Used (Lived) versus Offered (Plain) densities of human settlement in space: An instance of the probabilistic consumption model
To people living in areas, the denser is the area, the more numerous are the opportunities of interpersonal and social interaction, of employment and of amenities of all kinds. The spatial density of human settlement is basically studied according to places, that is, area weighted. The notion of population-weighted density, or lived density, puts human density in the perspective of the people that experience it. Considering, respectively, the land units and the people as statistical populations of their own, the article provides a probabilistic model of human density in a geographical space, as a random variable in each statistical population, with specific probability density functions (PDFs) and cumulative distribution functions. The PDF of lived, “Used density” is derived from that of the plain, “Offered density” through a consumption model: Thus, their relationship is a specific instance of a well-established probabilistic model. The average used density is systematically larger than its offered counterpart: The ratio amounts to one plus the squared coefficient of variation of offered density. The relation between the two statistical distributions is illustrated using a Lorenz curve; the associated Gini index constitutes an indicator of population heterogeneity in a geographical space. A case of France’s population as of 2019 is studied to demonstrate the methodology.
Albouy, D., & Stuart, B. (2012). Urban quantities and amenities: The neoclassical model of location. International Economic Review, 61(1): 127-158. https://doi.org/10.1111/iere.12419
Aliaga, C., Eusebio, P., & Levy, D. (2015). A novel approach to spaces with low or high density. In: France and its territories, 2015 edition, collection INSEE References. Available from https://www.insee.fr/fr/statistiques/fichier/1373022/FST15.pdf [Last accessed on 2022 Nov 09] [Book in French].
An, R., Wu, Z., Tong, Z., Qin, S., Zhu, Y., & Liu, Y. (2022). How the built environment promotes public transportation in Wuhan: A multiscale geographically weighted regression analysis. Travel Behaviour and Society, 29: 186-199. https://doi.org/10.1016/j.tbs.2022.06.011
Barnes, G. (2001). Population and Employment Density and Travel Behavior in Large U.S. Cities. Final Report 2001-24. St. Paul: Minnesota Department of Transportation. Available from: https://www.lrrb.org/pdf/200124.pdf [Last accessed on 2022 Oct 14].
Blitzstein, J.K., & Hwang, J. (2015). Introduction to Probability. 2nd ed. United States: CRC Press.
Bradford, C. (2008a). On Weighted Density. Available from: https://www.austinzoning.typepad.com/austincontrarian/2008/03/weighted-densit.html [Last accessed on 2022 Oct 14].
Bradford, C. (2008b). Density Calculations for U.S. Urbanized Areas, Weighted by Census Tract. Available from: https://www.austinzoning.typepad.com/austincontrarian/2008/03/ weighted-densit.html [Last accessed on 2022 Oct 14].
Bradford, C. (2008c). The Association between Density and Mode of Commute. Available from: https://www.austinzoning.typepad.com/austincontrarian/2008/09/the-association-between-density-and-mode [Last accessed on 2022 Oct 14].
Cowell, F.A. (2009). Measuring Inequality. LSE Perspectives in Economic Analysis. United Kingdom: Oxford University Press. p.241. Available from: https://darp.lse.ac.uk/papersdb/Cowell_measuringinequality3.pdf [Last accessed on 2022 Nov 9].
Craig, J. (1975). Population Density and Concentration in Great Britain 1931, 1951 and 1961. Studies on Medical and Population Subjects No 35: Office of Population Censuses and Surveys. London: HMSO.
Craig, J. (1979). Population density: Changes and patterns. Population Trends, 17: 12-16.
Craig, J. (1980). Population Density and Concentration in Great Britain 1951, 1961 and 1971. Studies on Medical and Population Subjects No 42: Office of Population Censuses and Surveys. London: HMSO.
Craig, J. (1984). Averaging Population Density. Demography, 21(3): 405-412. https://doi.org/10.2307/2061168
Cramer, J.S. (1962). The Ownership of Major Consumer Durables. Cambridge, United Kingdom: Cambridge University Press.
Dijkstra, L., & Poelman, H. (2014). A Harmonised Definition of Cities and Rural Areas: The New Degree of Urbanisation. Working Papers in 01/2014, European Commission General Directorate for Regional and Urban Policy. Available from: https://ec.europa.eu/regional_policy/sources/docgener/work/2014_01_new_urban.pdf [Last accessed on 2022 Oct 14].
Eidlin, E. (2010). What density doesn’t tell us about sprawl. Access Magazine, 37 (Fall): 2-9.
Eurostat. (2019). Methodological Manual on Territorial Typologies, 2018 edition. Available from: https://ec.europa.eu/eurostat/fr/web/products-manuals-and-guidelines/-/KS-GQ-18-008 [Last accessed on 2022 Oct 14].
Faberman, R.J., & Freedman, M. (2016). The urban density premium across establishments. Journal of Urban Economics, 93:71-84. https://doi.org/10.1016/j.jue.2016.03.006
Florida, R. (2012). America’s Truly Densest Metros. Available from: https://www.bloomberg.com/news/articles/2012-10-15/america-s-truly-densest-metro-areas [Last accessed on 2022 Oct 20].
Fujita, M., Krugman, P.R., & Venables, A.P. (1999). The Spatial Economy: Cities, Regions and International Trade. United States: MIT Press.
Fujita, M., & Thisse, J.F. (2002). The Economics of Agglomeration: Cities, Industrial Location and Regional Growth. Cambridge, United Kingdom: Cambridge University Press.
Gini, C. (1912). On variability and mutability. Reprinted in E. Pizetti and T. Salvemini (eds.) (1955) Italy’s Annals of Statistical Methodology. Roma: Libreria Eredi Virgilio Veschi, [In Italian].
Gionanni, G., & Gubbiotti, S. (2015). On Corrado Gini’s 1932 paper “About the concentration curve”: A selection of translated excerpts. Metron 73(1):1-24. Available from https://www.researchgate.net/publication/273515333 [Last accessed on 2022 Oct 14]. https://doi.org/10.1007/s40300-015-0062-7
Graham, D.J., & Gibbons, S. (2019). Quantifying wider economic impacts of agglomeration for transport appraisal: Existing evidence and future directions. Economics of Transportation 19: 100121 https://doi.org/10.1016/j.ecotra.2019.100121
Hanberry, B.B. (2022). Imposing consistent global definitions of urban populations with gridded population density models: Irreconcilable differences at the National Scale. Landscape and Urban Planning 226, 104493. https://doi.org/10.1016/j.landurbplan.2022.104493
Hansen, W.G. (1959). How accessibility shapes land use. Journal of the American Institute of planners, 25(2): 73-76. https://doi.org/10.1080/01944365908978307
Huang, G., & Brown, P.E. (2021). Population-weighted exposure to air pollution and COVID-19 incidence in Germany. Spatial Statistics 41:100480 https://doi.org/10.1016/j.spasta.2020.100480
INSEE. (2021a). “The Observatory of territories” website: file insee_rp_hist_1968 obtained from request: https://www.observatoire-des-territoires.gouv.fr/outils/cartographie-interactive/api/v1/functions/GC_API_download. php?type=stat&nivgeo=com2021&dataset=insee_rp_ hist_1968&indic=superf_choro [Last accessed on 2022 Jan 19].
INSEE. (2021b). Dataset of Communal Populations Up To 2019. Available from: https://www.insee.fr/fr/statistiques/fichier/3698339/base-pop-historiques-1876-2019.xlsx [Last accessed on 2022 Jan 19].
Kleinrock, L. (1975). Queuing Systems. vol. 1. New Jersey: Wiley Interscience. p. 169-173.
Koenig, J.G. (1974). An economic theory of urban accessibility. France’s Economic review 25(2):275-297. Available from; http://www.persee.fr/web/revues/home/prescript/article/reco_0035-2764_1974_num_25_2_408144 [Last accessed on 2022 Oct 14] [Article in French].
Koenig, J.G. (1980). Indicators of urban accessibility: Theory and application. Transportation, 9(2): 145-172. https://doi.org/10.1007/BF00167128
Krugman, P.R. (1997). Development, Geography, and Economic Theory. United States: MIT Press.
Krugman, P. (2013). Density. The Conscience of a Liberal. New York: New York Times (website). Available from: https://krugman.blogs.nytimes.com/2013/04/16/density [Last accessed on 2022 Oct 20].
Lee, S., & Lee, B. (2014). The influence of urban form on GHG emissions in the U.S. household sector. Energy Policy, 68: 534-549. https://doi.org/10.1016/j.enpol.2014.01.024
Leurent, F., Benezech, V., & Combes, F. (2012). A stochastic model of passenger generalized time along a transit line. Procedia Social and Behavioral Sciences, 54: 785-797. https://doi.org/10.1016/j.sbspro.2012.09.795
Leurent, F., Pivano, C., & Poulhes, A. (2017). On passenger traffic along a transit line: A stochastic model of station waiting and in-vehicle crowding under distributed headways. Transportation Research Procedia. 27: 1219-1226. https://doi.org/10.1016/j.trpro.2017.12.076
Lewontin, R.C., & Levins, R. (1989). On the characterization of density and resource availability. The American Naturalist 134(4): 513-524.
Lorenz, M.O. (1905). Methods of measuring the concentration of wealth. Publications of the American Statistical Association, 9(70): 209-219.
Lu, Y., Zhang, Y.Y., & Ma, K. (2022). The effect of population density on the suitability of biomass energy development. Sustainable Cities and Society 87: 104240. https://doi.org/10.1016/j.scs.2022.104240
NENAD (2021). Available from: https://gmnenad.com/2021/05/analysis-of-real-population-density-per-countries [Last accessed on 2022 Oct 14].
Ottensmann, J.R. (2016). Density of Large Urban Areas in the U.S., 1950-2010. Working Paper. p. 25. Available from: https://urbanpatternsblog.files.wordpress.com/2016/12/density-of-large-urban-areas.pdf [Last accessed on 2022 Nov 09].
Ottensmann, J.R. (2018a). On Population-Weighted Density. Working Paper. p.33. Available from: https://urbanpatternsblog.files.wordpress.com/2018/02/on-population-weighted-density.pdf [Last accessed on 2022 Nov 09].
Ottensmann, J.R. (2018b). An Alternative Approach to the Measurement of Urban Sprawl. Working Paper. p. 39.
Pascoal, R., & Rocha, H. (2022). Population density impact on COVID-19 mortality rate: A multifractal analysis using French data. Physica A, 593: 126979. https://doi.org/10.1016/j.physa.2022.126979
Poulit, J. (1974) On land-use and transport: Criteria for accessibility and urban development. SETRA – Urban Division, French Ministry of Infrastructures [Book in French].
Rappaport, J. (2008a). A productivity model of city crowdedness. Journal of Urban Economics, 63(2):715-722. https://doi.org/10.1016/j.jue.2007.04.008
Rappaport, J. (2008b). Consumption amenities and city population density. Regional Science and Urban Economics, 38/6: 533-552. https://doi.org/10.1016/j.regsciurbeco.2008.02.001
Stairs, R.A. (1977a). The concept of population density: A suggestion. Demography, 14: 243-244. https://doi.org/10.2307/2060580
Stairs, R.A. (1977b). Erratum to: The concept of population density: A suggestion. Demography, 14(3): 378. https://doi.org/10.2307/2060795
Townsend, C., & Ellis-Young, M. (2018). Urban population density and freeways in North America: A Re-assessment. Journal of Transport Geography, 73: 75-83. https://doi.org/10.1016/j.jtrangeo.2018.10.008
Vorobyev, A.N. (2019). The mapping of population density in a sparsely populated region: A case study of the Irkutsk Region. IOP Conference Series Earth Environment Science, 381: 012095. https://doi:10.1088/1755-1315/381/1/012095
Wardrop, J.G. (1952). Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, 1(3): 325-362. https://doi.org/10.1680/ipeds.1954.11628
Wikipedia. (2022). Available from: https://en.wikipedia.org/wiki/ Population_density [Last accessed on 2022 Oct 20].
Wonnacott, T.H., & Wonnacott, R.J. (1990). Introductory Statistics. 5th ed. New Jersey: Wiley.