The arithmetic of growth: Methods of calculation

This is a tutorial on the relations between population data and the rates of growth that are calculated from the data. For the calculation of rates of growth, discrete and continuous compounding will be compared so that the reader can see the reasons for using the mathematics of continuous compounding, which is the mathematics of exponential growth. Some properties of exponential growth are developed. Semi-logarithmic graphs will be discussed as a device for representing the size of growing populations and for analyzing the nature of the growth. Illustrative examples will be worked out in order to emphasize applications and utility.     

Population growth in colonial America: A study of Ipswich, Massachusetts

Abstract During the colonial period, the settlements that subsequently became the United States of America experienced a tremendous growth of population. Although part of this increase was due to emigration from England and other European countries, most of the growth must be laid to the natural increase of the immigrants and their descendants. We are only beginning to probe the mechanisms ofthis increase. By numerous local studies, using the methods of historical demography that have largely been developed with work in French and English sources, we should eventually be able to describe the demographic nature of New World communities, and to understand how their populations were responding to a new physical, social and economic environment.     

Short-Term and Long-Term Educational Mobility of Families: A Two-Sex Approach

We use a multigenerational perspective to investigate how families reproduce and pass their educational advantages to succeeding generations. Unlike traditional mobility studies that have typically focused on one-sex influences from fathers to sons, we rely on a two-sex approach that accounts for interactions between males and females—the process in which males and females mate and have children with those of similar educational statuses and jointly determine the educational status attainment of their offspring. Using data from the Panel Study of Income Dynamics, we approach this issue from both a short-term and a long-term perspective. For the short term, grandparents’ educational attainments have a direct association with grandchildren’s education as well as an indirect association that is mediated by parents’ education and demographic behaviors. For the long term, initial educational advantages of families may benefit as many as three subsequent generations, but such advantages are later offset by the lower fertility of highly educated persons. Yet, all families eventually achieve the same educational distribution of descendants because of intermarriages between families of high- and low-education origin.     

The grandmother role as experienced by lesbian women

This study explores the grandmother role as experienced by a nonrandom sample of nine lesbian women. It examines how they define the grandmother role, and the behaviors and actions through which they enact the role. During individual interviews each woman was asked to talk about what makes a woman a good grandmother, memories of her own grandmothers, and the relationship she has with one or more of her grandchildren. The effect of her sexual orientation on the relationship was not explored. These women define the grandmother role as providing emotional support to their grandchildren, providing varied experiences for their grandchildren, and providing support for the parents of their grandchildren.     

The Grandmother Role as Experienced by Lesbian Women

ABSTRACT

This study explores the grandmother role as experienced by a nonrandom sample of nine lesbian women. It examines how they define the grandmother role, and the behaviors and actions through which they enact the role. During individual interviews each woman was asked to talk about what makes a woman a good grandmother, memories of her own grandmothers, and the relationship she has with one or more of her grandchildren. The effect of her sexual orientation on the relationship was not explored. These women define the grandmother role as providing emotional support to their grandchildren, providing varied experiences for their grandchildren, and providing support for the parents of their grandchildren.     

Grandparents providing care for grandchildren and employment status of grandparents in South Korea

This study examines the association between providing care for grandchildren and the economic status of grandparents, focusing on the employment status. This study asks two questions. First, is providing care for grandchildren related to Korean grandparents’ employment status? Second, are the intensities of providing care for grandchildren related to grandparents’ employment status? In examining these research questions, this study focuses on gender and caregiving intensity. The findings suggest that providing care for grandchildren was associated with Korean grandmothers’ employment status. In addition, there are different relationships between providing care for grandchildren and grandparents’ employment status according to the caregiving intensities.     

Diverging Mobility Trajectories: Grandparent Effects on Educational Attainment in One- and Two-Parent Families in the United States

In recent years, sociological research investigating grandparent effects in three-generation social mobility has proliferated, mostly focusing on the question of whether grandparents have a direct effect on their grandchildren’s social attainment. This study hypothesizes that prior research has overlooked family structure as an important factor that moderates grandparents’ direct effects. Capitalizing on a counterfactual causal framework and multigenerational data from the Panel Study of Income Dynamics, this study examines the direct effect of grandparents’ years of education on grandchildren’s years of educational attainment and heterogeneity in the effects associated with family structure. The results show that for both African Americans and whites, grandparent effects are the strongest for grandchildren who grew up in two-parent families, followed by those in single-parent families with divorced parents. The weakest effects were marked in single-parent families with unmarried parents. These findings suggest that the increasing diversity of family forms has led to diverging social mobility trajectories for families across generations.     

Women in the middle: generational position and grandmothers' adjustment to raising grandchildren

This study compared the adjustment of two groups of grandmothers who were providing primary care for grandchildren in split-generation households: 25 grandmothers in the oldest generation of their families (G1), and 22 grandmothers who had living parents or in-laws (G2). It was hypothesized that because of potential demands on them as middle-generation women, G2 grandmothers would report greater burden and depression in their caregiving roles than G1 grandmothers. After controlling for numerous factors that are associated with generational position, the hypothesis was confirmed. In addition to being in the middle generation, having grandchildren with problems predicted elevated depression and burden. Grandmothers who were educated beyond high school also reported greater role burden.     

Insights from the Evaluation of Past Local Area Population Forecasts

Local area population forecasts have a wide variety of uses in the public and private sectors. But not enough is known about the errors of such forecasts, particularly over the longer term (20 years or more). Understanding past errors is valuable for both forecast producers and users. This paper (i) evaluates the forecast accuracy of past local area population forecasts published by Australian State and Territory Governments over the last 30 years and (ii) illustrates the ways in which past error distributions can be employed to quantify the uncertainty of current forecasts. Population forecasts from the past 30 years were sourced from State and Territory Governments. Estimated resident populations to which the projections were compared were created for the geographical regions of the past projections. The key features of past forecast error patterns are described. Forecast errors mostly confirm earlier findings with regard to the relationship between error and length of projection horizon and population size. The paper then introduces the concept of a forecast ‘shelf life’, which indicates how far into the future a forecast is likely to remain reliable. It also illustrates how past error distributions can be used to create empirical prediction intervals for current forecasts. These two complementary measures provide a simple way of communicating the likely magnitude of error that can be expected with current local area population forecasts.     

The multistate stable population model with immigration

This paper outlines the discrete‐time and continuous‐time formulations of the stable population model with immigration, showing their commonality. It then illustrates how the model can be extended to include multiple interacting populations, and goes on to consider a multistate version of reproductive value that further illuminates the evolutionary dynamics of an “open”; model of multistate population growth and redistribution. Attention is restricted to results arising from a fertility regime that is below replacement level.     

The new census question about ancestry: What did it tell us?

In addition to specific inquiries about race and Spanish origin, the censuses of 1980 and 1990 included an open-ended question about ancestry, which replaced the question about parents' place of birth that had been used since 1870. This paper examines findings from the new ancestry question from the perspective of measuring ethnicity. The question adds little information about Hispanics, racial minorities, or recent immigrants, who can be identified readily on the basis of other census inquiries. The ancestry question allows us to characterize the descendants of European immigrants, but because of ethnic intermarriage, the numerous generations that separate present respondents from their forebears, and the apparent unimportance of ancestry to many whites of European origin, responses appear quite inconsistent. In regard to these groups, we may now be in an era of optional ethnicity, in which no simple census question will distinguish those who identify strongly with a specific European group from those who report symbolic or imagined ethnicity.     

Framing the Problem of Sex Trafficking

News media play an important role in explaining the issue of sex trafficking and may influence discourse among the public and policymakers. Understanding the ways that mass media address sex trafficking has implications for the news industry and the global status of women. This study, a quantitative content analysis, analyzed news coverage of sex trafficking in major US newspapers to understand how the issue was framed during a year of coverage. Using Entman's typology to classify the function of frames, the study focused on how news coverage defined the problem of sex trafficking and identified the remedy. The study found that news coverage of trafficking was overwhelmingly framed as a crime issue (episodic not thematic) and proposed no remedies. Most news coverage favored official sources. Survivors of trafficking and their advocates were the least heard-from sources. The authors argue ultimately that if media are to fulfill their watchdog role where trafficking is concerned, a wider range of news frames and sources is needed.     

Evolution and population dynamics in stochastic environments

Inter-generational temporal variability of the environment is important in the evolution and adaptation of phenotypic traits. We discuss a population-dynamic approach which plays a central role in the analysis of evolutionary processes. The basic principle is that the phenotypes with the greatest long-term average growth rate will dominate the entire population. The calculation of longterm average growth rates for populations under temporal stochasticity can be highly cumbersome. However, for a discrete non-overlapping population, it is identical to the geometric mean of the growth rates (geometric mean fitness), which is usually different from the simple arithmetic mean of growth rates. Evolutionary outcomes based on geometric mean fitness are often very different from the predictions based on the usual arithmetic mean fitness. In this paper we illustrate the concept of geometric mean fitness in a few simple models. We discuss its implications for the adaptive evolution of phenotypes, e.g. foraging under predation risks and clutch size. Next, we present an application: the risk-spreading egg-laying behaviour of the cabbage white butterfly, and develop a two-patch population dynamic model to show how the optimal solution diverges from the ssual arithmetic mean approach. The dynamics of these stochastic models cannot be predicted from the dynamics of simple deterministic models. Thus the inclusion of stochastic factors in the analyses of populations is essential to the understanding of not only population dynamics, but also their evolutionary dynamics.     

Age-specific growth rates: The legacy of past population dynamics

Recent developments in population mathematics have focused attention on a function that is widely available but rarely examined: the set of age-specific growth rates in a population. In particular, this set of rates is sufficient for translating the current birth rate and age-specific mortality rates into the current age distribution. This growth-rate function contains all of the pertinent features of a population's demographic history that are required to relate major demographic functions for a particular period to one another. This article presents an expression for the age-specific growth rate and uses it to derive an equation for age distribution. We show how the value of the age-specific growth rate is determined by a population's demographic past and present various sets of growth rates corresponding to stylized demographic scenarios. Several noteworthy sets of growth rates observed in human populations are discussed. Finally, we explain why age-specific growth rates make it possible to determine the age distribution solely from information on current demographic conditions.     

The Effects of Grandparents on Children’s Schooling: Evidence From Rural China

The issue of whether the social class of grandparents affects grandchildren’s socioeconomic outcomes net of the characteristics of the middle generation is much debated in the social mobility literature. Using data from the 2002 Chinese Household Income Project, we investigate the direct effects of grandparents on grandchildren’s educational attainment in rural China. We find that the influence of grandparents is contingent on living arrangements. Although the educational level of coresident grandparents directly affects the educational attainment of their grandchildren, with an effect size similar to that of parental education, the education of noncoresident and deceased grandparents does not have any effect. These findings suggest that grandparents can directly affect grandchildren’s educational outcomes through sociopsychological pathways. Our study not only adds an important case study to the literature but also sheds new light on theoretical interpretations of grandparent effects when they are found.     

Dynamics of Spanish-Language Neighborhoods in Chicago and Atlanta: 1990–2000

This study examines and compares how the spatial arrangements of Spanish speakers have changed over time in a traditional immigrant gateway, Chicago, and in an emerging immigrant gateway, Atlanta. Using the 1990 and 2000 U.S. Census data, spatial autocorrelation analysis confirms that Spanish-language neighborhoods continue to be in the city and the suburbs of Chicago. Atlanta’s Spanish-language neighborhoods, on the other hand, are mainly located in the suburbs where major growth took place over the decade. However, Spanish-language neighborhoods in both the city and suburbs of Atlanta and Chicago share similar characteristics: higher percentages of residents who are foreign-born and limited English proficient, and households with low levels of income. While the model of spatial assimilation is still relevant to our understanding of residential patterns among contemporary immigrants and their descendants, the interpretation of findings, including those for new destinations such as Atlanta where large-scale immigration occurred after suburbanization, should place less emphasis on the central city/suburb distinction and suburban homogeneity. The growing diversity in language use among residents necessitates the provision of accessible social services and information.     

论女儿养老与隔代养老的可能性——来自武汉市的调查

在城市家庭养老的研究中 ,有人提出了女儿养老与隔代养老的问题。本文从探寻孙辈与祖辈的相互理解程度、孙辈的养老责任感来研究隔代养老在多大程度上是可能的 ,并从女性与男性在理解父母的养老需求、他们的养老责任感等方面来探讨女性在养老意识方面的特点 ,由此提出对女性养老的看法。     

A demographic examination of grandparent caregivers in the Census 2000 Supplementary Survey

As part of the 1996 Welfare Reform Act, the Census Bureau is required to determine how many grandparents are serving as caregivers to a grandchild. Using data from the Census 2000 Supplementary Survey, this paper presents demographic information on two types of grandparent households, and outlines the challenges associated with use of the new questions about grandparent care developed by the Census Bureau. We compare skipped-generation households, in which a grandparent and grandchild coreside but no parent is present, to three-generation shared-care households in which the grandparent claims primary responsibility for the grandchild. We focus on two geographic regions of the United States, New England and the Deep South, providing the first report on the prevalence and characteristics of these households, and the extent to which these attributes are geographically variable. We estimate that the population of three-generation shared-care families is at least as large as the population ofskipped-generation grandparent care families.We identify a number of differences between skipped-generation and shared-care households, especially with respect to the age of the grandchildren involved and the levels of economic hardship. Significant regional differences are also observed, with grandparent care households of both types being more common in the Deep South than in New England. We conclude that data using these new questions have the potential to greatly enrich our demographic understanding of grandparent households by shedding new light on a type of grandparent care often hidden from analysis: grandparents who are responsible for grandchildren in three-generation households.