Letter

Explaining the prevalence, scaling and variance of urban phenomena

  • Nature Human Behaviour 1, Article number: 0012 (2016)
  • doi:10.1038/s41562-016-0012
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Abstract

The prevalence of many urban phenomena changes systematically with population size 1 . We propose a theory that unifies models of economic complexity 2,3 and cultural evolution 4 to derive urban scaling. The theory accounts for the difference in scaling exponents and average prevalence across phenomena, as well as the difference in the variance within phenomena across cities of similar size. The central ideas are that a number of necessary complementary factors must be simultaneously present for a phenomenon to occur, and that the diversity of factors is logarithmically related to population size. The model reveals that phenomena that require more factors will be less prevalent, scale more superlinearly and show larger variance across cities of similar size. The theory applies to data on education, employment, innovation, disease and crime, and it entails the ability to predict the prevalence of a phenomenon across cities, given information about the prevalence in a single city.

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Acknowledgements

We thank A.-L. Barabasi, J. Lobo, L. M. A. Bettencourt, F. Neffke, S. Valverde, D. Diodato and C. Brummitt for their comments on this work. We also thank M. Akmanalp and W. Strimling for their suggestions about aesthetics. This work was funded by the MasterCard Center for Inclusive Growth, and Alejandro Santo Domingo. O.P-L. acknowledges support by National Institutes of Health (NIH) grant T32AI007358-26. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author information

Affiliations

  1. Center for International Development, Harvard University, Cambridge, Massachusetts 02138, USA

    • Andres Gomez-Lievano
    •  & Ricardo Hausmann
  2. Harvard T.H. Chan School of Public Health, Harvard University, Boston, Massachusetts 02115, USA

    • Oscar Patterson-Lomba
  3. Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

    • Ricardo Hausmann
  4. Harvard Kennedy School, Harvard University, Cambridge, Massachusetts 02138, USA

    • Ricardo Hausmann

Authors

  1. Search for Andres Gomez-Lievano in:

  2. Search for Oscar Patterson-Lomba in:

  3. Search for Ricardo Hausmann in:

Contributions

A.G-L. and O.P-L. collected the data, and conceived and designed the study. A.G-L. conducted the analyses. A.G-L. and R.H. developed the model. A.G-L., O.P-L. and R.H. wrote the manuscript. All three authors reviewed and approved the paper.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Andres Gomez-Lievano.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    Supplementary Discussion, Supplementary Figures 1–7, Supplementary Data, Supplementary References.

Zip files

  1. 1.

    Supplementary Data

    The file contains a set of single files, one for each urban phenomenon we studied (except for Sexually Transmitted Diseases, which we kept in a separate file), a README file, and an Excel file, which lists the different phenomena we used in our analysis with other parameters and field descriptions.