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Model Fertility Schedules: Variations in The Age Structure of Childbearing in Human Populations
Abstract
The nature of the roots for a set of fertility functions were explored in this study, resulting in tables from creation of a family of model fertility schedules. These model fertility schedules accurately represent the full range of age structures of fertility in large populations; they have close fit to various accurately recorded fertility schedules of very different form. The text for the tables includes discussions of: 1)the basis for the fertility schedules, 2)the age structure of the proportion ever married (G(a) specified by 2 parameters, 3)single parameter specified age structure of marital fertility, 4)the similarity of model schedules of age specific fertility to the age pattern of fertility in actual populations, 5)model fertility schedules' suitability during changing nuptuality. Possible uses of the schedules and their application to different countries (England, Wales, Peru) are also described.
... However, no data is available on the life expectancy, childbirth interval, or marriage age of Indigenous ancestors in Canada. Thus, we used statistical data on mortality and fertility that were used in previous studies on human migration to islands during the Last Glacial Maximum [20][21][22]. Because Indigenous newborns have Mongolian spots, we set the marriage age as 17 years old based on the oldest data on the marriage age of Japanese with Mongolian spots [23]. ...
... For the average childbirth interval, Henry [20] developed a table of age-specific natural fertility, and Coale and Trussell [21] proposed a model of fertility. Konner [25] quantified the data on female childbirth intervals ranging from 3-4 years in six hunting tribes. ...
... Konner [25] quantified the data on female childbirth intervals ranging from 3-4 years in six hunting tribes. We referred to the studies of Henry [20] and Coale and Trussell [21], which assumed that females gave birth at intervals in the range of 2.6-4.4 years; thus, cases in which a married female gave birth to one child on average every 2.6, 2.9, 3.2, 3.5, 3.8, 4.1, or 4.4 years were used.The assumption of maintaining a constant childbirth interval from first birth to last birth is not realistic, but we considered that this approached a value close to the maximum survival probability. We set the minimum and maximum values of 2.6 and 4.4 years because they completely covered the range of 3-4 years and at an appropriate resolution that matched that of the female life expectancy. ...
The purpose of this study is to examine the survival probability of the ancestors of the indigenous people of Canada during their migration to the last glacial maximum. The ancestors of the Indigenous people of Canada are believed to have migrated during the Last Glacial Maximum under severe ice-age conditions. However, the possibility of their survival is unclear. Creating a mathematical model, the survival probability of Indigenous ancestors who migrated to Canada and the effects of different factors were studied. Using logistic regression analysis, we evaluated the effects of different factors, such as the mean female life expectancy, average childbirth interval, and marriage age, on their survival probability. The results suggested that a polygamous community was more likely to survive. The survival probability was maximized in the cases of monogamy/unintentional migration (0.60), polygamy/unintentional migration (0.87), and marriage age of 15 years/monogamy/unintentional migration (0.76). However, the survival probability was low for many possible combinations of the mean female life expectancy and the average childbirth interval. The low survival probability would demonstrate the levels of resourcefulness, bravery, and wisdom that the Indigenous ancestors possessed to survive. A problem was that the available data on mortality and fertility were not specific to the ancestors of the Indigenous people of Canada. In the future, the accuracy of the survival probability of the ancestors of the Indigenous people of Canada will improve once quantitative research data on the ancestors’ life expectancy and childbirth are available.
... Recent attempts to find mathematical expressions to describe agespecific fertility rates include: polynomials (Brass, 196O;Brass et al, 1968); the Beta distribution (Mitra, 1967;Romanuik, 1973;Mitra and Romanuik, 1973); Johnson's (1949) functions (Talwar, 1974); the Lognormal and Gamma distributions (Duchene et al,I974); a specialised non-linear form due to Mazur (I965); and the Gompertz and Makeham funotiona (Wunsch, I966;Murphy and 1972;Murphy, 1982). As with mortality, a number of relational models of fertility involving empirically determined age distributions have also been proposed (Coale and Trussell, 1974;Brass, 1974b;McNeil and Thkey, 1975;Pittenger, I98O;Murphy, 1982), Eoem et al (198I) review and test several of these age-specific fertility models. Relational marriage-duration-specific fertility models have been developed by Farid (197$) and Page (I976). ...
... Numerous researches have demonstrated and modelled the relation ships between age and fertility, (for example: Coale and Trussell, 1974;Page, 1976; Hoem et al, I98I: Casterline and Hobcraft, I98I), ...
... This has been done in chapter 2 using quinquennial age-specific legitimate fertility rates from a variety of populations. The resulting regression model is shown to be similar in structure to the usual model for such data; that of Coale and Trussell (1974). This technique of model generation is a powerful demographic tool, and could find wide application especially in connection with deficient data and for projection. ...
... To overcome the limitations and measurement problems, Stover (1998) 5 revised the Bongaarts model. Coale and Trussell (1974) 6 published a model which is still fairly widely used today-it is a hybrid between an empirical and a parametric model. This is a model of fertility with four parameters. ...
... To overcome the limitations and measurement problems, Stover (1998) 5 revised the Bongaarts model. Coale and Trussell (1974) 6 published a model which is still fairly widely used today-it is a hybrid between an empirical and a parametric model. This is a model of fertility with four parameters. ...
... y=1x1+2x2+⋯+nxn+ε here, i's (i=1, 2, …, n) are the regression coefficients, which represent the value at which the criterion variable changes when the predictor variable changes. In the present study, the dependent variable is children ever born to a female and independent variables are factor scores obtained from equation (6). ...
It is widely known that fertility is determined by a complex set of biological, psychological, socioeconomic , cultural, political and legal factors. These factors affect the fertility dynamics directly or indirectly. Although the past studies have suggested about a lot of variables for the estimation of total fertility rate, and various fertility models have been developed for estimating the fertility parameters, yet it is difficult to include all the determining variables in a single estimation technique conveniently. In the present study, authors have used a multivariate technique i.e. factor analysis to examine the underlying patterns and relationships for a number of variables which affects fertility behaviour of a population. Also, authors have tried to summarize the information in smaller sets of distinct factors to estimate the children ever born. Present study is based on the data obtained from the fourth round of National Family Health Survey, India (NFHS-IV) dataset. The key finding of the present study is that the selected fertility parameters are classified into three distinct factors with a valid justification. On the basis of these estimated factors, the children ever born are estimated for 443 districts of India which is significantly good estimate of children ever born.
... Until relatively recently parity specific 'stopping' behavior (as put forward by the likes of Henry, 1961, andTrussell, 1974) was held to be the sign of 'modern' birth control. However, the importance of 'spacing' in the decline of fertility has now moved into the debating chamber. ...
... Coale-Trussell's methodology for calculating fertility is based on family limitation and thus a numerical family size preference is implicit within this methodology. 'Stopping' behavior implies that a desired family size has been reached and typically (in a population that is limiting its fertility) is reached while the mother still has a number of fecund years ahead of her (Coale and Trussell, 1974). There is a further complication in that the Coale-Trussell methodology encourages a distinction between fertility limitation within marriage and fertility limitation by marriage. ...
p>Britain’s fertility at the end of the nineteenth century and start of the twentieth century has been the subject of a certain amount of debate in recent years. Szreter (1996), Garrett & Reid (1995) and Anderson (1998) argue that birth spacing played a larger role in the Britain fertility transition than was previously thought. An implication of their argument is that there appear to be two distinct groups of players in the fertility decline; the late marrying couples, who through the use of birth control (Szreter stressing the role of abstinence), tend to space their children widely and thus end up with small families; and the early marriers, whose fertility patterns follow traditional lines, and thus end up with larger families.
This thesis explores the marital fertility experienced in Britain in the 1930s. The 1930s were a period of unprecedentedly low fertility, the Total Period Fertility Rate never going above 1.89 throughout the decade, and reaching a nadir of 1.72 in 1933. It is also known that by the 1930s a high proportion of couples ended up with only one child. Indeed, the 1946 Family Census (Glass & Grebenik, 1954), shows that of those couples marrying in 1925 as many had a completed family size of one as had a completed family size of two (25% in each case), a further 17% of couples remaining childless. This study uses data from the Royal Commission on Population 1944-1949 and from the 1944-1945 Mass Observation study, Britain and her Birth Rate .
Throughout the decade there are distinct social class differentials in marital fertility, with the ‘middle classes’ achieving lower fertility than the ‘artisan and skilled working classes’ who in turn achieved lower fertility than the ‘unskilled working classes’. Both quantitative and qualitative techniques have been employed to attempt reasons for the low fertility of the decade in general, and more specifically for the apparent social class differentials.
The study also addresses the subjective nature of research in general, and the position of traditional theories of fertility and their applicability to the British experience.</p
... Several models have been used to describe fertility. A notable example is the marital fertility model proposed by Coale and Trussell (1974), which is multiplicative for the rates and assumes natural fertility, meaning fertility is not purposely controlled (Henry 1961). The Bongaarts Fertility model incorporates data on contraceptive use, abortions, and infecundability (Bongaarts and Potter 1983). ...
Puerto Rico has one of the lowest total fertility rates (TFR) in the world. Combined with a negative net migration and a high proportion of older adults, its unique situation motivates the need for further demographic analysis. Determining whether low fertility rates are mostly due to period or cohort effects is crucial for developing effective public policies that adapt to changes in fertility and population structures. The main objective of this work is to develop an Age-Period-Cohort model, in order to describe fertility data in Puerto Rico, from 1948-1952 and determine the contribution of period and cohort effects to fertility decline. The APC model was developed following a Bayesian framework, with a Poisson likelihood, RW(2) autorregressive priors for the APC parameters, and Scaled Beta2 priors for the precision parameters.Both frequentist and Bayesian methodologies attribute more importance to cohort effects when explaining fertility changes in Puerto Rico. Birth cohorts born in 1963-1967 onward have notably low fertility rates. There is no evidence of postponement of births in Puerto Rico, contrary to other countries with lowest-low fertility. Both frequentist and Bayesian methodologies attribute more importance to cohort effects when explaining fertility changes in Puerto Rico. Birth cohorts born in 1963-1967 onward have notably low fertility rates. There is no evidence of postponement of births in Puerto Rico, contrary to other countries with lowest-low fertility. This is the first application of APC analysis to fertility data in Puerto Rico, which describes fertility changes in a unique scenario in terms of demographic indicators, and the first APC analysis that shows the predominance of cohort effects when explaining fertility.
... Some fertility models (e.g. Coale and Trussell, 1974;Lee, 1993) do the same. An alternative, sometimes deductive approach, can be found in the wide variety of parametric or functional-form mortality models (e.g. ...
BACKGROUND. The majority of countries in Africa and nearly one third of all countries require mortality models to infer complete age schedules of mortality, required for population estimates, projections/forecasts and many other tasks in demography and epidemiology. Models that relate child mortality to mortality at other ages are important because all countries have measures of child mortality. OBJECTIVE. 1) Design a general model for age-specific mortality that provides a standard way to relate covariates to age-specific mortality. 2) Calibrate that model using the relationship between child or child/adult mortality and mortality at other ages. 3) Validate the calibrated model and compare its performance to existing models. METHODS. A general, parametrizable component model of mortality is designed using the singular value decomposition (SVD-Comp) and calibrated to the relationship between child or child/adult mortality and mortality at other ages in the observed mortality schedules of the Human Mortality Database. Cross validation is used to validate the model, and the predictive performance of the model is compared to that of the Log-Quad model, designed to do the same thing. RESULTS. Prediction and cross validation tests indicate that the child mortality-calibrated SVD-Comp is able to accurately represent the observed mortality schedules in the Human Mortality Database, is robust to the selection of mortality schedules used to calibrate it, and performs better than the Log-Quad Model. CONCLUSIONS. The child mortality-calibrated SVD-Comp is a useful tool that can be used where child mortality is available but mortality at other ages is unknown. Together with earlier work on an HIV prevalence-calibrated version of SVD-Comp, this work suggests that this approach is truly general and could be used to develop a wide range of additional useful models.
... No particular price is then placed on whether each model parameter may be interpreted in any meaningful way. Other applications require models that can fit the data well while also providing a well-defined, ideally small set of parameters that represent quantities that can be interpreted in demographic terms [2][3][4][5][6]. ...
Fitting statistical models to aggregate data is still the dominant approach in many demographic and biodemographic applications. Although these macro-level models have proven useful for a variety of tasks, they often have no demographic interpretation. Individual-level modelling, on the other hand, offers a deeper understanding of the mechanisms underlying observed patterns. Their parameters represent quantities in the real world, instead of pure mathematical abstractions. However, estimating these parameters using real-world data has remained a challenge. The approach we introduce in this article attempts to overcome this limitation. Using a likelihood-free inference technique, we show that it is possible to estimate the parameters of a simple but demographically interpretable individual-level model of the reproductive process by exclusively relying on the information contained in a set of age-specific fertility rates. By estimating individual-level models from widely available aggregate data, this approach can contribute to a better understanding of reproductive behaviour and its driving mechanisms, bridging the gap between individual-level and population-level processes. We illustrate our approach using data from three natural fertility populations.
... The function b k (x,s) is commonly known as the standard age profile and the model describes how β in a certain year differs from the standard. This so-called relational approach has been used in the context of mortality (Brass, 1971;De Beer, 2012), fertility (Booth, 1984;De Beer, 2011;Zeng et al., 2000), and nuptiality (Coale & Trussell, 1974). The well-known Brass relational model is a special case of model (1), namely one for a fixed time t. ...
Demographic forecasters must be realistic about how well they can predict future populations, and it is important that they include estimates of uncertainty in their forecasts. Here we focus on the future development of the immigrant population of Norway and their Norwegian-born children (“second generation”), grouped by three categories of country background: 1. West European countries plus the United States, Canada, Australia, and New Zealand; 2. Central and East European countries that are members of the European Union; 3. other countries. We show how to use a probabilistic forecast to assess the reliability of projections of the immigrant population and their children. We employ the method of random shares using data for immigrants and their children for 2000–2021. We model their age- and sex-specific shares relative to the whole population. Relational models are used for the age patterns in these shares, and time series models to extrapolate the parameters of the age patterns. We compute a probabilistic forecast for six population sub-groups with immigration background, and one for non-immigrants. The probabilistic forecast is calibrated against Statistics Norway’s official population projection. We find that a few population trends are quite certain: strong increases to 2060 in the size of the immigrant population (more specifically those who belong to country group 3) and of Norwegian-born children of immigrants. However, prediction intervals around the forecasts of immigrants and their children by one-year age groups are so wide that these forecasts are not reliable.
Supplementary Information
The online version contains supplementary material available at 10.1007/s10680-023-09675-2.
... In the case of first births, however, the Kaplan-Meier estimates the proportion of women who remain childless at the end of the observation period. For our first birth analysis, we go against conventional demographic approaches to reproductive age (Coale & Trussell, 1974) by starting our process time at age 12 on the basis that it is the earliest age at which one woman from the sample birthed her first child, and this is generally regarded as the age of menarche. All women are either right-censored at time of first birth or up to age 45 years or until the survey interview date 12 , whichever occurs first. ...
The survival of Indigenous peoples in the CANZUS states of Canada, Australia, Aotearoa New Zealand, and the United States is nothing short of remarkable. Not only have Indigenous peoples thwarted colonial tropes of the vanishing native but, for decades, Indigenous population growth rates have significantly outpaced those of the dominant settler populations. The future survival of Indigenous peoples fundamentally rests on continued natural increase, and understanding the causes and consequences of fertility behaviour is critical. While total fertility rates for Indigenous women in CANZUS countries are relatively low, childbearing tends to be concentrated at younger ages in contrast to the dominant white populations. The fertility transitions of both settler and Indigenous populations in the CANZUS states are well documented, however, a significant gap remains: how cultural factors shape contemporary Indigenous fertility behaviours. Using Aotearoa as a case study, we explore the relationship between Māori cultural identity, birth timing, and the duration of birth intervals. We use the 1995 New Zealand Women: Family, Employment and Education survey data to further test the impact of cultural identity on birth transition rates using the piecewise exponential model and Kaplan-Meier estimates. We find that women who identify Mainly Māori (exclusively or primarily) are at greater risk of bearing much earlier to first birth but not necessarily subsequent births. However, because of the earlier start, Māori have a longer reproductive window to bear more children, and at higher birth orders still bear earlier than non-Māori. The empirical evidence strengthens our case to suggest that cultural orientation has some influence on Indigenous fertility and contributes to the development of Indigenous-centred theories of fertility and demography more broadly.
... Sudden drop-offs in these ratios at higher par ities beyond what can be expected from the effects of repro duc tive aging indi cate the prac tice of par ity-spe cific con trol. Coale and Trussell (1974) devel oped meth ods for infer ring par ity-spe cific con trol from the age pat tern of mar i tal fer til ity, with declines at older ages proxying for par ity-spe cific con trol. Both of these approaches are indirect in the sense that they infer paren tal intentionality from the age and par ity pat tern of fer til ity behav ior, not from state ments by par ents about the chil dren they would like to have. ...
Can the names parents gave their children give us insights into how parents in historical times planned their families? In this study, we explore whether the names given to the firstborn child can be used as indicators of family-size preferences and, if so, what this reveals about the emergence of intentional family planning over the course of the demographic transition. We analyze historical populations from 1850 to 1940 in the United States, where early fertility control and large sample sizes allow separate analyses of the White and Black populations. We also analyze Norway from 1800 to 1910, where there was a much later fertility transition. A split-sample method allows automated scoring of each name in terms of predicted family size. We find a strong relationship between naming and family size in the U.S. White population as early as 1850, for the Black population beginning in 1940, and for the Norwegian population in 1910. These results provide new evidence of the emergence of "conscious calculation" during the fertility transition. Our methods may also be applicable to modern high-fertility populations in the midst of fertility decline.
... The function bk(x,s) is commonly known as the standard age profile and the model describes how β in a certain year differs from the standard. This so-called relational approach has been used in the context of mortality (Brass 1971, De Beer 2012, fertility (Booth 1984, Zeng et al. 2000, De Beer 2011, and nuptiality (Coale and Trussell 1974). The well-known Brass relational model is a special case of model (1), namely one for a fixed time t. ...
We present a probabilistic forecast for the immigrant population of Norway and their Norwegian-born children ("second generation") broken down by age, sex, and three types of country background: 1. West European countries plus the United States, Canada, Australia, and New Zealand; 2. East European countries that are members of the European Union; 3. other countries. First, we compute a probabilistic forecast of the population of Norway by age and sex, but irrespective of migration background. The future development of the population is simulated 3 000 times by stochastically varying parameters for mortality, fertility and international migration to 2060. We add migrant group detail using stochastically varying random shares to split up each result from the previous step into six subgroups with immigration background, and one for the non-immigrants. The probabilistic forecast is calibrated against the Medium Variant of Statistics Norway's official population projection.
The results show that a few population trends that were predicted for Norway to 2060 are quite certain: strong increases in the size of the immigrant population (more specifically those who belong to group 3) and of Norwegian-born children of immigrants. As to the age structures of immigrants and their children, the prediction intervals around the forecasts of these persons in one-year age groups are so wide that there is little information in these forecasts. For the population as a whole (irrespective of migrant background), forecasts for the age structure in one-year age groups are reliable up to around 2040, except for children born after 2022. For later years, the intervals become very wide for all ages. But ageing is certain.
... Senescent aging thus appears to result inevitably from transferring net fertility into younger ages (Seymour & Doncaster 2007). Thus, age at first reproduction is strongly predicted by extrinsic adult mortality (Coale & Trussell 1974Roff 1992;Stearns 1992), but is also constrained by energy available and the relative profit to further selfinvestment (Sibley & Calow 1986). Even an anticipated increased mortality risk can accelerate the life history strategy. ...
... Among the models used to represent the age-specific fertility pattern of populations that do not show high early fertility, several have been shown to provide 'fairly' accurate fits to fertility distributions. These include, for example, the parametric fertility model proposed by [50,51], which is still widely used today; it is a hybrid model (empirical and parametric) and its basic form is ...
The transition from a demographic regime of high mortality and high fertility to one with low mortality and low fertility is universal and comes along with the process of socio-economic modernization. The Spanish total fertility rate has decreased to below replacement levels in the last decades. The decline has persisted since the 1960s and is diverse across the country. Based on that diversity, the use of population forecasts, not only at national but at regional levels, for planning purposes (governments and private sector) with large horizons has become a must to provide essential services. Using a Bayesian hierarchical model we constructed probabilistic fertility forecasts for Spain at the regional level. Although this approach is already issued by the United Nations little research has been done focusing on the Spanish subnational level. Our objective is to disaggregate the national projections of the total fertility rate for Spain into regional forecasts. The results of this research will show the model fitting, first to the national level and then using a multifaceted and continuous evolution of fertility over time, at the regional level, to check its convergence.
... In the international literature, research documenting the propensity to have children dates back to the 1950s, with the first models typically examining fertility in its biological context [2]. In addition to the biological determinants of fertility (conception rate, risk of miscarriage, and the age patterns of natural fertility of married women), the early research focused on different modes of birth control [3][4][5]. A key finding is that, in addition to biological endowments, fertility is ultimately determined by factors at the family level, including the extent to which marriage (the family) provides a positive, supportive environment for childbearing [6,7]. ...
The propensity to have children, which, according to the view accepted in the literature, is a good predictor of actual childbearing, is of particular importance in countries with low fertility rates and economic prosperity. In this paper, we report the results of a representative survey of 15,700 respondents in 2021 of university students in an emerging market economy in Central Europe, mapping their intentions to have children. The PLS-SEM data analysis method was used to test our hypotheses on the relationships between social, economic, and environmental variables of childbearing. Our results confirm the dominant role of socio-cultural inclusiveness in childbearing, over socio-economic and environmental-economic factors. The novelty of our research lies in the impact analysis of family policy incentives; however, our results are consistent with those documented in the literature, namely, the primacy of socio-cultural factors in the willingness of childbearing.
... The assumed total fertility values were 3.7 and 3.3 for the "top-band" and "low-band" fertility decline respectively. The variation in the pattern of age-specific fertility rates was achieved by varying the parameter m (degree of fertility control) in the Coale-Trussell (Coale and Trussell, 1974) models. ...
p>The thesis aims to draw on the existing studies and conduct further investigations in mortality, fertility and migration patterns in order to provide a systematic analysis of population processes in the Seychelles between 1770 and 1994. Several demographic methods are applied to census, vital registration and migration data and other associated qualitative materials. In achieving these objectives, the study examines four core issues. These are: (1) the factors that led to the long-term growth of the Seychellois population, (2) the divergence between male and female mortality since the 1980s, (3) the type of fertility transition pattern the Seychelles exhibits, and (4) the role of the family planning programme in the decline in fertility in the Seychelles since 1966.
Firm conclusions are arrived at with respect to the predominant growth factors between 1770 and 1994 and fertility transition patterns in the Seychelles. In the first hundred years of the existence of the Seychelles population, migration was the main determinant of growth, but it contributed to low population growth throughout the twentieth century. The Seychelles seems to be a half-way house between an African and Asian pattern of fertility transition. It was not possible to detect the cause for the divergence between male and female mortality. The timing of the decline in fertility and the increase in the number of contraceptive users from 1977 to 1996 strongly suggest that the family planning programme has had the greatest impact on fertility than the socioeconomic factors and other proximate determinants of fertility.
As well as estimating net intercensal internal migration between the administrative regions of the Seychelles, the type of international migrants pertaining to age and sex distribution, purpose and destination of migrants are also examined. On the basis of the derived trends in the components of population change, both national and sub national projections are performed.</p
... Za štandardnú schému vekovo-špecifických mier plodnosti sa pritom zvolila plodnosť žien náboženskej spoločnosti Hutteritov. Druhým nástrojom, ktorý bol vyvinutý na účely empirickej identifikácie úrovne vedomého obmedzovania plodnosti je Coale-Trussellov model (Coale a Trussell 1974). Jeho autori v ňom predpokladajú, že vedomá regulácia počtu narodených detí ako rozhodnutie (manželského) páru ukončiť svoju reprodukciu pod vplyvom predchádzajúcej reprodukčnej histórie sa odzrkadľuje na priebehu kriviek manželskej plodnosti (čisté miery plodnosti vydatých žien, miery 1. kategórie). ...
... For the first-birth analysis the process time starts at age 15, following the conventional demographic approach to reproductive ages (Coale & Trussell, 1974). Thus, we left-censor all women who gave birth before age 15. ...
This paper examines the childbearing behaviour of Polish migrant women and their descendants in Sweden. Also considering stayers in the country of origin, we rely on a country-of-origin and country-of-destination approach in a careful examination regarding the relevance of three hypotheses on migrant fertility: the socialisation, selection, and adaptation hypotheses. We analyse the transitions to first and second births based on a piecewise exponential model, using Swedish register data and the Polish Generations and Gender Survey (GGS) first wave. The results support the socialisation hypothesis, as the Polish stayers and the first-generation Polish migrants have their first child at younger ages and are less likely to remain childless than the other groups but are also more likely to not proceed to a second child, unlike the Swedish natives and the second generation. We find partial support for the selection hypothesis. Descriptively, we observe signs of selection into migration based on education, cohort, and marital status. Additionally, our study shows that the impact of marriage varies between stayers and migrants, in the first-birth transition, suggesting selection into migration when it comes to unobserved characteristics as well. The adaptation hypothesis is also supported, as the fertility behaviour of the second generation more closely resembles that of the Swedish natives than that of the first generation and differs more from that of the Polish stayers in terms of both quantum and timing of the first and second births.
The paper considers the use of a mixture of two Weibull densities to represent fertility patterns with a hump or bimodality behaviour, a pattern in fertility that has been noticed by researchers in the last two to three decades. Assuming the births to be distributed as a binomial variate and taking into account the period age-specific fertility rates, the paper relies on the Bayes paradigm to provide the complete posterior analysis. Guided by the results of the proposed mixture of two Weibull densities, the paper then proposes two other mixture models, that is, the mixture of normal and Weibull and the mixture of normal and generalized gamma densities. The Metropolis algorithm with a properly chosen candidate generating density is considered to generate the posterior samples in each case. The unabridged data are used for numerical illustration. Finally, the proposed models are compared to recommend the most appropriate model after establishing the compatibility of the proposed models with the data in hand. The work is, of course, motivated by the earlier studies that overlooked the use of more flexible lifetime models in studying fertility patterns with hump or bimodality and, as such, prompting us to integrate them into our analysis.
Due to the scarcity of data, the demographic regime of pre-plague England is poorly understood. In this article, we review the existing literature to estimate the mean age at first marriage for women (at 24) and men (at 27), the remaining life expectancy at first marriage for men (at 25 years), the mean household size (at 5.8), and marital fertility around 1300. Based on these values, we develop a macrosimulation that creates a consistent image of English demography at its medieval population peak that reflects a Western European marriage pattern with a relatively very high share of celibates.
Since the 1971 National Jewish Population Study, and throughout subsequent national surveys, data were collected on achieved fertility, detailed birth histories, current levels, planned family size, and other information on family formation. Cohort analysis shows that, although at lower levels, Jewish fertility followed the general trends of American population since World War II. However, Jews remarkably anticipated by a few years the rising and declining fertility waves of the US total population – from the Baby boom to the subsequent Baby bust. In this chapter Jewish fertility differentials are also examined by degree of religiosity and socioeconomic characteristics. More recent sources confirm the persisting low levels of Jewish fertility in the US. The 2020 Pew Survey of Jewish Americans hints at further decline in Jewish family size at a time when US fertility levels reached a historical minimum.
Estimates of population fertility characteristics are of critical importance for understanding short-term shifts in population age structure and related growth dynamics.As such, ethnic specific information on fertility among other demographic variables such as age, sex is often useful for planning purposes. In India, census or survey reports do not provide ethnic level estimates of fertility within the states. Using census 2011 data on fertility, this paper presents ethnic specific estimates of fertility in the eight NorthEast states identified by their religious background. The current age specific fertility rates are adjusted using the Brass P/F ratio method based on total children ever born. Total fertility rates, crude birth rates and general fertility rates are obtained from the adjusted rates for all ethnic groups identified by their religion. The adjusted rates shows underestimation of birth rates derived from current rates in all age groups. Results of TFR among ethnic groups consistently show that Muslim women tend to have higher fertility rates as compared to other religious groups. These results are in consistency as reported in NFHS-3.
In less developed countries, both traditional and non-traditional methods of mortality estimation have not been successful in providing complete and accurate information on mortality. To substitute these methods Demographers have tried to develop indirect methods of mortality estimation. For estimating adult mortality two methods based on orphanhood data and widowhood data are being developed. There is a fair literature on the theoretical background and practical application of these methods and by critically reviewing this scattered literature, the suitability and applicability of them can be assessed. The information for the method of widowhood can be collected by asking the simple question “Is your first husband/ wife alive”. The proportion can be converted to life table probabilities using model schedules of mortality, fertility, and nuptiality. The robustness of the method depends largely of the assumptions of the method. Some assumptions are not crucial. However the assumption on the independent of the mortality risks of respondent and spouse should be examined critically. Further development of the method should be carried out using computer simulation rather than depending on plausible estimates achieved by application of the method.
En este artículo se utilizan las preguntas del Censo de 1940 sobre la fecundidad retrospectiva ?hijos nacidos vivos e hijos supervivientes en el momento censal? de las mujeres casadas al menos una vez para estimar los niveles de supervivencia de sus descendientes y, por tanto, de mortalidad en la infancia (hasta los 15 años), según un método propuesto por W. Brass. Los resultados muestran que la Guerra Civil empeoró los niveles de supervivencia en la infancia en prácticamente todas las provincias españolas, pero tuvo un impacto diferencial muy contrastado. Comparando los niveles de supervivencia antes y durante el conflicto bélico, se obtiene que fueron las provincias meridionales y levantinas las más afectadas, mientras que en Cataluña y la Meseta septentrional los niveles de mortalidad en la infancia parecen haber empeorado menos, pese a que mostraban posiciones extremas respecto a los niveles de supervivencia antes de la guerra. De esto se deduce que, a pesar de que debiera existir una cierta relación entre el nivel de desarrollo demográfico y la vulnerabilidad que muestran las provincias ante una coyuntura desfavorable, tales características no parecen jugar un papel significativo como factor explicativo de los niveles de supervivencia durante el conflicto bélico.
Esta investigación tiene dos objetivos, por una parte, comprobar si el método indirecto para estimar tasas de mortalidad infantil en Bolivia conduce sistemáticamente a una sobrestimación del indicador y, por otra parte, corregir dicha sobrestimación si se constata la existencia de tal problema. Asumiendo que las tasas de mortalidad infantil obtenidas con el método directo son correctas, se confirma que con el método indirecto sistemáticamente se obtienen tasas sobrestimadas. Adicionalmente, hay evidencia estadística de que mayor sobrestimación se produce en niveles bajos de mortalidad infantil y que la sobrestimación ocurre con cualquiera de las familias modelo de mortalidad de Coale y Demeny que se use para su cálculo. Para corregir el problema de sobrestimación en la tasa de mortalidad infantil se seleccionó el modelo de regresión lasso, pues, las tasas de mortalidad infantil predichas con este modelo fueron más próximas a las tasas correctas que las tasas predichas con otros modelos. Se destaca que el modelo lasso seleccionado incluye una única variable predictora, cuyo cálculo es muy simple y no requiere el uso de modelos de mortalidad: la proporción de hijos muertos en mujeres de 25-29 años de edad. Debido a que países como Bolivia aún requieren del método indirecto principalmente para estimar tasas de mortalidad infantil para pequeñas áreas, como son gran parte de los municipios, es necesario seguir explorando modelos estadísticos que permitan obtener tasas de mortalidad infantil no sobrestimadas.
This open access book demonstrates the application of simulation modelling and network analysis techniques in the field of Roman studies. It summarizes and discusses the results of a 5-year research project carried out by the editors that aimed to apply spatial dynamical modelling to reconstruct and understand the socio-economic development of the Dutch part of the Roman frontier (limes) zone, in particular the agrarian economy and the related development of settlement patterns and transport networks in the area. The project papers are accompanied by invited chapters presenting case studies and reflections from other parts of the Roman Empire focusing on the themes of subsistence economy, demography, transport and mobility, and socio-economic networks in the Roman period.
The book shows the added value of state-of-the-art computer modelling techniques and bridges computational and conventional approaches. Topics that will be of particular interest to archaeologists are the question of (forced) surplus production, the demographic and economic effects of the Roman occupation on the local population, and the structuring of transport networks and settlement patterns. For modellers, issues of sensitivity analysis and validation of modelling results are specifically addressed. This book will appeal to students and researchers working in the computational humanities and social sciences, in particular, archaeology and ancient history.
This paper studies the marital fertility—broadly defined as the ratio of live births to married women—of five Chinese lineages since the 17th century, mainly in the Qing Dynasty (1644–1911). The results demonstrate a unique pattern of Chinese marital fertility by exploiting new genealogical data and studying more than 50,000 individuals from five lineages. Contrary to the conventional wisdom, the marital fertility rates in the period were moderate. On the other hand, in line with the classic ideas, this paper finds no clear indication of two fertility controls within marriages, parity‐dependent early stopping and longer spacing.
The lagging fertility transition in West Africa has important repercussions for global population growth but remains poorly understood. Inspired by Caldwell and colleagues' fertility transition framework, as well as by subsequent research, we examine diversity in women's holistic childbearing trajectories in Niakhar, Senegal, between the early 1960s and 2018 using a sequence analysis approach. We evaluate the prevalence of different trajectories, their contribution to overall fertility levels, and their association with women's socioeconomic and cultural characteristics. Four trajectories were observed: "high fertility," "delayed entry," "truncated," and "short." While the high fertility trajectory was most prevalent across cohorts, delayed entry grew in importance. The high fertility trajectory was more common among women born between 1960 and 1969 and was followed less often by divorced women and those from polygynous households. Women with primary education and those from higher status groups were more likely to experience delayed entry. The truncated trajectory was associated with lack of economic wealth, polygynous households, and caste membership. A short trajectory was related to lack of agropastoral wealth, divorce, and possibly secondary sterility. Our study advances knowledge on fertility transitions in Niakhar-and Sahelian West African contexts more generally-by showing the diversity of childbearing trajectories within high fertility regional contexts.
Wide-ranging and inclusive, this text provides an invaluable review of an expansive selection of topics in human evolution, variation and adaptability for professionals and students in biological anthropology, evolutionary biology, medical sciences and psychology. The chapters are organized around four broad themes, with sections devoted to phenotypic and genetic variation within and between human populations, reproductive physiology and behavior, growth and development, and human health from evolutionary and ecological perspectives. An introductory section provides readers with the historical, theoretical and methodological foundations needed to understand the more complex ideas presented later. Two hundred discussion questions provide starting points for class debate and assignments to test student understanding.
Wide-ranging and inclusive, this text provides an invaluable review of an expansive selection of topics in human evolution, variation and adaptability for professionals and students in biological anthropology, evolutionary biology, medical sciences and psychology. The chapters are organized around four broad themes, with sections devoted to phenotypic and genetic variation within and between human populations, reproductive physiology and behavior, growth and development, and human health from evolutionary and ecological perspectives. An introductory section provides readers with the historical, theoretical and methodological foundations needed to understand the more complex ideas presented later. Two hundred discussion questions provide starting points for class debate and assignments to test student understanding.
Wide-ranging and inclusive, this text provides an invaluable review of an expansive selection of topics in human evolution, variation and adaptability for professionals and students in biological anthropology, evolutionary biology, medical sciences and psychology. The chapters are organized around four broad themes, with sections devoted to phenotypic and genetic variation within and between human populations, reproductive physiology and behavior, growth and development, and human health from evolutionary and ecological perspectives. An introductory section provides readers with the historical, theoretical and methodological foundations needed to understand the more complex ideas presented later. Two hundred discussion questions provide starting points for class debate and assignments to test student understanding.
Wide-ranging and inclusive, this text provides an invaluable review of an expansive selection of topics in human evolution, variation and adaptability for professionals and students in biological anthropology, evolutionary biology, medical sciences and psychology. The chapters are organized around four broad themes, with sections devoted to phenotypic and genetic variation within and between human populations, reproductive physiology and behavior, growth and development, and human health from evolutionary and ecological perspectives. An introductory section provides readers with the historical, theoretical and methodological foundations needed to understand the more complex ideas presented later. Two hundred discussion questions provide starting points for class debate and assignments to test student understanding.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
In the space of one generation major changes have begun to take place in the field of human reproduction. A rapid increase in the control of fertility and the understanding and treatment of sexual health issues have been accompanied by an emerging threat to reproductive function linked to increasing environmental pollution and dramatic changes in lifestyle. Organised around four key themes, this book provides a valuable review of some of the most important recent findings in human reproductive ecology. Major topics include the impact of the environment on reproduction, the role of physical activity and energetics in regulating reproduction, sexual maturation and ovulation assessment and demographic, health and family planning issues. Both theoretical and practical issues are covered, including the evolution and importance of the menopause and the various statistical methods by which researchers can analyse characteristics of the menstrual cycle in field studies.
New data based on retrospective interviews with older informants enable us to review the history of contraceptive use among Spanish women over much of the twentieth century. This source is unique because it includes cohorts of women whose reproductive lives took place before, during, and after the baby boom. Traditional contraceptive methods (withdrawal and periodic abstinence) were central to the experience of the first set of women, while the last set made full use of modern as well as some traditional methods. For the first cohorts, traditional methods spearheaded the historic decline in fertility, while among the last set of women modern methods led to a precipitous decline towards the below-replacement fertility that continues in Spain today. There is no evidence that the modest increases in fertility during the baby boom in Spain were the result of a decline in the use of contraception among married women.
Background: Previous kinship models analyze female kin through female lines of descent, neglecting male kin and male lines of descent. Because males and females differ in mortality and fertility, including both sexes in kinship models is an important unsolved problem. Objective: The objectives are to develop a kinship model including female and male kin through all lines of descent, to explore approximations when full sex-specific rates are unavailable, and to apply the model to several populations as an example. Methods: The kin of a focal individual form an age×sex-classified population and are projected as Focal ages using matrix methods, providing expected age-sex structures for every type of kin at every age of Focal. Initial conditions are based on the distribution of ages at maternity and paternity. Results: The equations for two-sex kinship dynamics are presented. As an example, the model is applied to populations with large (Senegal), medium (Haiti), and small (France) differences between female and male fertility. Results include numbers and sex ratios of kin as Focal ages. An approximation treating female and male rates as identical provides some insight into kin numbers, even when male and female rates are very different. Contribution: Many demographic and sociological parameters (e.g., aspects of health, bereavement, labor force participation) differ markedly between the sexes. This model permits analysis of such parameters in the context of kinship networks. The matrix formulation makes it possible to extend the two-sex analysis to include kin loss, multistate kin demography, and time varying rates.
Demographic methods have been evolving ever since the birth of demography in response to changes in the field's research contents and theoretical orientations. An early core mission of finding regularities underlying macro-level population phenomena and a later interest in explaining population changes inductively facilitated the development of formal demographic techniques. A more radical methodological shift occurred after the 1960s, with the increasing availability of micro-level survey data and a shift of theoretical focus toward causal mechanisms, leading to the widespread adoption of regression-based models and methods from other social science disciplines. The future development of demographic methods will likely continue to incorporate new methods first developed in other disciplines, including techniques for analyzing unstructured “big” data, but formal demographic techniques will still play a role in population forecasting, measurements improvements, and correction of faulty data, providing foundational knowledge for other social science disciplines.
Variance among individuals in fitness components reflects both genuine heterogeneity between individuals and stochasticity in events experienced along the life cycle. Maternal age represents a form of heterogeneity that affects both the mean and the variance of lifetime reproductive output (LRO). Here, we quantify the relative contribution of maternal age heterogeneity to the variance in LRO using individual-level laboratory data on the rotifer Brachionus manjavacas to parameterize a multistate age × maternal age matrix model. In B. manjavacas, advanced maternal age has large negative effects on offspring survival and fertility. We used multistate Markov chains with rewards to quantify the contributions to variance in LRO of heterogeneity and of the stochasticity inherent in the outcomes of probabilistic transitions and reproductive events. Under laboratory conditions, maternal age heterogeneity contributes 26% of the variance in LRO. The contribution changes when mortality and fertility are reduced to mimic more ecologically relevant environments. Over the parameter space where populations are near stationarity, maternal age heterogeneity contributes an average of 3% of the variance. Thus, the contributions of maternal age heterogeneity and individual stochasticity can be expected to depend strongly on environmental conditions; over most of the parameter space, the variance in LRO is dominated by stochasticity.
Abstract The approach underlying the model proposed in this article constitutes a considerable departure from the conventional methods used for the projection of birth series. Instead of following the customary procedure of directly projecting the age-specific fertility rates, they can be derived with this model from only three relatively simple fertility measures, namely, total fertility rate, mean age of fertility, and modal age of fertility. The reduction of the number of fertility parameters offers appreciable operational and analytical advantages. Among these, the most significant is the fact that statistical manipulation is confined to only three fertility measures, all of which are particularly appropriate for the in-depth analysis which is required to provide a rationale for assumptions of future fertility.
Abstract In different populations there is a common curve describing first-marriage frequency (first marriages per woman) as a function of age for each cohort. To fit the variety of patterns of human nuptiality it suffices to choose the age that serves as origin for a standard curve of first-marriage frequency, and to choose appropriate horizontal and vertical scales for the curve. The prevalence of a standard form for first-marriage frequency implies that the proportion ever-married in any cohort also rises along a standard curve, subject to choice of origin (the earliest age of first marriage), vertical scale (the proportion ever-marrying by the end of life), and horizontal scale (the pace at which the proportion ever-married increases with age). A mathematical expression (a double exponential) is found to fit the risk offirst marriage (among those who ever marry), and some of the implications of uniform features of nuptiality in different populations are discussed.
PIP
The authors present 2 methods for the approximation of a representative schedule recording first marriage frequencies by age. Both treatments are mathematically complex. One method achieves a very close approximation with a simple closed form frequency function, which is the limiting distribution of the convolution of an infinite number of exponentially distributed components. The other method achieves an equal approximation by the convolution of a normal distribution of age of entry into a marriageable state and as few as 3 exponentially distributed delays. This latter convolution provides a feasible model of nuptiality, a model receiving surprising empirical support.
Data on the natural fertility (complete absence of birth control) of 13 populations are examined with the study restricted to legitimate birthrates and those of unmarried women in a stable union. Very different fertility levels were found among these populations despite a similar pattern of fertility as it varies from 1 age group to another. Where the fertility rates for European populations are greater than for the non-European differences can be attributed to variation in birth spacing. It is hypothesized that differences in fertility level are either the result of variations in behavior related to resumption of sexual relations and the duration of lactation or to the differences of a physiological nature related to frequency and duration of anovulation during lactation.
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- Sully Ledermann
Ledermann, Sully. 1969. Nouvelles tables-types de mortalite'. Institut National d'Etudes
~Lmographiques,Travaux et Documents, Cahier 53. Paris: Presses Universitaires de France.
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Chapel Hill: University of North Carolina.
. 1974. Model fertility patterns for population projections. Presented at the Annual
Meeting of the Population Association of America, New York.
On demographic models of age-specific fertility rates
- K Tekse
Tekse, K. 1967. On demographic models of age-specific fertility rates. Statistisk Tidskrift
5(3):189-207.
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The Distribution by Age of the Frequency of First Marriage in a Female Cohort
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S. Mitra; A. Romaniuk
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On the scale of mortality
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The Distribution by Age of the Frequency of First Marriage in a
The Distribution by Age of the Frequency of First Marriage in a Female Cohort
A. J. Coale; D. R. McNeil
Journal of the American Statistical Association, Vol. 67, No. 340. (Dec., 1972), pp. 743-749.
Stable URL: