Advertisement

Scaling Laws in Urban Geography. Linkages with Urban Theories, Challenges and Limitations

  • Olivier FinanceEmail author
  • Elfie Swerts
Chapter
Part of the Lecture Notes in Morphogenesis book series (LECTMORPH)

Abstract

Scaling laws are simple, easily usable and proven relevant models used in geography for validating various urban theories. These non-linear relationships may reveal physical constraints on the structure and evolution of complex systems, and underline the relationship between urban functions, size of cities and innovation cycles. In this contribution, we examine to what extent scaling laws are transferable towards urban theories and in which specific fields of urban geography these models may be relevant. We thus focus on the accuracy of scaling laws when exploring structures and processes of systems of cities, the diffusion of innovation, metropolization and intra-urban dynamics. We therefore use several examples taken in different regions of the world, embedded in various historical, political and economic contexts. However, in some cases, care must be taken not to over-interpret the results obtained from scaling laws and not to give scaling laws more explanatory power than they can describe. We illustrate this point by providing recommendations relying for instance on the sensitivity of measurements to the delineation of each object of the system under study and to the definition of the system itself. These recommendations can help to get robust results in order to understand the generic evolutionary mechanisms in urban systems.

References

  1. Arcaute, E., Hatna, E., Ferguson, P., Youn, H., Johansson, A., Batty, M.: Constructing cities, deconstructing scaling laws. J. R. Soc. Interface 12(102), 1–8 (2015).  https://doi.org/10.1098/rsif.2014.0745CrossRefGoogle Scholar
  2. Auerbach, F.: Das Gesetz der Bevölkerungskonzentration. Petermanns Geogr. Mitt. 59, 74–76 (1913)Google Scholar
  3. Barthelemy, M.: The Structure and Dynamics of Cities. Cambridge University Press, 278p (2016).  https://doi.org/10.1017/9781316271377
  4. Batty, M.: The new science of cities. The MIT Press, Cambridge, MA (2013)Google Scholar
  5. Berry, B.J.: Cities as systems within systems of cities. Pap. Reg. Sci. 13(1), 147–163 (1964).  https://doi.org/10.1111/j.1435-5597.1964.tb01283.xCrossRefGoogle Scholar
  6. Bettencourt, L.M., Lobo, J., Helbing, D., Kuhnert, C., West, G.B.: Growth, innovation, scaling, and the pace of life in cities. Proc. Nat. Acad.Sci. 104(17), 7301–7306 (2007a). https://doi.org/10.1073/pnas.0610172104
  7. Bettencourt, L.M., Lobo, J., Strumsky, D.: Invention in the city: increasing returns to patenting as a scaling function of metropolitan size. Res. Policy 36(1), 107–120 (2007b). https://doi.org/10.1016/j.respol.2006.09.026
  8. Bettencourt, L.M., Lobo, J., West, G.B.: The self-similarity of human social organization and dynamics in cities. In: Lane, D., Pumain, D., van der Leeuw, S., West GB. (eds.) Complexity Perspective in Innovation and Social Change, Methodos Series. Springer, Dordrecht, pp. 221–236 (2009). https://doi.org/10.1007/978-1-4020-9663-1_8
  9. Bettencourt, L.M.: The origins of scaling in cities. Science 340(6139), 1438–1441 (2013).  https://doi.org/10.1126/science.1235823CrossRefGoogle Scholar
  10. Bettencourt, L.M., Lobo J.: Urban scaling in Europe. J. R. Soc. Interface. 13(116), 20160005 (2016). https://doi.org/10.1098/rsif.2016.0005
  11. Bettencourt, L.M., Lobo, J., West, G.B.: Why are large cities faster? Universal scaling and self-similarity in urban organization and dynamics. Eur Phys J B 63(3), 285–293 (2008).  https://doi.org/10.1140/epjb/e2008-00250-6CrossRefGoogle Scholar
  12. Bettencourt, L.M., Lobo, J., Strumsky, D., West, G.B.: Urban scaling and its deviations: revealing the structure of wealth, innovation and crime across cities. PLoS ONE 5(11), 1–9 (2010).  https://doi.org/10.1371/journal.pone.0013541CrossRefGoogle Scholar
  13. Bretagnolle, A., Pumain, D., Vacchiani-Marcuzzo, C.: The organization of urban systems. In: Lane, D., Pumain, D., van der Leeuw, S., West G.B. (eds.) Complexity Perspective in Innovation and Social Change, Methodos Series. Springer, Dordrecht, pp. 197–220 (2009).  https://doi.org/10.1007/978-1-4020-9663-1_7
  14. Christaller, W.: Die zentralen Orte in Süddeutschland: eine ökonomisch-geographische Untersuchung über die Gesetzmässigkeit der Verbreitung und Entwicklung der Siedlungen mit städtischen Funktionen. University Microfilms (1933)Google Scholar
  15. Cottineau, C.: MetaZipf. A dynamic meta-analysis of city size distributions. PLoS ONE 12(8) (2017).  https://doi.org/10.1371/journal.pone.0183919
  16. Cottineau, C., Hatna, E., Arcaute, E., Batty, M.: Diverse cities or the systematic paradox of urban scaling laws. Comput. Environ. Urban Syst. 63, 80–94 (2017).  https://doi.org/10.1016/j.compenvurbsys.2016.04.006CrossRefGoogle Scholar
  17. Cottineau, C., Finance, O., Hatna, E., Arcaute, E., Batty, M.: Defining urban clusters to detect agglomeration economies. Environ. Plan. B Urban Anal. City Sci. 46(9), 1611–1626 (2018). https://doi.org/10.1177/2399808318755146
  18. Delloye, J., Lemoy, R., Caruso, G.: Alonso and the scaling of urban profiles. In: Geographical Analysis (2019)Google Scholar
  19. Feldman, M.P., Florida, R.: The geographic sources of innovation: technological infrastructure and product innovation in the United States. Ann. Assoc. Am. Geogr. 84(2), 210–229 (1994).  https://doi.org/10.1111/j.1467-8306.1994.tb01735.xCrossRefGoogle Scholar
  20. Finance, O.: Les villes françaises investies par les firmes transnationales étrangères: des réseaux d’entreprises aux établissements localisés. Ph.D. thesis, Université Paris I Panthéon-Sorbonne, France (2016)Google Scholar
  21. Finance, O., Cottineau, C.: Are the absent always wrong? Dealing with zero values in urban scaling. Environ. Plan. B Urban Anal. City Sci. OnlineFirst (2018).  https://doi.org/10.1177/2399808318785634
  22. Gipouloux, F.: Attractivité, concurrence et complémentarité: la place ambiguë des villes côtières chinoises dans la dynamique économique du corridor maritime de l’Asie de l’Est. Outre-Terre 2, 149–160 (2006)CrossRefGoogle Scholar
  23. Hägerstrand, T.: Innovation Diffusion as a Spatial Process (1968)Google Scholar
  24. Leitão, J.C., Miotto, J.M., Gerlach, M., Altmann, E.G.: Is this scaling nonlinear? R. Soc. Open Sci. 3(7), 1–13 (2016).  https://doi.org/10.1098/rsos.150649CrossRefGoogle Scholar
  25. Lemoy R., Caruso G.: Evidence for the homothetic scaling of urban forms. Environ. Plan. B Urban Anal. City Sci. (Online first) (2018). https://doi.org/10.1177/2399808318810532
  26. Levinson, D.: Network structure and city size. PLoS ONE 7(1), 1–11 (2012).  https://doi.org/10.1371/journal.pone.0029721CrossRefGoogle Scholar
  27. Louf, R., Barthelemy, M.: How congestion shapes cities: from mobility patterns to scaling. Sci. Rep. 4(5561), 1–9 (2014).  https://doi.org/10.1038/srep05561CrossRefGoogle Scholar
  28. Meirelles, J., Neto, C.R., Ferreira, F.F., Ribeiro, F.L., Binder, C.R.: Evolution of urban scaling: evidence from Brazil. PLoS ONE 13(10), 1–15 (2018).  https://doi.org/10.1371/journal.pone.0204574CrossRefGoogle Scholar
  29. Moriconi-Ébrard, F.: Geopolis: pour comparer les villes du monde. Paris: Anthropos, coll. “Villes”, pp. 246. ISBN: 2-7178-2721-8 (1994)Google Scholar
  30. Paulus, F.: Coévolution dans les systèmes de villes: croissance et spécialisation des aires urbaines françaises de 1950 à 2000. Ph.D. thesis, Université Paris I Panthéon-Sorbonne, France (2004)Google Scholar
  31. Paulus, F., & Pumain, D.: Lois d’échelle et activités urbaines: une comparaison France-États-Unis. In: Mattéi, MF., & Pumain, D. (eds.) Données urbaines 5. Economica-Anthorpos, Paris, 315–323 (2007)Google Scholar
  32. Paulus, F., Pumain, D.: Salaire et hiérarchie urbaine. In: Pumain, D., Mattéi, MF. (eds.) Données urbaines 6. Economica-Anthropos, Paris, 205–216 (2011)Google Scholar
  33. Pred, A.R.: City Systems in Advanced Economies: Past Growth, Present Processes, and Future Development Options. Wiley (1977)Google Scholar
  34. Pumain, D.: La dynamique des villes. Economica, Paris (1982)Google Scholar
  35. Pumain, D.: Pour une théorie évolutive des villes. L’Espace géographique 26(2), 119–134 (1997).  https://doi.org/10.3406/spgeo.1997.1063CrossRefGoogle Scholar
  36. Pumain, D.: Scaling laws in urban systems. Santa Fe Institute Working Papers, n°04-02-002, 26p (2004)Google Scholar
  37. Pumain, D.: Alternative explanations of hierarchical differentiation in urban systems. In: Pumain, D. (ed.) Hierarchy in Natural and Social Sciences, Methodos Series. Springer, Dordrecht, pp. 169–222 (2006)Google Scholar
  38. Pumain, D.: Urban systems dynamics, urban growth and scaling laws: the question of ergodicity. In: Portugali, J., Meyer, H., Stolk, E., Tan E. (eds.) Complexity Theories of Cities Have Come of Age. Springer, Berlin (2012).  https://doi.org/10.1007/978-3-642-24544-2_6
  39. Pumain, D., Paulus, F., Vacchiani-Marcuzzo, C., Lobo, J.: An evolutionary theory for interpreting urban scaling laws. Cybergeo Eur. J. Geogr. 343 (2006).  https://doi.org/10.4000/cybergeo.2519
  40. Pumain, D., Paulus, F., Vacchiani-Marcuzzo, C.: Innovation cycles and urban dynamics. In: Lane, D., Pumain, D., van der Leeuw, S., West GB. (eds.) Complexity Perspective in Innovation and Social Change, Methodos Series. Springer, Dordrecht, pp. 237–260 (2009).  https://doi.org/10.1007/978-1-4020-9663-1_9
  41. Pumain, D., Swerts, E., Cottineau, C., Vacchiani-Marcuzzo, C., Ignazzi, C.A., Bretagnolle, A., Delisle, F., Cura, R., Lizzi, L., Baffi, S.: Multilevel comparison of large urban systems. Cybergeo Eur. J. Geogr. document 706 (2015).  https://doi.org/10.4000/cybergeo.26730
  42. Rybski, D., Reusser, D.E., Winz, A.-L., Fichtner, C., Sterzel, T., Kropp, J.P.: Cities as nuclei of sustainability? Environ. Plan. B Urban Anal. City Sci. 44(3), 425–440 (2016).  https://doi.org/10.1177/0265813516638340CrossRefGoogle Scholar
  43. Sarkar, S., Phibbs, P., Simpson, R., Wasnik, S.: The scaling of income distribution in Australia: possible relationships between urban allometry, city size, and economic inequality. Environ. Plan. B Urban Anal. City Sci. 45(4), 603–622 (2018).  https://doi.org/10.1177/0265813516676488CrossRefGoogle Scholar
  44. Savage, V.M., Gillooly, J.F., Woodruff, W.H., West, G.B., Allen, A., Enquist, B.J., Brown, J.H.: The predominance of quarter-power scaling in biology. Funct. Ecol. 18, 257–282 (2004).  https://doi.org/10.1111/j.0269-8463.2004.00856.xCrossRefGoogle Scholar
  45. Svejnar, J.: China in light of the performance of Central and East European economies. Working Paper: 41p (2007)Google Scholar
  46. Swerts, E.: Les systèmes de villes en Inde et en Chine. Ph.D. thesis, Université Paris I Panthéon-Sorbonne, France (2013)Google Scholar
  47. Swerts, E.: A data base on Chinese urbanization: ChinaCities. Cybergeo Eur. J. Geogr. 830 (2018).  https://doi.org/10.4000/cybergeo.28554
  48. Taylor, P.J.: World City Network: A Global Urban Analysis. Routledge, London (2004)CrossRefGoogle Scholar
  49. Tobler, W.R.: A computer movie simulating urban growth in the detroit region. Econ. Geogr. 46(sup1), 234–240 (1970).  https://doi.org/10.2307/143141
  50. Um, J., Son, S.W., Lee, S.I., Jeong, H., Kim, B.J.: Scaling laws between population and facility densities. PNAS Proc. Natl. Acad. Sci. USA 106(34), 14236–14240 (2009).  https://doi.org/10.1073/pnas.0901898106CrossRefGoogle Scholar
  51. Vacchiani-Marcuzzo, C., Paulus, F.: Scalings laws and economic specialization: an experiment United States–France–South Africa. AAG Ann. Meet., Boston (2008)Google Scholar
  52. West, G.B., Brown, J.H., Enquist, B.J.: A general model for the origin of allometric scaling laws in biology. Science 276(5309), 122–126 (1997).  https://doi.org/10.1126/science.276.5309.122CrossRefGoogle Scholar
  53. West, G.B., Brown, J.H., Enquist, B.J.: The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284(5420), 1677–1679 (1999).  https://doi.org/10.1126/science.284.5420.1677CrossRefGoogle Scholar
  54. Zipf, G.K.: Human behaviour and the principle of least-effort. Addison-Wesley, Reading, Cambridge, MA (1949)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.UMR 7362 Laboratoire Image Ville EnvironnementUniversité de StrasbourgStrasbourgFrance
  2. 2.FORS—Swiss Centre of Expertise in the Social Sciences, Université de LausanneLausanneSwitzerland
  3. 3.UMR 8504 Géographie-citésParisFrance

Personalised recommendations