Departures from Gibrat's Law, Discontinuities and City Size Distributions

Cities are complex, self-organising, evolving systems and the emergent patterns they manifest provide insight into the dynamic processes in urban systems. This article analyses city size distributions, by decade, from the south-eastern region of the US for the years 1860—1990. It determines if the distributions are clustered into size classes and documents changes in the pattern of size classes over time. A statistical hypothesis test was also performed to detect dependence between city size and growth using discrete probability calculations under the assumption of Gibrat's law. The city size distributions for the south-eastern region of the US were discontinuous, with cities clustering into distinct size classes. The analysis also identified departures from Gibrat's law, indicating variable growth rates at different scales.

[1]  K. Bessey,et al.  Structure and Dynamics in an Urban Landscape: Toward a Multiscale View , 2002, Ecosystems.

[2]  Denise Pumain,et al.  City size distributions and metropolisation , 1997 .

[3]  D. Dendrinos,et al.  Fundamental issues in nonlinear urban population dynamic models , 1992, The Annals of regional science.

[4]  X. Gabaix.  Zipf's Law for Cities: An Explanation , 1999 .

[5]  C. Allen,et al.  Time-series Analysis of Clusters in City Size Distributions , 2005 .

[6]  B. Berry,et al.  Central places in Southern Germany , 1967 .

[7]  G. Duranton,et al.  Diversity and Specialisation in Cities: Why, Where and When Does it Matter? , 1999 .

[8]  M. York,et al.  ON THE CALIBRATION OF SILVERMAN'S TEST FOR MULTIMODALITY , 2001 .

[9]  Yuen Ren Chao,et al.  Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology , 1950 .

[10]  Lansun Chen,et al.  Dynamic complexities in a single-species discrete population model with stage structure and birth pulses , 2005 .

[11]  Shu-Li Huang,et al.  Ecological Energetics, Hierarchy, and Urban Form: A System Modelling Approach to the Evolution of Urban Zonation , 1998 .

[12]  Henry G. Overman,et al.  Spatial evolution of the US urban system , 2004 .

[13]  D. Andrews,et al.  City Sizes, Housing Costs, and Wealth , 2001 .

[14]  C. Perrings,et al.  Discontinuous change in multilevel hierarchical systems , 2007 .

[15]  John U. Marshall.  BEYOND THE RANK-SIZE RULE: A NEW DESCRIPTIVE MODEL OF CITY SIZES , 1997 .

[16]  C. S. Holling,et al.  Adaptive Inference for Distinguishing Credible from Incredible Patterns in Nature , 2002, Ecosystems.

[17]  Yannis M. Ioannides.  Spatial Evolution of the U . S . Urban System , 2003 .

[18]  Jianguo Wu,et al.  Modeling urban landscape dynamics: A review , 2004, Ecological Research.

[19]  Dimitrios S. Dendrinos,et al.  The Dynamics of Cities: Ecological Determinism, Dualism and Chaos , 1992 .

[20]  E J Malecki.  Growth and Change in the Analysis of Rank—Size Distributions: Empirical Findings , 1980 .

[21]  Empirical nonlinearities and neighbourhood effects in the intergenerational transmission of human capital , 2003 .

[22]  Yannis M. Ioannides,et al.  The Evolution of City Size Distributions , 2004 .

[23]  George Kingsley Zipf,et al.  Human Behaviour and the Principle of Least Effort: an Introduction to Human Ecology , 2012 .

[24]  Henry G. Overman,et al.  Cross-sectional evolution of the U.S. city size distribution , 2001 .

[25]  Yannis M. Ioannides,et al.  Zipf’s law for cities : an empirical examination , 2000 .

[26]  Hermann Haken,et al.  Slaving principle revisited , 1996 .

[27]  Roberto Tadei,et al.  Urban Systems: Contemporary Approaches to Modelling , 1987 .

[28]  Andrei Shleifer,et al.  Trade and Circuses : Explaining Urban Giants , 2007 .

[29]  K. Soo.  Zipf's law for cities: a cross-country investigation , 2005 .

[30]  Tomoya Mori,et al.  Structural stability and evolution of urban systems , 1997 .

[31]  Christopher H. Wheeler.  Evidence on agglomeration economies, diseconomies, and growth , 2003 .

[32]  J. Barkley Rosser,et al.  Dynamics of emergent urban hierarchy , 1994 .

[33]  K. Small,et al.  URBAN SPATIAL STRUCTURE. , 1997 .

[34]  Robert B. Potter,et al.  The Structure of Urban Systems , 1990 .

[35]  F. Guerin-pace,et al.  Rank-Size Distribution and the Process of Urban Growth , 1995 .

[36]  M. Batty.  Polynucleated Urban Landscapes , 2001 .

[37]  T. Holmes.  Scale of Local Production and City Size , 1999 .

[38]  P. Lachenbruch,et al.  Design Sensitivity: Statistical Power for Experimental Research. , 1989 .

[39]  Yannis M. Ioannides,et al.  Spatial interactions among U.S. cities: 1900–1990 , 2001 .

[40]  D. Rigby,et al.  Agglomeration economies and productivity differences in US cities , 2002 .

[41]  J. Eeckhout.  Gibrat's Law for (All) Cities , 2004 .

[42]  Craig R. Allen,et al.  Body Mass Patterns Predict Invasions and Extinctions in Transforming Landscapes , 1999, Ecosystems.

[43]  陳心蘋.  The Simulation of the Proposed Nonlinear Dynamic Urban Growth Model , 1993 .

[44]  Se-il Mun,et al.  Transport Network and System of Cities , 1997 .

[45]  Craig R. Allen,et al.  Cross-scale Structure and Scale Breaks in Ecosystems and Other Complex Systems , 2002, Ecosystems.

[46]  Roberto Tadei,et al.  An historical review of approaches to urban modelling , 1987 .

[47]  A. Sen.  On Economic Inequality , 1974 .

[48]  Roger White,et al.  Cellular Automata and Fractal Urban Form: A Cellular Modelling Approach to the Evolution of Urban Land-Use Patterns , 1993 .

[49]  Population growth and its distribution between cities: positive and normative aspects , 2004 .