Scaling Laws and Urban Systems

Céline Vacchiani-Marcuzzo is Geographer and Professor at Université Paris Cité, France. Her work focuses on the functional and relational aspects of cities (demographic dynamics, economic trajectories, mobility, etc.) from a comparative global perspective.Denise Pumain is Geographer and Emeritus Professor at Université Paris 1 Panthéon-Sorbonne, France. As a specialist in urban dynamics, she questions the relevance of transferring models between the natural sciences and social sciences.

• Introduction XIIICéline VACCHIANI-MARCUZZO and Denise PUMAINPart 1 Consolidating the Significance of Urban Scaling Laws 1Chapter 1 Scaling Laws in Complex Systems Dynamics 3Denise PUMAIN1.1 Scaling laws: definition and interpretations 31.1.1 Definition of scaling laws 41.1.2 Interpretations derived from statistical physics 81.1.3 Interpretations incorporating social science theories 91.2 A difficult synthesis 131.3 Applications of scaling laws 161.3.1 Scaling laws and urban morphology 161.3.2 Scaling laws and the social and functional typology of cities 181.3.3 Scaling laws and zones of influence around cities 191.3.4 Scaling laws and degree of development 191.3.5 Scaling laws and renormalization 201.4 Scaling laws: challenges for urban policy 201.4.1 Promoting the equitable distribution of urban services 211.4.2 Productivity and city size 211.4.3 Large and small cities in the ecological transition 231.5 Conclusion 231.6 References 25Chapter 2 Epistemological and Critical Examination of Urban Scaling Laws 35Cécile TANNIER and Denise PUMAIN2.1 Introduction 362.2 Concept of scale in urban geography 362.2.1 Scale as a dimension of geographic objects 372.2.2 Scale as a level of spatial organization of societies 402.3 Scale invariance of the rank-size distribution of cities and central place systems 462.3.1 Distribution of city size: a scaling law like any other? 472.3.2 Central place systems and their possible scale invariance 512.3.3 Attempts to reconcile the rank-size law of cities and central places theory 532.4 Scaling laws: theoretical challenges 552.4.1 Transition from transversal to longitudinal and the question of ergodicity 562.4.2 Poor integration of scaling laws into urban spatialities and temporalities 592.5 Practical issues still unresolved 602.5.1 Uncertainties related to the definition and delimitation of cities 602.5.2 Uncertainties related to statistical estimation methods 612.6 Conclusion 622.7 References 64Chapter 3 Generative Models of Hierarchical Systems of Cities: The Role of Individuals and Firms 75Cécile TANNIER3.1 Introduction 753.2 Explanatory processes for the hierarchization of systems of cities 773.3 Intraurban agglomeration and competition processes explaining interurban hierarchies 793.4 Interurban hierarchies explained by the intensity and diversity of intraurban social interactions 803.4.1 Settlement scaling theory models 803.4.2 Models incorporating the diversity of intraurban economic and social activity 853.5 City hierarchies and urban scaling laws resulting from migration or individual interurban interactions 873.5.1 Central place models 873.5.2 Models of the new economic geography 883.5.3 Altmann’s (2020) model 933.6 Properties of the modeled structures and dynamics 943.6.1 Fundamental role of space: an aspect that is more or less present in the models 953.6.2 Absence of historical (evolutionary) processes and interactions between levels in models 1013.7 Conclusion 1053.8 References 106Chapter 4 Modeling Interactions Between Cities to Simulate Urban Hierarchies 115Cécile TANNIER4.1 Introduction 1154.2 Three categories of processes at work in the dynamics of systems of cities 1174.2.1 Spatial interactions between cities 1174.2.2 Functional specialization of cities and spatial division of labor 1184.2.3 Hierarchical diffusion of innovations 1214.2.4 Evolutionary theory of cities 1214.3 Models 1234.3.1 So-called “parsimonious” models 1234.3.2 Models closer to concepts and theories of social sciences 1304.3.3 More complex models incorporating numerous empirically observed processes 1374.4 Components of model dynamics 1494.4.1 Role of space in the models 1504.4.2 Role of demographic and economic changes 1514.4.3 Role of the diversity and diversification of functions and activities in cities 1534.5 Conclusion 1554.6 References 156Part 2 Revisiting International Comparison of Urban Systems with Scaling Laws 165Chapter 5 Urban Functions and Scaling Laws: South Africa, United States, France 167Céline VACCHIANI-MARCUZZO and Fabien PAULUS5.1 Scaling laws to the test: a comparative analysis of South Africa, France and the United States 1685.2 A hybrid system of cities between the new world and developing countries 1695.3 Scaling laws and industry (economic sectors) 1715.4 Exploration of occupations 1785.5 Conclusion 1865.6 References 186Chapter 6 Scaling Laws and Integration Dynamics in Cities of the European Union 191Olivier FINANCE and Denise PUMAIN6.1 Scaling laws and the diffusion of innovations 1936.1.1 Urban growth or decline and the diffusion of innovations 1936.1.2 Scaling laws and stages in the diffusion of innovation waves 1996.2 Foreign investment flows into European cities 2006.2.1 Quantitative selectivity of new investments and jobs 2016.2.2 Variations in scaling laws across city activity sectors 2046.2.3 Source of investments 2066.3 Scaling laws and indicators of metropolization 2076.4 Conclusion 2096.5 References 209Chapter 7 The Integration of Cities with Globalization, From 2010 to 2022, Through the Lens of Scaling Laws 215Céline ROZENBLAT7.1 Understanding the scaling laws of cities in multinational corporation networks 2177.1.1 Integration of cities and systems of cities into multisectoral corporation networks 2177.1.2 Cities and multinational corporations in network 2187.1.3 Cities in networks of different geographic scopes 2187.1.4 City ranking and scaling laws 2197.2 Contribution of scaling laws to understanding the processes of city integration into multinational corporation networks 2237.3 Reliable database and rigorous methodology 2247.3.1 Firms’ ownership networks 2257.3.2 Comparable cities defined as large urban regions 2267.3.3 Data construction by city (LUR) 2277.3.4 Number of companies as a measure of city size for calculating scaling laws based on enterprise networks 2327.3.5 City rankings based on company concentration 2337.4 Scaling laws for cities based on multinational enterprise networks 2357.4.1 The scaling laws of cities at the global level for multinational enterprise links and their orientations 2357.4.2 Scaling the laws of cities by the scope of multinational enterprise links at the global level 2377.4.3 Scaling laws of cities by the scope of multinational enterprise links at the continental level 2387.4.4 Scaling laws of cities based on their multinational enterprise links by industry 2397.5 Network properties in urban systems revealed by scaling laws 2437.5.1 Strength of local links 2437.5.2 Advantages of diversity 2447.5.3 Concentration of power 2467.5.4. Differentiated regimes between the center and the periphery? .. 2467.5.5 Scaling laws revealing the diffusion of benefits from business concentration in cities 2487.6 Conclusion 2497.7 References 250Part 3 Scaling Laws to Better Characterize Urban Forms 255Chapter 8 Intra-Urban Radial Scaling Laws 257Justin DELLOYE, Estelle MENNICKEN, Paul KILGARRIFF, Rémi LEMOY and Geoffrey CARUSO8.1 Introduction 2578.2 Literature and definitions 2598.3 Radial approach: concept and empirical measurements 2618.4 Results 2658.5 Discussion and conclusion 2708.6 References 271Chapter 9 A Method to Define Multiscalar Systems of Cities in France 275Florent LE NÉCHET, Benoit CONTI and Sylvestre DUROUDIER9.1 Introduction 2759.2 Mobility dynamics and functional interpretations of urbanized spaces 2779.2.1 Functional areas sometimes lose coherence 2779.2.2 What frameworks can be used to understand everyday relations between cities? 2809.2.3 The challenge of multiscalar analysis on the functioning of urban spaces 2819.3 Proposal for an original method for analyzing the existence of “multiscalar” urban systems 2829.3.1 Choice of a parametric algorithm for exploratory purposes 2829.3.2 Description of the first iteration and outputs of the algorithm 2839.3.3 Two examples of primitive and CUS construction 2859.3.4 Characterization of the diversity of organizational forms and degrees of multiscalarity in CUSs 2879.4 Diversity in the spatial organization of urban systems in France 2899.4.1 National analysis of the role of the α parameter in the construction of CUSs 2899.4.2 CUSs to multiscalar consolidated urban systems 2949.4.3 Test on typology of MCUSs for α = 4% 2959.4.4 Analysis of multiscalarity by the morphological organization of the 24 MCUSs (α = 4%) 2999.4.5 Typology of city multiscalarity 3019.5 Conclusion 3059.6 References 306Conclusion What Role will Scaling Laws Play in the Future of Cities? 311Céline VACCHIANI-MARCUZZO and Denise PUMAINList of Authors 323Index 325