Explaining the prevalence, scaling and variance of urban phenomena

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Abstract

The prevalence of many urban phenomena changes systematically with population size1. We propose a theory that unifies models of economic complexity2,3 and cultural evolution4 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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Figure 1: Four facts across ten different urban phenomena that we seek to explain.
Figure 2: Relationship between inferred values of parameters G, H and G H ln N , across 43 different urban phenomena.
Figure 3: Predictions.

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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

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.

Correspondence to Andres Gomez-Lievano.

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Competing interests

The authors declare no competing interests.

Supplementary information

Supplementary Information

Supplementary Discussion, Supplementary Figures 1–7, Supplementary Data, Supplementary References. (PDF 2714 kb)

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. (ZIP 364 kb)

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Gomez-Lievano, A., Patterson-Lomba, O. & Hausmann, R. Explaining the prevalence, scaling and variance of urban phenomena. Nat Hum Behav 1, 0012 (2017) doi:10.1038/s41562-016-0012

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