IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v136y2020ics0960077920302095.html
   My bibliography  Save this article

Distance distributions of human settlements

Author

Listed:
  • Fernández-Rosales, Iván Yair
  • Angulo-Brown, Fernando
  • Pérez-Campuzano, Enrique
  • Guzmán-Vargas, Lev

Abstract

City-size distributions have been studied from different perspectives in past decades. However, spatial properties of city distributions have not been widely explored. Here, we study distance distribution between pairs of cities by considering their sizes for data from ten countries. We find that distance distributions present different shapes, from quasi-symmetrical to right-skewed, which exhibit changes as the lower threshold of the city size is increased. The Gini index G and the normalized Shannon entropy ES were calculated to evaluate the inequality and heterogeneity (diversity) in the distance distributions. Our results show that quasi-symmetrical distributions are characterized by a low inequality and intermediate value of entropy, while right-skewed distributions lead to higher inequality indexes with different levels of diversity. We introduce the big-club (set of the largest cities) coefficient to evaluate the tendency of big settlements to be located close to (or far away from) each other, finding that most of the countries have a high big-club value. Finally, we consider a simple model based on node sizes to generate three configurations with different spatial correlations (random, correlated and anti-correlated), which roughly reproduce similar values of G and ES to those found in actual distance distributions.

Suggested Citation

  • Fernández-Rosales, Iván Yair & Angulo-Brown, Fernando & Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev, 2020. "Distance distributions of human settlements," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302095
    DOI: 10.1016/j.chaos.2020.109808
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920302095
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.109808?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Gilles Duranton, 2007. "Urban Evolutions: The Fast, the Slow, and the Still," American Economic Review, American Economic Association, vol. 97(1), pages 197-221, March.
    2. John B. Parr, 2017. "Central Place Theory: An Evaluation," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 29(3), pages 151-164, November.
    3. Chen, Yanguang, 2011. "Fractal systems of central places based on intermittency of space-filling," Chaos, Solitons & Fractals, Elsevier, vol. 44(8), pages 619-632.
    4. Chen, Yanguang, 2015. "The distance-decay function of geographical gravity model: Power law or exponential law?," Chaos, Solitons & Fractals, Elsevier, vol. 77(C), pages 174-189.
    5. Chen, Yanguang, 2014. "Multifractals of central place systems: Models, dimension spectrums, and empirical analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 266-282.
    6. Eaton, Jonathan & Eckstein, Zvi, 1997. "Cities and growth: Theory and evidence from France and Japan," Regional Science and Urban Economics, Elsevier, vol. 27(4-5), pages 443-474, August.
    7. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    8. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2018. "Zipf’s law and city size distribution: A survey of the literature and future research agenda," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 75-92.
    9. Chen, Yanguang & Huang, Linshan, 2018. "A scaling approach to evaluating the distance exponent of the urban gravity model," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 303-313.
    10. Clémentine Cottineau, 2017. "MetaZipf. A dynamic meta-analysis of city size distributions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-22, August.
    11. Wen‐Tai Hsu, 2012. "Central Place Theory and City Size Distribution," Economic Journal, Royal Economic Society, vol. 122(563), pages 903-932, September.
    12. Duncan Black & Vernon Henderson, 2003. "Urban evolution in the USA," Journal of Economic Geography, Oxford University Press, vol. 3(4), pages 343-372, October.
    13. Chen, Yanguang & Zhou, Yixing, 2008. "Scaling laws and indications of self-organized criticality in urban systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 85-98.
    14. Krugman, Paul, 1996. "Confronting the Mystery of Urban Hierarchy," Journal of the Japanese and International Economies, Elsevier, vol. 10(4), pages 399-418, December.
    15. Moura, Newton J. & Ribeiro, Marcelo B., 2006. "Zipf law for Brazilian cities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 441-448.
    16. Pérez-Campuzano, Enrique & Guzmán-Vargas, Lev & Angulo-Brown, F., 2015. "Distributions of city sizes in Mexico during the 20th century," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 64-70.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arshad, Sidra & Hu, Shougeng & Ashraf, Badar Nadeem, 2019. "Zipf’s law, the coherence of the urban system and city size distribution: Evidence from Pakistan," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 87-103.
    2. Duranton, Gilles & Puga, Diego, 2014. "The Growth of Cities," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 2, chapter 5, pages 781-853, Elsevier.
    3. Hasan Engin Duran & Andrzej Cieślik, 2021. "The distribution of city sizes in Turkey: A failure of Zipf’s law due to concavity," Regional Science Policy & Practice, Wiley Blackwell, vol. 13(5), pages 1702-1719, October.
    4. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    5. Inna Manaeva, 2019. "Distribution of Cities in Federal Districts of Russia: Testing of the Zipf Law," Economy of region, Centre for Economic Security, Institute of Economics of Ural Branch of Russian Academy of Sciences, vol. 1(1), pages 84-98.
    6. Kim, Ho Yeon, 2012. "Shrinking population and the urban hierarchy," IDE Discussion Papers 360, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    7. Desmet, Klaus & Henderson, J. Vernon, 2015. "The Geography of Development Within Countries," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 1457-1517, Elsevier.
    8. Angelina Hackmann & Torben Klarl, 2020. "The evolution of Zipf's Law for U.S. cities," Papers in Regional Science, Wiley Blackwell, vol. 99(3), pages 841-852, June.
    9. Tomoya Mori & Tony E. Smith, 2009. "A Reconsideration of the NAS Rule from an Industrial Agglomeration Perspective," KIER Working Papers 669, Kyoto University, Institute of Economic Research.
    10. Ho Yeon KIM & Petra de Jong & Jan Rouwendal & Aleid Brouwer, 2012. "Shrinking population and the urban hierarchy [Housing preferences and attribute importance among Dutch older adults: a conjoint choice experiment]," ERSA conference papers ersa12p350, European Regional Science Association.
    11. Lee, Sanghoon & Li, Qiang, 2013. "Uneven landscapes and city size distributions," Journal of Urban Economics, Elsevier, vol. 78(C), pages 19-29.
    12. Chen, Yanguang, 2021. "Exploring the level of urbanization based on Zipf’s scaling exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    13. Ronan Lyons & Elisa Maria Tirindelli, 2022. "The Rise & Fall of Urban Concentration in Britain: Zipf, Gibrat and Gini across two centuries," Trinity Economics Papers tep0522, Trinity College Dublin, Department of Economics.
    14. Clémentine Cottineau, 2022. "What do analyses of city size distributions have in common?," Scientometrics, Springer;Akadémiai Kiadó, vol. 127(3), pages 1439-1463, March.
    15. Christian Düben & Melanie Krause, 2021. "Population, light, and the size distribution of cities," Journal of Regional Science, Wiley Blackwell, vol. 61(1), pages 189-211, January.
    16. Rafael Gonz�lez-Val & Luis Lanaspa, 2016. "Patterns in US Urban Growth, 1790-2000," Regional Studies, Taylor & Francis Journals, vol. 50(2), pages 289-309, February.
    17. Rosenthal, Stuart S. & Ross, Stephen L., 2015. "Change and Persistence in the Economic Status of Neighborhoods and Cities," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 1047-1120, Elsevier.
    18. Marco Percoco, 2013. "Geography, institutions and urban development: Italian cities, 1300–1861," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 50(1), pages 135-152, February.
    19. González-Val, Rafael & Lanaspa, Luis & Sanz, Fernando, 2008. "New Evidence on Gibrat’s Law for Cities," MPRA Paper 10411, University Library of Munich, Germany.
    20. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302095. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.