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Quelles invariances d'échelle entre densité de la population et des équipements ? Une approche empirique sur données communales françaises

Abstract : Social scientists have often mixed feelings when physicists venture in their supposed field of expertise. But when fresh views are proposed on location theories developed at the crossing of economics and geography since the mid-XIXth century, they cannot be so easily dismissed as disincarnate', abstract' or irrelevant'. With a focus on density―rather unusual in the literature―and elegant theoretical proposals, recent works by (Gastner et al., 2006) and (Um et al., 2009) fall in such a category. Their argument is the following: (i) there is a relationship between the density of population (ρ) and facilities (D) of the form D ≈ ρ α; (ii) the optimal values of α are either 1 or 2/3, whether the facilities are respectively of a commercial or a public kind; (iii) a simple model can account for the latter kind. We will not question here the model itself, but focus instead on the empirical assessment on which the analysis is buttressed, that appears problematic in at least two dimensions: the treatment of scale, the public/private conceptual division. Humans and their activities are unevenly spread on the globe, resulting from such interwoven processes (through the use of resources and amenities, associating economic development, the rise of urbanization and metropolization, and historical contingencies) that establishing robust relationships between the density of population and facilities is not a straightforward endeavour. Even as a starting point, an empirical focus at the level of administrative regions entails specific dangers. Social processes such as those driving the patterns of human settlements typically exhibit some degrees of spatial autocorrelation that are not necessarily captured by political zonings, thus resulting in inconsistencies during upscaling. As well, the scarcity of a given facilityand its more or less metropolitan naturehas to be taken into account. As a result, establishing the empirical relationship at the level of large administrative regions is not equivalent to an analysis at a local municipal level, especially when considering facilities as diverse as universities, post offices or small grocery stores. We wish here to address the following questions: can the location patterns of a given facility in a country be reasonably summarized by a power law of population density? If yes, does the α coefficient fit in a [2/3 ; 1] interval? Are those empirical values in coherence with the public and private theoretical optima? Is it possible to identify groups of facilities that, irrespective of this public/private divide, share similar location patterns? What are the most appropriate statistical methods to explore such relationships? Basing our discussion on a statistical analysis of French local data, the Base Permanente des Équipements 2008' on metropolitan France, covering more than 140 types of public and commercial facilities in 36615 municipalities, we follow two distinctive strategies: (i) Aspatial but hierarchical. Starting with a linear regression for a given facility, we fit the model on municipalities were it is actually present (due to the need of log-transforming the data). We then introduce multilevel models (Gelman et al., 2007), that take into account population densities at the levels of both municipalities and upper-level administrative regions (here the départements, or Eurostat NUTS3). (ii) Spatially explicit. After attributing point locations to each facility, we construct new tessellations (clipped Voronoi maps in ESRI ArcInfo) approximating potential attraction basins in a continuous Euclidean space. Estimating the populations covered by these basins with two methods, we are thus able to build a new tabular dataset of population and facility densities, on which we fit linear models.. The interpretation of results from the aspatial models has first to take into account presence/absence thresholds for each facility (with logit models able to identify zero-density areas). In this complicated process, the multilevel models only slightly outperform the classic linear regressions. The Voronoi' method, while computationally demanding, bears much more straightforward results, with relevant α values for most of the facilities. We discuss how these discrepancies affects the empirical outcomes in a restricted set of facilitiesα values for eg. nursery schools (maternelles) are close to 1 in the 1st method but to 2/3 in the 2ndas well as their statistical causes and their possible interoperability. Relying on the 2nd method for the detailed analysis, we confirm a general public/private trend but identify groups of facilities that, while of a public nature, scale proportionally with population density. We also discuss non-trivial patterns, such as very low α values for commercial facilities such as hypermarkets, or why very similar facilities may bear very different location patterns (eg. car repair vs. care rental). In a final step, we propose a refined typologybased on location patternsof the facilities, relying on novel techniques of variable classification.
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Submitted on : Friday, May 15, 2020 - 7:12:42 PM
Last modification on : Wednesday, March 24, 2021 - 10:52:04 AM


  • HAL Id : hal-02594720, version 1
  • IRSTEA : PUB00031380


B. Hautdidier, V. Kuentz. Quelles invariances d'échelle entre densité de la population et des équipements ? Une approche empirique sur données communales françaises. Rencontres de Théo Quant 2011, Feb 2011, Besançon, France. pp.32. ⟨hal-02594720⟩



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