On the Rank-Size Distribution for Human Settlements

An explanation for the rank-size distribution for human settlements based on simple stochastic models of settlement formation and growth is presented. Not only does the analysis of the model explain the rank-size phenomenon in the upper tail, it also predicts a reverse rank-size phenomenon in the lower tail. Furthermore it yields a parametric form (the double Pareto-lognormal distribution) for the complete distribution of settlement sizes. Settlement-size data for four regions (two in Spain and two in the U.S.) are used as examples. For these regions the lower tail rank-size property is seen to hold and the double Pareto-lognormal distribution shown to provide an excellent fit, lending support to the model and to the explanation for the rank-size law.     

湖南省市镇规模等级结构的动态研究

本文应用市镇人口规模分布理论,研究了湖南省城市人口规模分布结构的动态变化及其基本特征。同时构造了2000年湖南省市镇序秩--规模分布模型,并利用logistic函数对预测结果进行了验证。预测表明:2000年南省市镇人口、市镇化水平分别约为2174万和32%,特大城市和大城市将扩大为长沙、衡阳、湘潭、株洲、岳阳和常德六市。据此对2000年湖南省市镇等级体系进行了规划。     

The Return of Zipf: Towards a Further Understanding of the Rank-Size Distribution

We offer a general-equilibrium economic approach to Zipf's Law or, more generally, the rank-size distribution—the striking empirical regularity concerning the size distribution of cities. We provide some further understanding of Zipf's Law by incorporating negative feedbacks (congestion) in a popular model of economic geography and international trade. This model allows the powers of agglomeration and spreading to be in long-run equilibrium, which enhances our understanding of the existence of a rank-size distribution of cities.     

基于Kernel密度解释的江苏省城市规模结构演化研究

城市规模结构研究可以反映城市在不同规模等级中的分布状况及城市人口集聚或分散程度,有助于认识城市体系发展所处的阶段以及该区域城市化进程的特征。研究运用Kernel城市空间密度分析方法,直观的反映了江苏省城市规模分布格局的连续变化。分别从城市体系的空间格局、城镇密集带的结构变化和长三角城市群城镇网络构建等视角对城市规模结构进行探讨,指出全省城市规模空间分布的Kernel密度在整体上具有西高东低、南密北疏的态势;城市体系的空间模式由最初的核心-边缘结构,逐渐向点-轴-面结构演化;南京都市圈的进一步延伸,将促进长三角多核心巨型城市网络向更大地域范围拓展。由此提出全省在不断优化城市体系的同时,需要更加注重大中城市及小城镇协调发展机制的建设,加强对苏中、苏北地区城市人口规模的扩张和城市规模布局的均衡,建立具备完整城市功能的网络城市发展模式,以更好的促进区域一体化发展。     

A PROPERTY OF THE RANK-SIZE DISTRIBUTION AND ITS USE IN AN URBAN HIERARCHY CONTEXT

This paper proves the symmetry of the classical rank-size distribution with respect to any city according to a criterion of relative population difference. This property is used to characterize the distribution of city sizes around the median center of their hierarchical level by the existence of symmetry, of an upper bound to dispersion, and of a regular spacing. An interpretation is suggested.     

中国城市群空间结构演化的影响因素分析——基于铁路客运的功能联系视角

以中国13个城市群为研究对象,采用铁路客运班次构造多中心指数来表征基于功能联系的城市群空间结构,在分析城市群空间结构演变基础上重点分析其影响因素。研究发现,基于功能联系视角的城市群空间结构总体呈单中心化趋势,但地区差异化明显,珠三角、山东半岛和闽东南城市群已表现出多中心化特征;城市群空间结构的多中心程度随经济发展水平的提高表现为先单中心后多中心的演变过程;城市群规模的增大和城市间联系加强促进了城市群向多中心方向演化;而面积小、三产比重高的城市群更有利于形成单中心的结构;政府干预作用对城市群空间结构影响并不显著。鉴于不同城市群空间结构演化趋势不同,未来政策取向应该遵从各个城市群自身规律。     

Properties of a General Hierarchial City-size Model

Beckmann and McPherson recently outlined a general hierarchial model of city size. The authors argued that by imposing particular constraints upon this general model they would make it compatible both with the rank-size rule and a much simpler (basic progression component) model previously outlined in the literature. The present paper challenges these two contentions. It is first demonstrated that the constraints proposed by Beckmann and McPherson do not lead to either form of compatibility. Then the author illustrates how such compatibility may in fact exist under somewhat different conditions.     

Increasing Unevenness in the Distribution of City Sizes in Post-Soviet Russia

This paper describes the distribution of urban areas in post-Soviet Russia using the rank-size method for quantifying longitudinal change. As many studies show, urbanization under state socialism achieved a relatively uniform city-size distribution in accordance to Marxist ideals. I test the initial hypothesis that variation in city size would increase after dissolution of the USSR, to converge toward distributions found in market economies. The analysis shows that increasing unevenness in city-size depends on the nature of variation that existed prior to the USSR's disintegration, as well as on geographic location within Russia. Journal of Economic Literature, Classification Numbers: J61, O18, R58. 7 figures, 4 tables, 46 references.     

EVOLUTION OF URBAN SYSTEMS IN THE PARETO PLANE*

ABSTRACT Distributions of city sizes are usually characterized by their Pareto index. This, however, turns out to be a rather restrictive view, for the Pareto distribution is known to become singular whenever the Pareto index becomes smaller than one, a case which is fairly frequent in empirical distributions. We show that the introduction of finite Pareto distributions in which city sizes are bounded from above solves a number of difficulties encountered by the rank-size rule and by the unbounded Pareto distribution. Combined with the use of finite Pareto distributions, the green-belt model that has been introduced previously is reexamined. It implies definite constraints for the long-run evolution of urban systems; it is in the cases of countries experiencing a process of fast urbanization that these constraints are of greatest significance. The implications of the model are confronted with empirical evidence concerning the evolution of urban systems in major industrialized countries during the nineteenth and twentieth centuries.     

Stone circles and the structure of Bronze Age society

Analyses of modern human societies have consistently demonstrated the presence of recurrent grouping levels forming a nested, hierarchical structure. That this structure exists in both hunter-gatherer and western industrialized societies suggests that it may be a fundamental organizing principle of considerable antiquity. Stone circles are perceived as being foci of aggregation for prehistoric groups and thus provide a proxy for the sizes of those aggregations. Combining an empirical analysis of a sample of 140 stone circles with a Monte Carlo simulation model that derives expectations for a continuous size distribution based on the nested hierarchy concept, the current paper suggests that similar organizing principles were already in place during the Bronze Age. Furthermore, it is suggested that findings traditionally attributed to the operation of the ‘rank-size rule’ may in fact reflect the basic underlying structure of human society.     

Zones of Influence of Middle-Size Cities,Their Boundaries and Passenger Flows

A modified gravity model is used to describe the flows of commuters between a central city and concentric zones around it. A multiplier-type model of a central-place system (after Christaller) is then used to calculate the number of residents for service centers at each level of the hierarchy within the system. The rank-size rule (Zipf's formula) is also considered as a criterion of a true system of urban places. Results are presented for the urban network of the Ukraine.     

风险视角下的城市聚落形成模拟

幂次法则是普遍存在于自然科学和社会科学界的现象,而城市位序-规模法则是幂次法则在城市科学中的体现之一,然而特定城市规模分布一直缺乏完整的解释。本文尝试结合城市增长过程中土地开发行为的报酬递增规则与土地开发主体的风险认知行为,以城市增长的微观过程为切入视角模拟宏观城市聚落演化过程,进而探讨风险态度对城市聚落形态,尤其是对其规模分布的影响。研究结果表明：①即使城市聚落演化过程中存在多种风险态度,幂次法则在城市聚落的规模分布中仍保持着稳健性; ②现实世界中城市聚落规模分布的变异和稳定可能来自城市主体风险态度的多样性。     

An archaeological signature of multi-level social systems: The case of the Irish Bronze Age

Recent research suggests that contemporary human social groups are structured according to principles of fission and fusion that are also observed in some of our primate relatives, raising the possibility that such social systems have been a feature of hominin society throughout prehistory. The current paper examines the possibility of identifying archaeological signatures of multi-level social structures through the examination of site size distributions. Data on the sizes of Irish Bronze Age stone circles and predictions for the size of aggregations they could accommodate are compared with simulations parameterized using data on modern human groups. The results suggest that the presence of hierarchically inclusive, multi-level social structures provides a better explanation for the data than more traditional archaeological accounts based on the rank-size rule and related inferences concerning the emergence of political elites.     

基于分形理论的长株潭城市群等级规模结构研究及对策

运用城市群等级规模结构分形理论和方法,对长株潭"3+5"城市群(以下简称"3+5"城市群)的等级规模结构进行了实证研究,通过测算几年来"3+5"城市群等级规模分布的分维值,得出结论:"3+5"城市群规模分布符合分形特征;模型拟合认为其人口、经济分布的分维值均大于1,表明"3+5"城市群等级规模结构集中,已处于发展的相对成熟阶段。为此在对这些特征做出解释的基础上,认为可从强化首位城市、加快长株潭一体化建设、提升次中心城市、重点发展中小城市、加快小城镇建设等方面着手对长株潭城市群等级规模结构进行优化。     

The Dynamics of Growth in a Regional Urban System: Southern Ontario, 1851–1971

This study has four objectives: (1) to describe the dynamics of growth in the urban system of southern Ontario over the period from 1851 to 1971; (2) to determine whether this system has evolved in accordance with the Gibrat process of growth; (3) to contribute to the debate on the relationship between city-size distributions and economic development; and (4) to offer some technical and definitional suggestions with regard to the rank-size rule, urban primacy, and the measurement of population concentration. Related Canadian studies covering similar time periods are those of Simmons (1974), who has analysed the growth of larger cities (10,000 and over) at the national scale, and Bannister (1975), who has described the extent of spatial autocorrelation in the growth rates of southern Ontario's incorporated centres. Like Simmons and Bannister we are less concerned with the fortunes of particular places than with the response of the urban system as a whole to expansionary forces. We are centrally concerned with the phenomenon of differential growth (Borchert, 1967; Ward, 1971, pp. 11–49; Muller, 1976, 1977). The fact that towns grow at different rates implies changes in the frequency distribution of city size and in the level of concentration of the urban population. These changes, in turn, have interesting consequences for urban systems theory.     

中国互联网与区域经济

文章运用指数定律分析了中国互联网的域名地区分布、地区人均国内生产总值分布和地区人口分布,得出的结论是:中国互联网分布是地区人均国内生产总值的反映,与地区人口分布联系不大。这证实了互联网与区域经济的紧密相关性。研究中还发现,中国互联网仍然处于高速增长期;最后给出了中国互联网增长的速度,以及到达成熟稳定时期所需的时间。     

Distribution parameters of guanaco (Lama guanicoe), pampas deer (Ozotoceros bezoarticus) and marsh deer (Blastocerus dichotomus) in Central Argentina: Archaeological and paleoenvironmental implications

In this paper we use non-ambiguous collections and sightings data from the 18th century to generate potential distribution models of three species of South American ungulates. These ungulates (Lama guanicoe -guanaco-; Ozotoceras bezoarticus -pampas deer- and Blastoceros dichotomus -marsh deer-) have different and specific environmental requirements. Through MaxEnt software, twenty-two environmental variables that characterize the distribution area of each species are defined. Once the models are generated, they are compared with the faunal associations found at Late Holocene archaelogical sites in order to infer paleoenvironmental conditions. We also discuss the role played by humans in the faunal associations which are "anomalous" or inconsistent with those models, like the spatial overlap of guanaco and marsh deer.     

Emergence of fusion/fission cycling and self-organized criticality from a simulation model of early complex polities

A spatial-temporal model of early complex polities is described in which cycles of consolidation and collapse emerged during simulations. Self-organized criticality (SOC) also was clearly observed. SOC is characteristic of simulations for iterative physical phenomena such as earthquakes and forest fires. Social scientists are interested in SOC as a theoretical framework to understand cyclical human cultural processes. In particular there has been considerable speculation that SOC underlies polity cycling. The current model is an attempt to move beyond speculation by demonstrating that: 1) the model unequivocally exhibits SOC, 2) there is a self-evident correspondence between the model’s structure and actual polities as indicated in the archaeological record, 3) hierarchical settlement patterns emerge during simulations, and 4) simulated population distributions are consistent with empirical rank-size survey data typical of early complex polities.     

华北平原农村居民点演变及社会经济影响因素分析

基于遥感图像分类解译数据,利用位序-规模模型、洛伦兹曲线、景观指数,定量识别了2000-2015年华北平原农村居民点空间分布、规模与形态演变特征,分析了社会经济因素的驱动机制。结果表明：华北平原农村居民点南-北方向呈显著的空间分异与集聚特征,密度分布呈现南密北疏的态势,与面积规模分布存在局域负相关;农村居民点景观指数显示出密度增大、形状更加规则、斑块面积差异增大、斑块间邻近距离不断缩短的变化特征;总人口数量和乡村户数等对农村居民点用地扩张具有促进作用,乡村常住人口、乡村从业人员数量等的作用为负。     

A GENERAL FRAMEWORK FOR THE INTEGRATION OF A LAND-USE MODEL WITH A TRANSPORTATION MODEL COMPONENT

Integrated land-use—transportation models are characterized as models in which the redistributive effects of one subsystem upon the other are explicitly defined and incorporated into the model's structure. At the core of integrated models is a linking procedure whose function is to transform the outputs of one model component into inputs for the other. Despite major efforts made in the past to build operational large scale integrated models, the structural properties of such models remain largely unexplored. This paper describes a general framework for an integrated model consisting of prototype model components. These are an iterative activity allocation model of the Garin-Lowry type, an equilibrium-assignment transportation network model, and a linking procedure. Given the level of analysis, this framework is shown useful for exploring the analytics of integrated models and, in particular, their equilibrium properties. By means of many simulation experiments based on an hypothetical numerical example, the operation of the model is demonstrated with an emphasis on the locational interpretation of the integration procedure. On the basis of the empirical results and considering the model's intrinsic assumptions, the following major findings can be cited. First, the effects of nontravel factors (such as basic employment and zonal attractions) upon activity distribution are stronger than effects caused by changes in the transportation system. The latter effects were found to yield nonlinear and, spatially, nonuniform changes in activity location which also tended to be larger in peripheral regions. Second, implicit in the specification of the integration procedure are behavioral assumptions regarding time-lags in locational adjustments made by activities in reaction to rising cost of travel. The present formulation implies that once located, activities do not revise their locational decisions despite substantial increases in travel costs. At the other extreme, all activities are permitted to readjust their locational preferences after the final interzonal travel costs are derived. The effect upon activity distribution of the latter specification is, of course, larger than that of the former, although less than the effect yielded by changes in nontravel factors. Regarding the equilibrium properties of the integrated system, both the theoretical and empirical analyses show that the entire model will converge into an equilibrium solution and that the corresponding trip patterns are also at equilibrium. These results will hold as long as the operation of the integrated models is completely controlled by the generation functions of the land-use model and the transportation model component only affects the spatial distribution of activities. Finally, the results from the simulation experiments indicate that the computed mean travel cost parameter tends to stabilize around a certain value as the level of demand for travel, within the system, rises. There is evidence that compensating changes in the location and composition of this demand are the main causes of this phenomenon. In light of these findings, it is possible to point to three key problems whose resolution could largely improve the predictive power of integrated models. First, it would be useful to define activity models in which the generation of activities is, among other things, a function of travel conditions. Second, currently formulated integrated models do not contain trip demand functions and, thus, demand for travel by an activity unit is regarded as completely inelastic. Third, different locating activities respond differently—over time and space—to changíng travel conditions, and models should, therefore, reflect explicitly such differences in activity behavior. A recent paper by Los [14], is an important contribution to the analysis of this issue.