Spatial patterns and size distributions of cities (original) (raw)
Related papers
Beyond the power law - a new approach to analyze city size distributions
Computers, Environment and Urban Systems, 2007
This work proposes a new approach to analyze the city size distribution (CSD). We present a general equation for the rank size logarithmic plot, with a new positive exponent a. When a = 1, the Pareto distribution is yielded; when a 5 1, the log of the curves exhibits a concave distribution. We studied the CSDs of 41 cases in 35 countries (in several countries we examined cities and metropolitan areas or agglomerations) in order to apply our new equation. We determined accurately the exponent a for 31 cases. In 18 cases we received a = 1, in one case a < 1, and in 12 cases a > 1. However, for the other cases, either the distributions were not homogeneous, or the data exhibited significant fluctuations which precluded a good determination of the exponent a. Based on this analysis, we developed a series of models (based on the models of town growth of Gabaix and of Blank and Solomon) in order to describe the different CSDs. The results of these models include power laws as well as cases that are represented by concave distributions on a logarithmic plot of the rank size.
City size distributions and metropolisation
Géographes associés
Many controversial questions about the shape and evolution of city size distributions can be solved if reliable, large and comparable set of data are used for several countries. We provide new empirical evidence by using the large data base 'Geopolis', which has strictly comparable figures for all towns and cities of the world over 10,000 inhabitants between 1950 and 1990. A Pareto model is used for identifying as metropolises one or a few large cities for each national urban system. From those data, two empirical power laws are established, linking the size of the metropolises to the size of their national urban system. The first is a transversal law: for a set of countries at a given date, the share of population concentrated in metropolises tends to decrease when larger countries are considered. The second law, which is longitudinal, shows that metropolises in the past have grown in a systematic way more rapidly than the rest of their urban system, invalidating Gibrat's urban growth model. Such empirical regularities could help for predicting the future of nowadays observed metropolisation trends.
On the distribution of city sizes
2008
The city size distribution in many countries is remarkably well described by a Pareto distribution. We derive conditions that standard urban models must satisfy in order to explain this regularity. We show that under general conditions urban models must have (i) a balanced growth path and (ii) a Pareto distribution for the underlying source of randomness. In particular, one of the following combinations can induce a Pareto distribution of city sizes: (i) preferences for different goods follow reflected random walks, and the elasticity of substitution between goods is 1; or (ii) total factor productivities of different goods follow reflected random walks, and increasing returns are equal across goods.
The evolution of city size distributions
2004
Abstract We review the accumulated knowledge on city size distributions and determinants of urban growth. This topic is of interest because of a number of key stylized facts, including notably Zipf's law for cities (which states that the number of cities of size greater than S is proportional to 1/S) and the importance of urban primacy. We first review the empirical evidence on the upper tail of city size distribution. We offer a novel discussion of the important econometric issues in the characterization of the distribution.
City Size Distribution and Growth
2000
We discuss theoretical approaches to study the relationship between the size distribution of a nation's cities and macroeconomic growth. The discussion is based on the hypothesis of the New Growth Theory that inter-personal spillovers of education and skills determine the long-run growth of the economy. Growth theory treats such externalities as being uniformly effective over national territories and completely internal to nation-state. This suggests a link to urban economics which has a long tradition of considering human capital externalities as driving forces of the growth of urban centers, with productivity increases inducing immigration. From the perspective of the urbanization literature long-run macroeconomic growth is thus determined by the functioning of cities as a catalysts for human capital accumulation. Theoretical avenues to the relationship between the development of cities of different sizes and aggregate growth can be distinguished according to whether the spill...
On the number and size of cities
Journal of Economic Geography, 2005
We study the effects of a decrease in trade costs on the spatial distribution of industry in a multi-regional economy, when a rise in the regional population of workers generates higher urban costs. When the number of cities is unaffected by falling trade costs, small cities become smaller for large trade costs, medium-sized cities for medium values of trade costs, and large cities for small trade costs. Furthermore, when urban costs are identical across cities,there exists a path of stable equilibria such that the industry, first, experiences progressive agglomeration into a decreasing number of cities and, then, dispersion into a growing number of cities.
A Spatial network explanation for a hierarchy of urban power laws
Power laws in socioeconomic systems are generally explainedas being generatedby multiplicative growth of aggregate objects. In this paper we formulate a model of geographic activity distribution with spatial correlations on the level of land lots where multiplicative growth is assumedto be dominant but not exclusive. The purpose is to retain the explanatory power of earlier models due to Simon, Gibrat and others while attaining some additional properties that are attractive for both empirical and modelling purposes. In this sense, the model presented here is a combination of the two factors that have been identified as central to urban evolution but rarely appear unifiedin the same model: transportation costs andmultiplicative growth. The model is an elaboration of a previously reportedcomplex network model of geographical landvalue evolution. We reproduce statistical properties of an empirical geographical distribution of land values on multiple hierarchical levels: landvalue per unit area, cluster areas, aggregatedlandvalue per cluster andcluster area/perimeter ratios. It is foundthat transportation effects are not strong enough to disturb the power law distribution of land values per unit area but strong enough to sort nodes to generate a new set of power laws on a higher level of aggregation. The main hypothesis is that all these relations can be understood as consequences of an underlying growing scale-free network of geographic economic interdependencies.
Dynamic evolution of the US city size distribution
1998
ABSTRACT We present a model of city size distributions that emphasizes the importance of human capital accumulation. We then use it to explore the evolution of city size distributions in the United States by means of a newly constructed data set. The data are from the US Census and cover metropolitan areas from 1900 to 1990.
Physical Review E, 2013
Urban agglomerations exhibit complex emergent features of which Zipf's law, i.e. a power-law size distribution, and fractality may be regarded as the most prominent ones. We propose a simplistic model for the generation of city-like structures which is solely based on the assumption that growth is more likely to take place close to inhabited space. The model involves one parameter which is an exponent determining how strongly the attraction decays with the distance. In addition, the model is run iteratively so that existing clusters can grow (together) and new ones can emerge. The model is capable of reproducing the size distribution and the fractality of the boundary of the largest cluster. While the power-law distribution depends on both, the imposed exponent and the iteration, the fractality seems to be independent of the former and only depends on the latter. Analyzing land-cover data we estimate the parameter-value γ ≈ 2.5 for Paris and it's surroundings.
An Across-Country Comparison of the Hierarchical Spatial Structures of Cities
GEOMATICA, 2014
This paper investigates the hierarchical structures of 29 selected European countries from the perspective of blocks and natural cities and makes an across-country comparison among the countries. Blocks are minimum cycles consisting of road segments in the road network of a whole country; natural cities are defined as the aggregations of small blocks. We test the size distributions of blocks and natural cities at the country level and find that both exhibit heavy-tailed distributions. The power law distribution of city sizes indicates the presence of the scaling property. Therefore, the cities in a country can be repeatedly grouped into a similar two-tier structure of head and tail via the head/tail division rule. The ascending tiers represent the small, medium, large and mega cities. Accordingly, a simple model is developed to evaluate and cross compare the degree of similarity and stability of the scaling properties and hierarchical structures of cities. Moreover, cities and blocks are the functional units of a country, and the correlation coefficient values between city sizes/number of blocks and economic factors (i.e., gross domestic product and population) are up to 0.87. We further conjecture that the compared results of hierarchies can serve as an indicator to assess a country's economic system.