The temporal and spatial dynamics of city-size distributions in China

Under the communist regime, the Chinese government has developed policies both to limit the growth of large cities and to promote spatial equity in population distribution. The literature provides only very general and inconclusive results regarding the impact of these policies. This paper aims at evaluating the effectiveness of China's urban policies by investigating the temporal and spatial dynamics of the size distribution of China's cities during the period 1922–82. The research framework — which is based on a function relating population size to rank —is used to test for trends of deconcentration (where smaller cities grow faster than larger cities) and spatial decentralization (with a more even spatial distribution) of population over the study period. More formally, the ‘expansion methodology’ is used to investigate the dynamics of the rank-size function in both temporal and spatial dimensions. The findings show that from 1953 to 1970 there was significant population deconcentration, which appeared to be reversed subsequently. However, policies of spatial decentralization were not found to be successful. Among the reasons suggested for the apparent failure are political upheavals and shifts in policies, the inertia within the urban system, the harsh physical environment in the interior, and current trends in economic policies that focus on the coastal areas. In spite of recent criticisms of studies on city-size distributions (which this paper also discusses), the research framework proposed and utilized here is able to portray the dynamics of a national urban system, and the framework can be used to evaluate national urban policies.     

Inconstancy of Taylor'sb: Simulated sampling with different quadrat sizes and spatial distributions

Summary Taylor's power law,s ² =am ^b , provides a precise summary of the relationship between sample variance (s ² ) and sample mean (m) for many organisms. The coefficientb has been interpreted as an index of aggregation, with a characteristic value for a given species in a particular environment, and has been thought to be independent of the sample unit. Simulation studies were conducted that demonstrate that the value ofb may vary with the size of the sample unit in quadrat sampling, and this relationship, in turn, depends on the underlying spatial distribution of the population. For example, simulated populations with hierarchical aggregation on a large scale produced values ofb that increased with the size of the sample unit. In contrast, for a simulated population with randomly distributed clusters of individuals, the value ofb eventually decreased with increasing quadrat size, as sample counts became more uniform. A single value ofTaylor'sb, determined with a particular sample unit, provides neither a fixed index of aggregation nor a complete picture of a species' spatial distribution. Rather, it describes a consistent relationship between sample variance and sample mean over a range of densities, on a spatial scale related to the size of the sample unit. This relationship may reflect, but not uniquely define, density-dependent population and behavioral processes governing the spatial distribution of the organism. Interpretation ofTaylor'sb for a particular organism should be qualified by reference to the sample unit, and comparisons should not be made between cases in which different sample units were used. Whenever possible, a range of sample units should be used to provide information about the pattern of distribution of a population on various spatial scales.     

Measuring change and continuity in parity distributions

Procedures are developed to allocate the change in mean fertility to the change in specific parities or groups of parities. One procedure uses the proportion at each parity and another uses parity progression ratios. Both are based on the delta method for approximating change in a function of several variables. Drawing on an analogy to survival in a life table, the relational logit model is applied to parity progression. This method allows several parity distributions to be synthesized and to have differences summarized with two parameters. The three procedures are applied to successive cohorts of white U.S. women who completed their childbearing between 1920 and 1980.     

Postcensal estimates of household income distributions

This article develops and evaluates a method for deriving postcensal estimates of household income distributions for counties. A modified lognormal probability curve is used as a model of income distribution. The function is closely related to the classical lognormal model, but it contains a nonlinear component in its derivation. Simulated postcensal estimates of household income distributions are compared with 1980 census data for the counties in California. The results indicate that the modified lognormal curve approximates observed income distributions well and produces reliable postcensal estimates for areas with a wide variety of median income levels and numbers of households.     

Analysing open birth interval distributions

Summary This paper began with the recognition that open birth interval distributions are analogous to age distributions. It then became clear that closed birth interval distributions are, somewhat more loosely, analogous to mortality schedules, and that the relationship between open and closed birth interval distributions could be explored by imitating the formal demography of mortality and age distribution. Pursuing this programme, we develop the formal demography of open and closed birth interval distributions and show that under certain assumptions open interval distributions may be used to estimate closed interval distributions, just as age distributions may be used to estimate mortality. An illustrative application to Indonesian data is given.     

Stable age by region distributions

If the pattern of fertility, mortality and interregional migration exhibited by the United States population during 1950–60 were to continue in the future, the proportions of persons in the various age groups and regions would fluctuate from decade to decade. These fluctuations would become less marked with time, however, and eventually all the proportions would stabilize at certain fixed values. This collection of values may be called astable age by region composition corresponding to the given schedule of fertility, mortality and migration. The same phenomenon may be observed when individuals move between socioeconomic categories as, for example, socioeconomic status or educational attainment levels. The substantial differences between these various situations conceal remarkable similarities. In each case the continued operation of schedules of fertility, mortality and mobility between categories may result in a stable composition. The purpose of this paper is to shed some light on the nature of these stable compositions, on the interrelation between their various components, and on their relation to the patterns of fertility, mortality and mobility which generate them.     

Changing vital rates and age distributions

Abstract In a time of rapid change in birth and death rates demographers need to know the consequences of such changes for age distribution. Does the fall in death rates tend to make the age distribution older? It certainly enables individuals to grow older, but for population aggregates the effect depends on the ages at which mortality improves. Coale, Stolnitz, Schwarz, Lorimer, the United Nations and other writers have investigated trends in age-specific birth and death rates. In particular they have demonstrated that the falling mortality which is now nearly universal does not generally make the population older and sometimes makes it younger. The present article contributes a technique for further examination of this phenomenon.     

Some spatial aspects of poverty in the USA

The social problem of poverty in the USA. has important spatial dimensions. The great migration of poor persons from the agricultural South to the industrial North shaped the nation's process of urbanization in the period after World War II. Subsequent suburbanization in the nation's cities was profoundly influenced by this movement and, in turn, had important implications for the urban poor. Also, the changing structure of employment opportunities within urban areas has had direct effects on the nature of the poverty problem in terms of spatial segregation and the persistence of poverty in urban areas. This paper offers a survey of the spatial aspects of poverty in the USA. and relates the problem of poverty to the forces of change that have contributed to the spatial transformation of the US economy.     

Measuring spatial focusing in a migration system

Equality indexes used in other geographical contexts may be used to gauge the degree of spatial focusing in an entire migration system or within the gross in- and out-migration fields of specific regions. They provide useful indicators of overall shifts in the patterns of interregional migration and can help give insight into the population redistributive roles played by specific regions. Perhaps the most common equality index used to measure income distribution is the Gini coefficient, yet it appears almost never to have been applied in migration research. In this paper we set forth a variety of Gini indexes to be used for different migration analyses and illustrate their application with recent data on U.S. interstate movements. We argue that the Gini index provides some singularly useful insights that differ from those afforded by other measures more commonly found to date in the migration analyst’ s toolkit.     

Stationary distributions in Kolmogorov-Petrovski- Piskunov-type models with an infinite number of particles

A model of population dynamics in continuous time on the lattice contains the Kolmogorov-Petrovski-Piskunov equation as a special case. A limit distribution exists. The first three moments and the correlation function are expressed.     

An index of spatial distribution

Summary The index , which takes the value of −1 for a perfectly regular distribution, +1 for a highly aggregated distribution and 0 for the distribution implied by the theoretical varianceσ ², is proposed and a significance table provided.     

Temporal and spatial analysis of fertility decline in Taiwan

Abstract The conventional mode of evaluating the success of family planning programmes has frequently emphasized the activities of the programmes, rather than their ultimate effects. This paper examines the role of family planning programmes in inducing fertility decline in Taiwan. First it presents the secular trends of Taiwanese fertility changes, pointing out that family planning programmes began only after the birth rate had already shown a substantial decline. Secondly, it specifically evaluates the impact of family planning programmes in the Taichung areas, since its success has been widely proclaimed. Finally, it is stipulated that the dynamics of Taiwanese fertility changes may be related to declining infant mortality and accelerating educational development, and that these institutional effects, rather than the family planning programmes, should be credited with changes in fertility.     

The spatial separation of the poor in Canadian cities

We used the 1991 Canadian census to examine the extent of spatial separation of the poor in Canadian cities. Although there were no extensive areas of blight, decay, or housing abandonment, we found high spatial separation of poor visible minorities in the selected cities. The index of dissimilarity indicates high segregation of poor blacks and moderate separation of poor Asians from the nonpoor population. We tested the effects of three major structural factors--racial and ethnic segregation, income segregation, and urban redevelopment--and found that racial and ethnic residential patterns are related strongly to the spatial separation of poor persons. The relationship between income segregation and spatial separation of the poor is not significant, however. We also found that the relationship between urban redevelopment and spatial separation of the poor pertains only to blacks. These findings suggest that blacks are vulnerable in the process of urban redevelopment.     

On some probability distributions for forward birth interval

Parents’ decisions to have children are modeled by a simple stopping rule that describes the probability of having another child as a function of the number of boys and girls already born to the parents. Because the stopping rule depends on the sex of the offspring, the rule may introduce a correlation between sex of offspring and the number of siblings the offspring has. When this is coupled with a correlation between number of siblings and well‐being, a correlation between sex and well‐being may emerge despite equal treatment of the two sexes within each family. The author provides sufficient conditions on a stopping rule for it to be sexist in the sense that the average well‐being of one sex is higher than that of the other sex.     

On some probability distributions for forward birth interval

Statisticians from Varanasi, India have proposed 2 mathematical models for forward birth interval which are more realistic than past models. For example, past models have assumed fecundability to be constant throughout a woman's reproductive life. On the other hand, the proposed models assume fecundability changes with parity. Further the statisticians use all types of marital durations making their models usable even for short marriage durations. The 1st model uses a parity specific model to develop a model for forward birth interval regarless of parity. The statisticians also include moments of the 1st and 2nd models as expressed for the rth order raw movement of these models to estimate some of their parameters. These models can be used to conduct prospective surveys of family planning programs since birth intervals can best evaluate the effect of these programs. These models have not yet been advanced enough to follow women over a fixed period, however. They only observe women until the last woman conceives. The statisticians do not apply the models to parity specific data because they were not available. Yet they do run the models with parities 0 and 1. The models reveal that the mean length of forward birth interval is strongly influenced by the conception rate which the woman has at the time of the survey. Thus, if women with a certain parity in a community begin an effective family planning method on the survey day, which in effect would reduce the prevailing conception rate, that method would significantly postpone the next live birth.     

A distance measure of spatial pattern in a biological population

Summary Suppose thatn individuals locate independently and randomly on a segment of line of finite length (habitat). Let the theoretical and observed ranges of the sites of the individuals on the segment be μ _n-1 andr _n-1, respectively. Then, the degree of dispersion of the individual sites is measured by the ratio, T _n =n _n-1/μ _n-1, as follows: A random spatial pattern forI _r−1 =1 An aggregated spatial pattern for 0≤I _r <1 A uniform spatial pattern for (n+1)/(n−1)≥I _r >1. Another method was derived. Let the probability that an observed range is less thanr _n−1 beI _p , under the hypothesis of a Beta distribution. Then indicates A random spatial pattern forI _p =1/2 An aggregated spatial pattern forI _p <1/2 A uniform spatial pattern forI _p >1/2. The first index can be used for comparing populations having the same number of individuals, whereas the second one can be used for comparing populations with different numbers of individuals.     

Relation of transition probabilities in the Leslie model to those from experimental cumulative distributions

Summary We explore the relationship between transition probabilities in the Leslie model and those derived from experimental cumulative distributions. The nature of the two kinds of probabilities are discussed, and a formula derived for converting from one to the other. A numerical example is given to illustrate the differences.