Clémentine Cottineau

Diverse cities or the systematic paradox of Urban Scaling Laws

Scaling laws are powerful summaries of the variations of urban attributes with city size. However, the validity of their universal meaning for cities is hampered by the observation that different scaling regimes can be encountered for the same territory, time and attribute, depending on the criteria used to delineate cities. The aim of this paper is to present new insights concerning this variation, coupled with a sensitivity analysis of urban scaling in France, for several socio-economic and infrastructural attributes from data collected exhaustively at the local level. The sensitivity analysis considers different aggregations of local units for which data are given by the Population Census. We produce a large variety of definitions of cities (approximatively 5000) by aggregating local Census units corresponding to the systematic combination of three definitional criteria: density, commuting flows and population cutoffs. We then measure the magnitude of scaling estimations and their sensitivity to city definitions for several urban indicators, showing for example that simple population cutoffs impact dramatically on the results obtained for a given system and attribute. Variations are interpreted with respect to the meaning of the attributes (socio-economic descriptors as well as infrastructure) and the urban definitions used (understood as the combination of the three criteria). Because of the Modifiable Areal Unit Problem (MAUP) and of the heterogeneous morphologies and social landscapes in the cities’ internal space, scaling estimations are subject to large variations, distorting many of the conclusions on which generative models are based. We conclude that examining scaling variations might be an opportunity to understand better the inner composition of cities with regard to their size, i.e. to link the scales of the city-system with the system of cities.

Multilevel comparison of large urban systems

For the first time the systems of cities in seven countries or regions among the largest in the world (China, India, Brazil, Europe, the Former Soviet Union (FSU), the United States and South Africa) are made comparable through the building of spatio-temporal standardised statistical databases. We first explain the concept of a generic evolutionary urban unit (“city”) and its necessary adaptations to the information provided by each national statistical system. Second, the hierarchical structure and the urban growth process are compared at macro-scale for the seven countries with reference to Zipf’s and Gibrat’s model: in agreement with an evolutionary theory of urban systems, large similarities shape the hierarchical structure and growth processes in BRICS countries as well as in Europe and United States, despite their positions at different stages in the urban transition that explain some structural peculiarities. Third, the individual trajectories of some 10,000 cities are mapped at micro-scale following a cluster analysis of their evolution over the last fifty years. A few common principles extracted from the evolutionary theory of urban systems can explain the diversity of these trajectories, including a specific pattern in their geographical repartition in the Chinese case. We conclude that the observations at macro-level when summarized as stylised facts can help in designing simulation models of urban systems whereas the urban trajectories identified at micro-level are consistent enough for constituting the basis of plausible future population projections.

Beyond Corroboration: Strengthening Model Validation by Looking for Unexpected Patterns

Models of emergent phenomena are designed to provide an explanation to global-scale phenomena from local-scale processes. Model validation is commonly done by verifying that the model is able to reproduce the patterns to be explained. We argue that robust validation must not only be based on corroboration, but also on attempting to falsify the model, i.e. making sure that the model behaves soundly for any reasonable input and parameter values. We propose an open-ended evolutionary method based on Novelty Search to look for the diverse patterns a model can produce. The Pattern Space Exploration method was tested on a model of collective motion and compared to three common a priori sampling experiment designs. The method successfully discovered all known qualitatively different kinds of collective motion, and performed much better than the a priori sampling methods. The method was then applied to a case study of city system dynamics to explore the model’s predicted values of city hierarchisation and population growth. This case study showed that the method can provide insights on potential predictive scenarios as well as falsifiers of the model when the simulated dynamics are highly unrealistic.

A Modular Modelling Framework for Hypotheses Testing in the Simulation of Urbanisation

In this paper, we present a modelling experiment developed to study systems of cities and processes of urbanisation in large territories over long time spans. Building on geographical theories of urban evolution, we rely on agent-based models to 1) formalise complementary and alternative hypotheses of urbanisation and 2) explore their ability to simulate observed patterns in a virtual laboratory. The paper is therefore divided into two sections : an overview of the mechanisms implemented to represent competing hypotheses used to simulate urban evolution; and an evaluation of the resulting model structures in their ability to simulate—efficiently and parsimoniously—a system of cities (between 1000 and 2000 cities in the Former Soviet Union) over several periods of time (before and after the crash of the USSR). We do so using a modular framework of model-building and evolutionary algorithms for the calibration of several model structures. This project aims at tackling equifinality in systems dynamics by confronting different mechanisms with similar evaluation criteria. It enables the identification of the best-performing models with respect to the chosen criteria by scanning automatically the parameter space along with the space of model structures (the different combinations of mechanisms).

MetaZipf. A dynamic meta-analysis of city size distributions

The results from urban scaling in recent years have held the promise of increased efficiency to the societies who could actively control the distribution of their cities’ size. However, little evidence exists as to the factors which influence the level of urban unevenness, as expressed by the slope of the rank-size distribution, partly because the diversity of results found in the literature follows the heterogeneity of analysis specifications. In this study, I set up a meta-analysis of Zipf’s law which accounts for technical as well as topical factors of variations of Zipf’s coefficient. I found 86 studies publishing at least one empirical estimation of this coefficient and recorded their metadata into an open database. I regressed the 1962 corresponding estimates with variables describing the study and the estimation process as well as socio-demographic variables describing the territory under enquiry. A dynamic meta-analysis was also performed to look for factors of evolution of city size unevenness. The results of the most interesting models are presented in the article, whereas all analyses can be reproduced on a dedicated online platform. The results show that on average, 40% of the variation of Zipf’s coefficients is due to the technical choices. The main other variables associated with distinct evolutions are linked to the urbanisation process rather than the process of economic development and population growth. Finally, no evidence was found to support the effectiveness of past planning actions in modifying this urban feature.Zipfs law for cities is probably the most famous regularity in social sciences. So much that, a hundred years of publication later, its status is not clear: is it a law of social organisation? Is it an instrument of description of city size distributions? Is it an element of validation of geographical objects (cities and systems of cities in particular)? Empirical estimations of the rank-size parameters are very numerous and contradict each other. In this study, we present the results of a reproducible meta-analysis of the largest pool of papers regarding this issue, obtained from the collection of data made open and the construction of an online interactive application which allows the reader to explore this literature. We find that a large part of the variations observed in the measure of Zipfs coefficient is unnecessary as it comes from the choice of different technical specifications in the way cities are defined, whereas some of the current theories to explain the remaining share of variations are challenged by our results.

The Russian Urban System: Evolution Engaged with Transition

Russian urbanization has been a fascinating process shaped by a unique set of geographical, economic, and political constraints. The settlement pattern and the speed at which urban hierarchies have changed hold the mark of Soviet policies but also that of a gigantic territory endowed with numerous resources. Nowhere in the world had such a rapid industrialization and urban growth been met in the mid-twentieth century. However, since the 1990s, the transition to capitalism and a significant demographic shrinkage once again put Russian cities in a position of unprecedented evolution. In this chapter, we use two databases and a generic set of analytic tools to describe and model this urban evolution and analyze the impact of the transition on Russian cities. We do so quantitatively by looking at factors of growth and shrinkage before and after 1991 and qualitatively by looking at the specific features of cities in the post-Soviet world. We discuss the challenges that Russian cities face with respect to sustainability in the years to come and conclude with a discussion of multiscale governance.

Are the absent always wrong? Dealing with zero values in urban scaling

Both theoretical and empirical studies have shown the ability of scaling laws to reveal processes of emergence in urban systems. Nevertheless, a controversy about the robustness of results obtained with these models on empirical cases remains, regarding for instance the definition of the ‘city’ considered or the way the estimations are performed. Another source of bias is highlighted in this contribution, with respect to the non-ubiquitous character of some urban attributes (i.e. their partial absence from several cities of the system). The problem with the zero count for cities where these attributes are absent is that the technical necessities of usual estimation procedures make the analysis ignore them altogether even when they represent some valid information. This could seriously impact the results. A precise exploration of the effects of this arbitrary filtering is conducted here, and several solutions are proposed to overcome this limitation. In a case study about foreign investment towards French cities, we show that some erroneous conclusions about a hierarchical diffusion could be drawn when adopting the classical ordinary least squares approach. The framework we suggest specifies how it is possible to avoid misinterpretations deriving from the exclusion of zero values by using methods of analysis which deal with zero values specifically. The conclusion of a diffusion of foreign investment in the French urban system is then rejected.

Defining urban clusters to detect agglomeration economies

Agglomeration economies are a persistent subject of debate in regional science and city planning. Their definition turns on whether or not larger cities are more efficient than smaller ones. Here, we complement existing discussions on agglomeration economies by providing a sensitivity analysis of estimated externalities to the definitions of urban agglomeration. We regress wages versus population and jobs over thousands of different definitions of cities in France, based on an algorithmic aggregation of spatial units. We also search for evidence of larger inequalities in larger cities. This paper therefore focuses on the spatial and economic complexity of the mechanisms defining agglomeration within and between cities.

Using Models to Explore Possible Futures (Contingency and Complexity)

This chapter considers models of urban systems as virtual laboratories to explore possible trajectories that a ‘real’ geographical system could have taken instead of the evolution path that is observed historically. It therefore builds on the concept of historical contingency, and regards simulation modelling as an opportunity to explore historical contingency in silico. This approach is illustrated by an experiment performed on a model of systems of cities applied to the urbanization of the (Former) Soviet Union, MARIUS, using a new algorithm seeking to maximize diversity in a model’s outcomes. The discovery of possible trajectories of the target system through the model provides insight into the singularity of the realized trajectory, and can be used for prediction to define a range of possible outcomes resulting from a simulation of the model, not based on predefined scenarios but on the maximum diversity allowed by the model within reasonable parameter bounds.