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.
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Notes
- 1.
“Everything is related to everything else, but near things are more related than distant things” (Tobler 1970).
- 2.
The Gini index is based on the Lorenz curve which summarizes the distribution of an attribute among elements (the cumulative frequency of the elements is plotted on the x-axis and the cumulative frequency of the attribute is plotted on the y-axis). The value of the Gini index corresponds to the area between the line of perfect equality (dotted line on Fig. 4) and the Lorenz curve computed for a given attribute. The index varies from 0, a situation of perfect homogeneity, to 1, the maximal inequality or heterogeneity of distribution.
- 3.
Zipf and some of his predecessors (Auerbach 1913; Zipf 1949) have formulated an empirical law, the rank-size rule or Zipf’s law, used in urban geography to illustrate the general hierarchical regularity of city size found in each system of cities in the world. This regularity is expressed as an inverse geometric progression between the population Pi of a city and its rank Ri, as Pi = K/Rα, where K and α are constants, α being the slope of the trend line on a bi-logarithmic graph. α is found to not pull away strongly from 1 (see meta-analysis by Cottineau 2017; see also an application of Zipf’s law on diverse urban systems by Pumain et al. 2015).
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Finance, O., Swerts, E. (2020). Scaling Laws in Urban Geography. Linkages with Urban Theories, Challenges and Limitations. In: Pumain, D. (eds) Theories and Models of Urbanization. Lecture Notes in Morphogenesis. Springer, Cham. https://doi.org/10.1007/978-3-030-36656-8_5
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