Rich and Poor Cities in Europe. An Urban Scaling Approach to Mapping the European Economic Transition

Tracing trajectories and co-evolution of metropolitan urbanization in the United States, Europe, and China

Metropolization has emerged as a prominent feature of 21st-century urbanization. To gain a comprehensive understanding of global urbanization patterns and pathways, as well as to interpret their consequences and implications, we aimed to provide a comparative characterization on urban transformation in metropolitan areas of developed and developing countries. Here, we quantified and compared the urban growth rates, growth modes, urban landscape metrics, and the co-evolution of urban land and population in 21 representative metropolitan areas across the United States, Europe, and China from 1985 to 2020, using remotely sensed impervious-surface dynamic dataset and patch-based analyses. The results showed that each metropolitan area has experienced substantial urban expansion with different scales and growth rates. Developing China possessed a relatively lower urbanization level but urbanized faster compared to the developed counterparts. Spatially, with infilling expansion increasing and even dominating, American and European metropolitan areas developed into more compact central urban cores, demonstrating the coalesced trajectories. Chinese metropolitan areas showed point-axis urban development mainly via edge-expansion in concentric rings. Furthermore, the horizontal co-evolution of urban area and population generally showed stable economies of scale in the United States and Europe whereas transitioned from diseconomy to economy of scale in China, evidencing that the century-long urbanization journey traversed by developed countries can be completed by emerging-developing ones within several decades. Temporally, the urban expansion greatly outpaced population growth in all metropolitan areas except London, signifying that urban land use efficiency is still a grand challenge in the Metropolitan Century. Effective metropolitan governance should be tailored to spatial configuration for efficient urban land use and intercity coordinated development towards a sustainable urban future, particularly for developing countries with emerging metropolization.

Effects of municipal boundaries measured by combining urban scaling and spatial interaction

Urban scaling, the superlinear increase of socio-economic measures with increasing population, is a well-researched phenomenon. This article is focused on socio-economic performance scaling, which could possibly be driven by increasing returns of the size and density of interaction networks. If this is indeed the case, we should also find that spatial barriers to interaction affect scaling and cause local performance deviations. Possible barring effects of municipal boundaries are important from the perspective of urban and regional governance. We test the hypothesis of barring effects by correlating municipal boundaries with the structure of commuter networks within a large densely urbanized region, the Randstad in The Netherlands. The measured impacts of these boundaries are correlated with local employment-scaling deviations. Applying spatially weighted modelling techniques, we find that municipal borders have significant effects on inter-municipal commuting and indicate these effects on the map. The results show particularly significant correlations along dividing lines between large urban agglomerations and rural communities. The southern part of the Randstad is more fragmented by such dividing lines than the northern part, which could partly explain the diverging economic development between the two parts.

Understanding urban concentration of complex manufacturing activities in China

The increasing prominence of urban scaling laws highlights the importance of a systematic understanding of the variational scaling rates for different economic activities. In this article, we utilize several datasets to provide the first systematic investigation of the urban scaling of manufacturing industries in China. Most existing literature assumes that the divergence in urban scaling can be explained by returns to agglomeration, with a few exceptions instead highlighting the role of knowledge complexity or a mixture of both. Our main purpose in this paper is to explain the inter-sector variation of urban scaling rates. In doing this, we provide a clearer approach to demonstrating the relations between urban scaling, returns to agglomeration, and knowledge complexity. Our findings are twofold. First, after uncovering the scaling rates (denoted as urban concentration) and returns to agglomeration (denoted as urban productivity) for each sub-manufacturing sector, we prove that, rather than being a positive predictor, returns to agglomeration is slightly negatively associated with urban scaling rates. This finding reveals that urban concentration of manufacturing may not simply be a natural consequence driven by the maximization of performance. We also show that this result of the manufacturing system contrasts with what would be found in other pure knowledge systems such as patents. Secondly, we measure the complexity for each sector and demonstrate that the variation of urban concentration can be largely explained by their complexity, consistent with the knowledge complexity perspective. Specifically, complex manufacturing sectors are found to concentrate more in large cities than less complex sectors in China. This result provides support for the view that the growth of complex activities hinges more on diversity than on efficiency. The findings above can greatly reduce the current level of ambiguity associated with urban scaling, returns to agglomeration and complexity, and have important policy implications for urban planners, highlighting the significance of a more balanced and diversified configuration of urban productive activities for the growth of innovation economy.

Recent advances in urban system science: Models and data

Cities are characterized by the presence of a dense population with a high potential for interactions between individuals of diverse backgrounds. They appear in parallel to the Neolithic revolution a few millennia ago. The advantages brought in terms of agglomeration for economy, innovation, social and cultural advancements have kept them as a major landmark in recent human history. There are many different aspects to study in urban systems from a scientific point of view, one can concentrate in demography and population evolution, mobility, economic output, land use and urban planning, home accessibility and real estate market, energy and water consumption, waste processing, health, education, integration of minorities, just to name a few. In the last decade, the introduction of communication and information technologies have enormously facilitated the collection of datasets on these and other questions, making possible a more quantitative approach to city science. All these topics have been addressed in many works in the literature, and we do not intend to offer here a systematic review. Instead, we will only provide a brief taste of some of these above-mentioned aspects, which could serve as an introduction to the collection ‘Cities as Complex Systems’. Such a non-systematic view will lead us to leave outside many relevant papers, and for this we must apologise.

Scaling behavior of public procurement activity

Public procurement refers to the purchase by public sector entities—such as government departments or local authorities—of Services, Goods, or Works. It accounts for a significant share of OECD countries’ expenditures. However, while governments are expected to execute them as efficiently as possible, there is a lack of methodologies for an adequate comparison of procurement activity between institutions at different scales, which represents a challenge for policymakers and academics. Here, we propose using methods borrowed from urban scaling laws literature to study public procurement activity among 278 Portuguese municipalities between 2011 and 2018. We find that public procurement expenditure scales sublinearly with population size, indicating an economy of scale for public spending as cities increase their population size. Moreover, when looking at the municipal Scale-Adjusted Indicators (the deviations from the scaling law) by contract categories—Works, Goods, and Services—we are able to identify a richer local characterisation of municipalities based on the similarity of procurement activity. These results make up a framework for quantitatively studying local public expenditure by enabling policymakers a more appropriate foundation for comparative analysis.

Commuting network effect on urban wealth scaling

Urban scaling theory explains the increasing returns to scale of urban wealth indicators by the per capita increase of human interactions within cities. This explanation implicitly assumes urban areas as isolated entities and ignores their interactions. Here we investigate the effects of commuting networks on the gross domestic product (GDP) of urban areas in the US and Brazil. We describe the urban GDP as the output of a production process where population, incoming commuters, and interactions between these quantities are the input variables. This approach significantly refines the description of urban GDP and shows that incoming commuters contribute to wealth creation in urban areas. Our research indicates that changes in urban GDP related to proportionate changes in population and incoming commuters depend on the initial values of these quantities, such that increasing returns to scale are only possible when the product between population and incoming commuters exceeds a well-defined threshold.

How the geometry of cities determines urban scaling laws

Urban scaling laws relate socio-economic, behavioural and physical variables to the population size of cities. They allow for a new paradigm of city planning and for an understanding of urban resilience and economics. The emergence of these power-law relations is still unclear. Improving our understanding of their origin will help us to better apply them in practical applications and further research their properties. In this work, we derive the basic exponents for spatially distributed variables from fundamental fractal geometric relations in cities. Sub-linear scaling arises as the ratio of the fractal dimension of the road network and of the distribution of the population embedded in three dimensions. Super-linear scaling emerges from human interactions that are constrained by the geometry of a city. We demonstrate the validity of the framework with data from 4750 European cities. We make several testable predictions, including the relation of average height of cities and population size, and the existence of a critical density above which growth changes from horizontal densification to three-dimensional growth.

Association between population distribution and urban GDP scaling

Urban scaling and Zipf’s law are two fundamental paradigms for the science of cities. These laws have mostly been investigated independently and are often perceived as disassociated matters. Here we present a large scale investigation about the connection between these two laws using population and GDP data from almost five thousand consistently-defined cities in 96 countries. We empirically demonstrate that both laws are tied to each other and derive an expression relating the urban scaling and Zipf exponents. This expression captures the average tendency of the empirical relation between both exponents, and simulations yield very similar results to the real data after accounting for random variations. We find that while the vast majority of countries exhibit increasing returns to scale of urban GDP, this effect is less pronounced in countries with fewer small cities and more metropolises (small Zipf exponent) than in countries with a more uneven number of small and large cities (large Zipf exponent). Our research puts forward the idea that urban scaling does not solely emerge from intra-city processes, as population distribution and scaling of urban GDP are correlated to each other.

Urban scaling, geography, centrality: Relation with local government structures

We investigate socio-economic urban scaling behavior of municipalities in Denmark, the Netherlands, and in particular in Germany. Our interest is twofold. First we investigate whether, and to what extent, scaling occurs in various types of urban areas. The second important topic of research concerns the comparison of specific types of urban areas with regard to the values of the gross urban product. This is a new approach: two scaling systems are compared not only in terms of the scaling exponent, but also in terms of the differences in the gross urban product. We are specifically interested in the role of urban governance in terms of local urban government structures. Germany is our central case because it works as a natural experiment: a large number of urban areas is one-governance, but others are not. More specifically, we distinguish between cities of which the surrounding urban area belongs to the municipality of the city (kreisfreie cities), and those specific districts (Kreise) which are urban areas consisting of several municipalities. Our findings suggest that urban areas with one municipality perform better than urban areas with fragmented governance structures. We also investigate the relation between scaling of Kreise and simple measures of centrality, including the Zipf-distribution. A strong relation is found between the measured residuals of the scaling equations and the socio-economic position of cities assessed with a set of different socio-economic indicators. Given the debate on the effectiveness of municipal reform, our results may lead to challenging conclusions about the importance of one-municipality instead of multi-municipality governance in urban areas. These results are relevant for policy as they suggest that there is a benefit to unifying the governance structure of compact urban agglomerations.

On the relation between transversal and longitudinal scaling in cities

Does the scaling relationship between population sizes of cities with urban metrics like economic output and infrastructure (transversal scaling) mirror the evolution of individual cities in time (longitudinal scaling)? The answer to this question has important policy implications, but the lack of suitable data has so far hindered rigorous empirical tests. In this paper, we advance the debate by looking at the evolution of two urban variables, GDP and water network length, for over 5500 cities in Brazil. We find that longitudinal scaling exponents are city-specific. However, they are distributed around an average value that approaches the transversal scaling exponent provided that the data is decomposed to eliminate external factors, and only for cities with a sufficiently high growth rate. We also introduce a mathematical framework that connects the microscopic level to global behaviour, finding good agreement between theoretical predictions and empirical evidence in all analyzed cases. Our results add complexity to the idea that the longitudinal dynamics is a micro-scaling version of the transversal dynamics of the entire urban system. The longitudinal analysis can reveal differences in scaling behavior related to population size and nature of urban variables. Our approach also makes room for the role of external factors such as public policies and development, and opens up new possibilities in the research of the effects of scaling and contextual factors.

Tomography of scaling

Scaling describes how a given quantity Y that characterizes a system varies with its size P. For most complex systems, it is of the form Y∼Pβ with a non-trivial value of the exponent β, usually determined by regression methods. The presence of noise can make it difficult to conclude about the existence of a nonlinear behaviour with β ≠ 1 and we propose here to circumvent fitting problems by investigating how two different systems of sizes P₁ and P₂ are related to each other. This leads us to define a local scaling exponent β_loc that we study versus the ratio P₂/P₁ and provides some sort of 'tomography scan' of scaling across different values of the size ratio, allowing us to assess the relevance of nonlinearity in the system and to identify an effective exponent that minimizes the error for predicting the value of Y. We illustrate this method on various real-world datasets for cities and show that our method reinforces in some cases the standard analysis, but is also able to provide new insights in inconclusive cases and to detect problems in the scaling form such as the absence of a single scaling exponent or the presence of threshold effects.

Combining urban scaling and polycentricity to explain socio-economic status of urban regions

The fast pace of urbanisation may benefit or be detrimental to the socio-economic status of urban areas. Understanding how the configuration of urban areas influences the socio-economic status of their inhabitants is of crucial importance for urban planning. In theory, urban scaling laws and polycentric development are two well-known concepts developed to increase our understanding of urbanisation and its socio-economic effects. In practice, however, they fall short to explain the socio-economic status of urban regions. The urban scaling concept is constructed from a theoretical perspective, but functional relationships between urban centres are not taken into account in scaling models. In contrast, the concept of polycentricity is developed from a practical perspective and incorporates the socio-economic effect of relationships between urban centres in the process of urban development. However, polycentricity lacks a theoretical foundation, which would explain the socio-economic status of urban regions. In this study, we assess whether combining both concepts improves the ability to explain personal incomes in metropolitan areas in Switzerland. We first delineated metropolitan areas by implementing a modularity maximisation algorithm on the settlement network. Nodes in this network are Swiss municipalities and links are inter-municipal commuter flows. We found a strong relationship between the hierarchical organisation of functional connections within metropolitan areas and the socio-economic status of these areas. Both concepts were complementary and combining them proved to enhance the ability to explain socio-economic status. The combined model is a theoretical progress, which complements the traditional approaches and increases our understanding of cities and urbanisation processes.

Evolution of urban scaling: Evidence from Brazil

During the last years, the new science of cities has been established as a fertile quantitative approach to systematically understand the urban phenomena. One of its main pillars is the proposition that urban systems display universal scaling behavior regarding socioeconomic, infrastructural and individual basic services variables. This paper discusses the extension of the universality proposition by testing it against a broad range of urban metrics in a developing country urban system. We present an exploration of the scaling exponents for over 60 variables for the Brazilian urban system. Estimating those exponents is challenging from the technical point of view because the Brazilian municipalities’ definition follows local political criteria and does not regard characteristics of the landscape, density, and basic utilities. As Brazilian municipalities can deviate significantly from urban settlements, urban-like municipalities were selected based on a systematic density cut-off procedure and the scaling exponents were estimated for this new subset of municipalities. To validate our findings we compared the results for overlaying variables with other studies based on alternative methods. It was found that the analyzed socioeconomic variables follow a superlinear scaling relationship with the population size, and most of the infrastructure and individual basic services variables follow expected sublinear and linear scaling, respectively. However, some infrastructural and individual basic services variables deviated from their expected regimes, challenging the universality hypothesis of urban scaling. We propose that these deviations are a product of top-down decisions/policies. Our analysis spreads over a time-range of 10 years, what is not enough to draw conclusive observations, nevertheless we found hints that the scaling exponent of these variables are evolving towards the expected scaling regime, indicating that the deviations might be temporally constrained and that the urban systems might eventually reach the expected scaling regime.

Contemporary evolution and scaling of 32 major cities in China

Most of the planet's population currently lives in urban areas, and urban land expansion is one of the most dramatic forms of land conversion. Understanding how cities evolve temporally, spatially, and organizationally in a rapidly urbanizing world is critical for sustainable development. However, few studies have examined the coevolution of urban attributes in time and space simultaneously and the adequacy of power law scaling across cities and through time, particularly in countries that have experienced abrupt, widespread, political and economic changes. Here, we show the temporal coevolution of multiple physical, demographic, socioeconomic, and environmental attributes in individual cities, and the cross-city scaling of urban attributes at six time points (i.e., 1978, 1990, 1995, 2000, 2005, and 2010) in 32 major Chinese cities. We found that power law scaling could adequately characterize both the cross-city scaling of urban attributes across cities and the longitudinal scaling describing the temporal coevolution of urban attributes within individual cities. The cross-city scaling properties demonstrated substantial changes over time signifying evolved social and economic forces. A key finding was that the cross-city linear or superlinear scaling of urban area with population contradicts the theoretical sublinear power law scaling proposed between infrastructure and population. Furthermore, the cross-city scaling between area and population transitioned from linear to superlinear over time, and the superlinear scaling in recent times suggests decreased infrastructure efficiency. Our results demonstrate a diseconomy of scale in urban areal expansion that indicates a significant waste of land resources in the urbanization process. Future planning efforts should focus on policies that increase urban land use efficiency before continuing expansion.

The scaling structure of the global road network

Because of increasing global urbanization and its immediate consequences, including changes in patterns of food demand, circulation and land use, the next century will witness a major increase in the extent of paved roads built worldwide. To model the effects of this increase, it is crucial to understand whether possible self-organized patterns are inherent in the global road network structure. Here, we use the largest updated database comprising all major roads on the Earth, together with global urban and cropland inventories, to suggest that road length distributions within croplands are indistinguishable from urban ones, once rescaled to account for the difference in mean road length. Such similarity extends to road length distributions within urban or agricultural domains of a given area. We find two distinct regimes for the scaling of the mean road length with the associated area, holding in general at small and at large values of the latter. In suitably large urban and cropland domains, we find that mean and total road lengths increase linearly with their domain area, differently from earlier suggestions. Scaling regimes suggest that simple and universal mechanisms regulate urban and cropland road expansion at the global scale. As such, our findings bear implications for global road infrastructure growth based on land-use change and for planning policies sustaining urban expansions.

Population patterns in World's administrative units

Whereas there has been an extended discussion concerning city population distribution, little has been said about that of administrative divisions. In this work, we investigate the population distribution of second-level administrative units of 150 countries and territories and propose the discrete generalized beta distribution (DGBD) rank-size function to describe the data. After testing the balance between the goodness of fit and number of parameters of this function compared with a power law, which is the most common model for city population, the DGBD is a good statistical model for 96% of our datasets and preferred over a power law in almost every case. Moreover, the DGBD is preferred over a power law for fitting country population data, which can be seen as the zeroth-level administrative unit. We present a computational toy model to simulate the formation of administrative divisions in one dimension and give numerical evidence that the DGBD arises from a particular case of this model. This model, along with the fitting of the DGBD, proves adequate in reproducing and describing local unit evolution and its effect on the population distribution.

Scaling Laws in City Growth: Setting Limitations with Self-Organizing Maps

Do scaling relations always provide the means to anticipate the relationships between the size of cities, costs of maintenance, and the socio-economic benefits resulting from their growth? Scaling laws are considered a universal principle that describes the development of complex systems such as cities. It seems that regardless of their location or history, the growth of cities is associated with the super-linear or sublinear scaling of features such as the amount of space required, infrastructure, or human activities. However, the results of our research, based on grouping by Self-Organizing Maps, reveal some limitations in the application of scaling laws: the trends of urban growth behave in a different manner when we consider both a large and diverse collection of cities and a subset of cities alike. This finding complements the existing body of knowledge on the growth of cities and allows for a more accurate prediction of their future.

International Collaboration and Spatial Dynamics of US Patenting in Central and Eastern Europe 1981-2010

How did post-socialist transition and a parallel shift in international labor division restructure regional innovation systems in Central and Eastern Europe? This question is increasingly important, because current EU innovation policy is combined with regional development in Smart Specialization Strategies; however, spatial trends of innovation in Central and Eastern Europe are not fully understood which might lead to less than perfectly efficient policy. In this paper we describe the spatial dynamics of inventor activity in the Czech Republic, Hungary, Poland and Slovakia between 1981 and 2010 –a period that covers both the late socialist era and the post-socialist transition. Cleaning and analyzing the publicly available data from the United States Patent and Trademark Office we illustrate that Central and Eastern European patents made in international co-operations with partners outside the region receive more citations than those Central and Eastern European patents that lack international co-operation. Furthermore, the technological portfolio of the former patents has become increasingly independent from the technological portfolio of the latter class. A town-level analysis of the applicant-inventor ties reveals that inventors have started to work for foreign assignees in those towns where no innovation activity had been recorded before. However, the positive effect does not last long and patenting seems to be only periodic in the majority of these towns. Therefore, innovation policy in Central and Eastern European countries, as well as in other less developed regions, shall foster synergies between international and domestic collaborations in order to decrease regional disparities in patenting.