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

South Carolina Co-operative Fish and Wildlife Research Unit and Program in Policy Studies, Clemson University, G27 Lehotsky Hall, Clemson, South Carolina 29634, USA, agarmes{at}clemson.edu

Craig R. Allen

USGS-Nebraska Co-operative Fish and Wildlife Research Unit and Program in Policy Studies, University of Nebraska, 423 Hardin Hall, Lincoln, NE 68583-0984, USA, callen3{at}unl.edu

Colin M. Gallagher

Department of Mathematical Sciences, Clemson University, 0-104 Martin Hall, Clemson, SC 29634-0975, USA, cgallag{at}clemson.edu

John D. Mittelstaedt

Department of Marketing, Clemson University, 253 Sirrine Hall, Box 341325, Clemson, SC 29634-1325, USA, jmittel{at}clemson.edu

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.

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