Demography, Symmetry and the Emergence of Universal Patterns in Urban Systems

32 Pages Posted: 17 Oct 2019

See all articles by Luis Bettencourt

Luis Bettencourt

University of Chicago - Mansueto Institute for Urban Innovation

Daniel Zünd

University of Chicago

Date Written: October 15, 2019

Abstract

Urban areas exist in a wide variety of population sizes, from small towns to huge megaci- ties. The statistics of city size distributions have been under scrutiny for over a century. No proposed form has received more attention than Zipf’s law, a Pareto distribution with power value one. Data from many urban systems approximately support Zipf’s distribution while typically also violating its expectations for small and large cities and showing variations in ex- ponents. No theory presently exists to derive city size distributions from demographic choices while also explaining consistent variations. Here we show how the structure of migration flows between cities together with the differential magnitude of their vital rates determine a variety of size distributions. These results provide a powerful framework for deriving Zipf’s law and other size distributions under specific additional conditions, and to resolve puzzles associated with their deviations in terms of concepts of symmetry, information, and selection.

Keywords: city size distribution, Zipf's law, urban systems, symmetry, system integration

Suggested Citation

Bettencourt, Luis and Zünd, Daniel, Demography, Symmetry and the Emergence of Universal Patterns in Urban Systems (October 15, 2019). Mansueto Institute for Urban Innovation Research Paper . Available at SSRN: https://ssrn.com/abstract=3470821 or http://dx.doi.org/10.2139/ssrn.3470821

Luis Bettencourt (Contact Author)

University of Chicago - Mansueto Institute for Urban Innovation ( email )

5735 S Ellis Avenue
Chicago, IL 60637
United States

Daniel Zünd

University of Chicago ( email )

1101 East 58th Street
Chicago, IL 60637
United States

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