertility is below replacement, a constant number and age distribution of immigrants (with fixed fertility and mortality schedules) lead to a stationary population. Neither the level of the net reproduction rate nor the size of the annual immigration affects this conclusion; a stationary population eventually emerges. How this stationary population is created is studied, as is the generational distribution of the constant annual stream of births and of the total population. It is also shown that immigrants and their early descendants may have fertility well above replacement (as long as later generations adopt and maintain fertility below replacement), and the outcome will still be a long-run stationary population.     

Attitudes towards demographic trends and population policy: Italy and the Netherlands in a comparative perspective

A comparative analysis was carried out using survey data on attitudes regarding population trends and policy in Italy and in the Netherlands. The results show that current trends and the determinants of those trends are perceived similarly in both countries. With regard to policy, the Italians exhibit much more positive attitudes toward suggested new family policy measures than the Dutch. In the Netherlands, family policy generally is given a much lower priority than other areas of social policy. It appears that having children reflects different values in the two countries. Those who attach greater value to having children are also more in favour of new family policy measures than others. However, the results suggest that introduction of these measures would not raise the reproduction rate to anywhere near a stationary level.