Urban scaling and the production function for cities

Reverse social contagion as a mechanism for regulating mass behaviors in highly integrated social systems

Mass behavior is the rapid adoption of similar conduct by all group members, with potentially catastrophic outcomes such as mass panic. Yet, these negative consequences are rare in integrated social systems such as social insect colonies, thanks to mechanisms of social regulation. Here, we test the hypothesis that behavioral deactivation between active individuals is a powerful social regulator that reduces energetic spending in groups. Borrowing from scaling theories for human settlements and using behavioral data on harvester ants, we derive ties between the hypermetric scaling of the interaction network and the hypometric scaling of activity levels, both relative to the colony size. We use elements of economics theory and metabolic measurements collected with the behavioral data to link activity and metabolic scalings with group size. Our results support the idea that metabolic scaling across social systems is the product of different balances between their social regulation mechanisms.

Scaling behavior for electric vehicle chargers and road map to addressing the infrastructure gap

Enabling widespread electric vehicle (EV) adoption requires a substantial build-out of charging infrastructure in the coming decade. We formulate the charging infrastructure needs as a scaling analysis problem and use it to estimate the EV infrastructure needs of the USA at a county-level resolution. We find that gasoline and EV charging stations scale sub-linearly with their respective vehicle registrations, recovering the sub-linear scaling typical of infrastructure. Surprisingly, we find that EV charging stations scale super-linearly with population size within counties, deviating from the sub-linear scaling of gasoline stations. We discuss how this demonstrates the infancy of both EVs and EV infrastructure while providing a framework for estimating future EV infrastructure demands. By considering the power delivery of existing gasoline stations, and appropriate EV efficiencies, we estimate the EV infrastructure gap at the county level, providing a road map for future EV infrastructure expansion.

Dynamic multi-dimensional scaling of 30+ year evolution of Chinese urban systems: Patterns and performance

Understanding the co-evolution and organizational dynamics of urban properties (i.e., urban scaling) is the science base for pursuing synergies toward sustainable cities and society. The generalization of urban scaling theory yet requires more studies from various developmental regimes and across time. Here, we extend the universality proposition by exploring the evolution of longitudinal and transversal scaling of Chinese urban attributes between 1987 and 2018 using a global artificial impervious area (GAIA) remotely sensed dataset, harmonized night light data (NTL), and socioeconomic data, and revealed agreements and disagreements with theories. The superlinear relationship of urban area and population often considered as an indicator of wasting land resources (challenging the universality theory β_c = 2/3), is in fact the powerful impetus (capital raising) behind the concurrent superlinear expansion of socio-economic metabolisms (e.g., GDP, total wage) in a rapidly urbanizing country that has not yet reached equilibrium. Similarly, infrastructural variables associated with public services, such as hospitals and educational institutions, exhibited some deviations as well and were scaled linearly. However, the temporal narrowing of spatial deviations, such as the decline in urban land diseconomies of scale and the stabilization of economic output, clearly indicates the Chinese government's effort in charting urban systems toward balanced and sustainable development across the country. More importantly, the transversal sublinear scaling of areal-based socio-economic variables was inconsistent with the theoretical concept of increasing returns to scale, thus validating the view that a single measurement cannot unravel the intricate web of diverse urban attributes and urbanization. Our dynamic urban scaling analysis across space and through time in China provides new insights into the evolving nexus of urbanization, socioeconomic development, and national policies.

Superlinear urban scaling by functional organization: A metabolic interpretation of sectoral water consumption

Prevailing view asserts that the disproportionately greater productivities of larger cities, or superlinear urban scaling, are the result of human interactions channeled by urban networks. But this view was established by considering the spatial organization of urban infrastructure and social networks-the urban "arteries" effects-but neglecting the functional organization of urban production and consumption entities-the urban "organs" effects. Here, adopting a metabolic view and using water consumption as a proxy for metabolism, we empirically quantify the scaling of entity number, size, and metabolic rate for the functionally specific urban residential, commercial, public or institutional, and industrial sectors. Sectoral urban metabolic scaling is highlighted by a disproportionate coordination between residential and enterprise metabolic rates, attributable to the functional mechanisms of mutualism, specialization, and entity size effect. The resultant whole-city metabolic scaling exhibits a constant superlinear exponent for water-abundant regions in numerical agreement with superlinear urban productivity, with varying exponent deviations for water-deficient regions explainable as adaptations to climate-driven resource constraints. These results present a functional organizational, non-social-network explanation of superlinear urban scaling.

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.

Rediscovering the Scaling Law of Urban Land from a Multi-Scale Perspective—A Case Study of Wuhan

The law of urban scaling implies that there is a universally applicable nonlinear scaling relationship between population size and urban indicators, which is a method of quantitative analysis that can reflect the growth law and internal logic of the urban system. However, most present research is conducted at the municipal scale, and studies of scaling law in the inner-city system are scarce, especially from the perspective of compact urban form development. The goal of this paper is to discover the scaling law within urban systems from a multi-scale perspective. Through the empirical analysis of Wuhan, this paper examines the internal scale law of the urban system from the municipal and district scales. Moreover, we use the landscape expansion index to perform spatial autocorrelation analysis. In this way, we assess the relationship between the compactness of urban morphological development and the urban scaling law. The results indicate that the temporal scaling law on the city scale has a more significant linear law than the single-year scaling law. The analysis also shows the scaling law relationship within the inner-city system. Nevertheless, there is a deviation between the temporal scaling law and the cross-section scaling law. Namely, the time series development of a district does not follow the section scaling law of the urban system. Furthermore, the urban scaling law shows a negative correlation with the compactness of the urban form development. It is crucial to understand the current economic development and resource endowment of an urban system in the urbanization process, as it significantly contributes to urban development and regional coordinated planning.

The urban wage premium is disappearing in U.S. micropolitan areas

A key driver of urbanization is the pursuit of economic opportunities in cities. One such opportunity is the promise of higher wages in larger cities, a phenomenon known as the urban wage premium. While an urban wage premium has been well-documented among U.S. metropolitan areas, little is known about its existence in micropolitan areas, which represent an important link between rural and dense urban areas. Here we measure the power law scaling coefficient of annual wages versus employment for both U.S. metropolitan and micropolitan areas over a 37-year period. We take this coefficient to be a quantification of the urban wage premium for each type of urban area and find the relationship is superlinear in all years for both area types. Though both area types once had wage premiums of similar magnitude, the wage premium in micropolitan areas has steadily declined since the late 1980s while in metropolitan areas it has generally increased. This growing gap between micropolitan and metropolitan wage premiums is ongoing in parallel to other diverging characteristics, such as inequality and voting behavior, suggesting that our result is part of a broader social, cultural, and political divergence between small and large cities. Finally, we speculate that if urban residents respond to the COVID-19 crisis by migrating, the trends we describe may change significantly.

Cultural Sustainability of US Cities: The Scaling of Non-Profit Arts Footprint with Population

The functional characteristics of urban systems vary predictably with Metropolitan Statistical Area (MSA) population, with certain metrics increasing apace with population (e.g., housing stock), some increasing faster than population (e.g., wealth), and others increasing slower than population (infrastructure elements). Culture has been designated the fourth pillar of sustainability. The population-dependent scaling of operating revenue, work space, and number of employees was investigated for almost 3000 arts organizations in the US, both in aggregate and by arts discipline (music, theater, visual and design arts, dance, and museums). Unlike general measures of creativity, the three measures of economic footprint did not scale supra-linearly with the population of metropolitan areas. Rather, operating revenue scaled linearly (e.g., like amenities), and work space and employee number scaled sub-linearly (e.g., like infrastructure). The cost of living, proxied by housing costs, increased with MSA population, though not as rapidly as did arts organization operating revenue, indicating a degree of uncoupling. The generally higher educational attainment of adults in larger cities, coupled with the growth of the education-dependent arts patronage, suggest a funding focus on less populous (50,000–1,000,000), as well as on under-performing, cities.

A Conceptual Model for Assessing the Relationship between Urban Morphology and Sustainable Urban Form

The built environment witnessed rapid transformation after the industrial revolution. This transformation came along with some negativities, which gave rise to the concept of sustainability in urban form. In this regard, the current study aimed to assess and validate the reciprocal relationship between urban morphology and sustainable urban form. This study proposes a conceptual model which integrates and presents the holistic correlation between sustainable urban form and urban morphology, by using qualitative grounded theory as the research methodology. The model was developed by introducing analytical tools to evaluate sustainability, along with integrating typo-morphology and the concept of scale hierarchy. The findings of this study reveal that every single component of sustainable urban form interacts significantly with the typo-morphology approach. Consequently, the outcomes help urban planners to get more informed decisions about the geometric analysis of urban morphology from a sustainability point of view.

Detect Megaregional Communities Using Network Science Analytics

Urban science research and the research on megaregions share a common interest in the system of cities and its implications for world urbanization and sustainability. The two lines of inquiry currently remain largely separate efforts. This study aims to bridge urban science and megaregion research by applying network science’s community detection algorithm to explore the spatial pattern of megaregions in the contiguous United States. A network file was constructed consisting of county centroids as nodes, the direct links between each pair of counties as edges, and inter-county commuting flows as the weight to capture spatial interactions. Analyses were carried out at two levels, one at the national level using Gephi and the other for the State of Texas involving NetworkX, an open-source Python programming package to implement a weighted community detection algorithm. Results show the detected communities largely conforming to the qualitative knowledge on megaregions. Despite a number of limitations, the study indicates the great potential of applying network science analytics to improve understanding of the spatial process of megaregions.

German Cities with Universities: Socioeconomic Position and University Performance

A much debated topic is the role of universities in the prosperity of cities and regions. Two major problems arise. First, what is a reliable measurement of prosperity; second, what are the characteristics, particularly research performance of a university that matter? We focus on the research question: Is there a significant relation between having a university and a city’s socioeconomic strength? And if so, what are the determining indicators of a university, for instance how important is scientific collaboration? What is the role scientific quality measured by citation impact? Does size of a university in number of publications, or in number of students matter? We composed a database of city and university data: gross urban product and population data of nearly 200 German cities and 400 districts. University data are derived from the Leiden Ranking 2020 and supplemented with data on the number of students. The socioeconomic strength of a city is determined with the urban scaling methodology. Our study shows a significant relation between the presence of a university in a city and its socioeconomic indicators, particularly for larger cities, and that this is especially the case for universities with higher values of their output, impact and collaboration indicators.

Peer Review

https://publons.com/publon/10.1162/qss_a_00182

Scaling of mortality in 742 metropolitan areas of the Americas

We explored how mortality scales with city population size using vital registration and population data from 742 cities in 10 Latin American countries and the United States. We found that more populated cities had lower mortality (sublinear scaling), driven by a sublinear pattern in U.S. cities, while Latin American cities had similar mortality across city sizes. Sexually transmitted infections and homicides showed higher rates in larger cities (superlinear scaling). Tuberculosis mortality behaved sublinearly in U.S. and Mexican cities and superlinearly in other Latin American cities. Other communicable, maternal, neonatal, and nutritional deaths, and deaths due to noncommunicable diseases were generally sublinear in the United States and linear or superlinear in Latin America. Our findings reveal distinct patterns across the Americas, suggesting no universal relation between city size and mortality, pointing to the importance of understanding the processes that explain heterogeneity in scaling behavior or mortality to further advance urban health policies.

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.

The structure, centrality, and scale of urban street networks: Cases from Pre-Industrial Afro-Eurasia

Cities and towns have often developed infrastructure that enabled a variety of socio-economic interactions. Street networks within these urban settings provide key access to resources, neighborhoods, and cultural facilities. Studies on settlement scaling have also demonstrated that a variety of urban infrastructure and resources indicate clear population scaling relationships in both modern and ancient settings. This article presents an approach that investigates past street network centrality and its relationship to population scaling in urban contexts. Centrality results are compared statistically among different urban settings, which are categorized as orthogonal (i.e., planned) or self-organizing (i.e., organic) urban settings, with places having both characteristics classified as hybrid. Results demonstrate that street nodes have a power law relationship to urban area, where the number of nodes increases and node density decreases in a sub-linear manner for larger sites. Most median centrality values decrease in a negative sub-linear manner as sites are larger, with organic and hybrid urban sites’ centrality being generally less and diminishing more rapidly than orthogonal settings. Diminishing centrality shows comparability to modern urban systems, where larger urban districts may restrict overall interaction due to increasing transport costs over wider areas. Centrality results indicate that scaling results have multiples of approximately ⅙ or ⅓ that are comparable to other urban and road infrastructure, suggesting a potential relationship between different infrastructure features and population in urban centers. The results have implications for archaeological settlements where urban street plans are incomplete or undetermined, as it allows forecasts to be made on past urban sites’ street network centrality. Additionally, a tool to enable analysis of street networks and centrality is provided as part of the contribution.

The US COVID Atlas: A dynamic cyberinfrastructure surveillance system for interactive exploration of the pandemic

Distributed spatial infrastructures leveraging cloud computing technologies can tackle issues of disparate data sources and address the need for data-driven knowledge discovery and more sophisticated spatial analysis central to the COVID-19 pandemic. We implement a new, open source spatial middleware component (libgeoda) and system design to scale development quickly to effectively meet the need for surveilling county-level metrics in a rapidly changing pandemic landscape. We incorporate, wrangle, and analyze multiple data streams from volunteered and crowdsourced environments to leverage multiple data perspectives. We integrate explorative spatial data analysis (ESDA) and statistical hotspot standards to detect infectious disease clusters in real time, building on decades of research in GIScience and spatial statistics. We scale the computational infrastructure to provide equitable access to data and insights across the entire USA, demanding a basic but high-quality standard of ESDA techniques. Finally, we engage a research coalition and incorporate principles of user-centered design to ground the direction and design of Atlas application development.

Orderliness in Tourism Enterprise Dynamics in United States Micropolitan Statistical Areas

Micropolitan statistical areas (micropolitans) are important elements in understanding the small-town economic forces operating in the United States. This study focuses on the tourism enterprise dynamics of micropolitans. These dynamics are an oft-neglected element in tourism analyses and reports. Power law (log-log) regression analyses are central to the examination of complex socio-economic systems, and have been used here. Micropolitan tourism enterprises are ubiquitous and there is much non-linear orderliness in the interplay between their demographic and entrepreneurial characteristics. The dynamics of the orderliness result in important differences. For instance, total micropolitan employment increases sub-linearly (more slowly) than increases in tourism enterprise numbers, while tourism employment increases super-linearly (more rapidly). This difference could be important in considerations of micropolitan employment. The relationship of tourism and poverty has often been debated. Here, a statistically significant negative correlation was observed between the number of tourism enterprises and a measure of community prosperity/wealth of the micropolitans. Expansion of the tourism sector apparently reduces community poverty in micropolitans. However, community poverty is also lower in larger micropolitans. Therefore, further analyses are needed to examine the potentially spurious correlation. Overall, future decision-making could be supported by the quantified information about the tourism dynamics of micropolitans.

City size based scaling of the urban internal nodes layout

The size of a city is not only essential for depicting the scale of the urban system, but also crucial to support the prosperity, order, and high-speed developments. However, its relation to the underlying urban structure has not been empirically investigated in detail. To examine the impact of city size on the city structure and quantify structural features, in this study, a statistical analysis was performed based on network science and an interdisciplinary theoretical system. To obtain the statistical law of internal node layout, the urban system was regarded as a complete graph weighted by the Euclidean distance. The relationship between the urban internal nodes layout (points of interest data, Weibo check-in data, and central point of road intersection data) and the city size was established. The results confirmed the existence of statistical laws in the layout of urban spatial elements, and explored the relationship between the changes in urban node network structure and inequality. This study provided a new perspective of urban structure to understand the complexity of the city, and suggested an approach to adjust this structure to narrow down the gap between the urban and rural areas.

Cooperation among unrelated ant queens provides persistent growth and survival benefits during colony ontogeny

The fitness consequences of cooperation can vary across an organism's lifespan. For non-kin groups, especially, social advantages must balance intrinsic costs of cooperating with non-relatives. In this study, we asked how challenging life history stages can promote stable, long-term alliances among unrelated ant queens. We reared single- and multi-queen colonies of the primary polygynous harvester ant, Pogonomyrmex californicus, from founding through the first ten months of colony growth, when groups face high mortality risks. We found that colonies founded by multiple, unrelated queens experienced significant survival and growth advantages that outlasted the colony founding period. Multi-queen colonies experienced lower mortality than single-queen colonies, and queens in groups experienced lower mortality than solitary queens. Further, multi-queen colonies produced workers at a faster rate than did single-queen colonies, even while experiencing lower per-queen worker production costs. Additionally, we characterized ontogenetic changes in the organization of labor, and observed increasing and decreasing task performance diversity by workers and queens, respectively, as colonies grew. This dynamic task allocation likely reflects a response to the changing role of queens as they are increasingly able to delegate risky and costly tasks to an expanding workforce. Faster worker production in multi-queen colonies may beneficially accelerate this behavioral transition from a vulnerable parent-offspring group to a stable, growing colony. These combined benefits of cooperation may facilitate the retention of multiple unrelated queens in mature colonies despite direct fitness costs, providing insight into the evolutionary drivers of stable associations between unrelated individuals.

City of Waste—Importance of Scale

By 2050, the world population is expected to reach 9.7 billion, almost 90% of which will live in urban areas. With such a fast growth in population and urbanization, it is anticipated that the annual waste generation will increase by 70% in comparison with current levels, and will reach 3.40 billion tons in 2050. A key question regarding the sustainability of the planet is the effect of city size on waste production. Are larger cities more efficient at generating waste than smaller cities? Do larger cities show economies of scale over waste? This article examines the allometric relationship between the amount of municipal waste (total and per capita) and the populations, city area, density, and wealth of city residents. The scope of the research concerned 930 Polish cities. Using the allometric equation, the waste scaling factors were calculated for selected parameters, and the Hellwig method was used to optimize their selection for cities with more than 50,000 inhabitants. The calculations show that the parameter population (1.059) and then the city area (0.934) are important elements influencing the scaling of the amount of municipal waste in cities of all sizes, but none came close to the value of the animal metabolism model (0.75). In response to the question of whether larger cities show benefits from economies of scale, it should be stated that, for the model of city size in Poland, such a regularity does not exist.

Socio-economic urban scaling properties: Influence of regional geographic heterogeneities in Brazil

The recent efforts dedicated to understanding important features and consequences of city growth have profited from the scaling approach to urban indicators. This kind of analysis can be conveniently used to investigate the impact of geo-economic transformations, like fast urbanization and industrial development, which occurred in continental size countries (e.g., India, China, and Brazil) during the past half-century. Profiting from high quality data, this work explores how scaling relationships among urban indicators are influenced by strong regional heterogeneities in Brazil. It is based on economic, infrastructure and violence related data sets for the time interval 2002-2016. Results indicate that regional specificities related to infrastructure, economic development, and geography have a larger influence on the absolute value of the urban indexes. Regional scaling similarities and differences among Brazilian regions were also uncovered. Interesting enough, the results indicate that the richest and poorest Brazilian regions share similar scaling behavior, despite all huge different local influences. By contrast, the results for the two richest regions, with similar average values of urban indexes and the same kind of local influences have rather different scaling properties. Thus, scaling analysis suggests that distinct political solutions might be necessary to improve life's quality, even for two regions with similar average values of urban indicators.

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.

Analysis on urban scaling characteristics of China's relatively developed cities

China is undergoing rapid urbanization, but the speed and stage of urban development are quite heterogeneous among different regions and city types. Understanding the urban scaling characteristics of China’s relatively developed cities is important for addressing environmental and social challenges. Within the scope of 114 third-tier-and-above Chinese cities, the research calculate the scaling parameters of various urban development variables with respect to urban population and urban GRP in different city types based on urban scaling quantitative models. Also, univariate and multivariate regression analyses were performed on the factors affecting urban electricity consumption. The research results show that the urban scaling characteristics of Chinese cities differ between different types of cities, industrial cities show unique scaling features compared to commercial cities and mixed-economy cities. Additionally, urban electricity consumption is found to be closely related to urban population, urban construction land area and street lamp number. The results can help different types of cities make targeted policies and provide insights for reducing resource consumption during the urbanization process.

Evidence for localization and urbanization economies in urban scaling

We study the scaling of (i) numbers of workers and aggregate incomes by occupational categories against city size, and (ii) total incomes against numbers of workers in different occupations, across the functional metropolitan areas of Australia and the USA. The number of workers and aggregate incomes in specific high-income knowledge economy-related occupations and industries show increasing returns to scale by city size, showing that localization economies within particular industries account for superlinear effects. However, when total urban area incomes and/or gross domestic products are regressed using a generalized Cobb-Douglas function against the number of workers in different occupations as labour inputs, constant returns to scale in productivity against city size are observed. This implies that the urbanization economies at the whole city level show linear scaling or constant returns to scale. Furthermore, industrial and occupational organizations, not population size, largely explain the observed productivity variable. The results show that some very specific industries and occupations contribute to the observed overall superlinearity. The findings suggest that it is not just size but also that it is the diversity of specific intra-city organization of economic and social activity and physical infrastructure that should be used to understand urban scaling behaviours.

The interpretation of urban scaling analysis in time

Scaling is a general analytical framework used by many disciplines-from physics to biology and the social sciences-to characterize how population-averaged properties of a collective vary with its size. The observation of scale invariance over some range identifies general system types, be they ideal gases, ecosystems or cities. The use of scaling in the analysis of cities quantifies many of their arguably fundamental general characteristics, especially their capacity to create interrelated economies of scale in infrastructure and increasing returns to scale in socio-economic activities. However, the measurement of these effects, and the relationship of observable parameters to theory, hinge on how scaling analysis is used empirically. Here, we show how two equivalent approaches to urban scaling-cross-sectional and temporal-lead to the measurement of different mixtures of the same fundamental parameters describing pure scale and pure temporal phenomena. Specifically, temporal exponents are sensitive to the intensive growth of urban quantities and to circumstances when population growth vanishes, leading to instabilities and infinite divergences. These spurious effects are avoided in cross-sectional scaling, which is more common and closer to theory in terms of quantitative testable expectations for its parameters.

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.

Scaling in words on Twitter

Scaling properties of language are a useful tool for understanding generative processes in texts. We investigate the scaling relations in citywise Twitter corpora coming from the metropolitan and micropolitan statistical areas of the United States. We observe a slightly superlinear urban scaling with the city population for the total volume of the tweets and words created in a city. We then find that a certain core vocabulary follows the scaling relationship of that of the bulk text, but most words are sensitive to city size, exhibiting a super- or a sublinear urban scaling. For both regimes, we can offer a plausible explanation based on the meaning of the words. We also show that the parameters for Zipf's Law and Heaps' Law differ on Twitter from that of other texts, and that the exponent of Zipf's Law changes with city size.

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.

The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.

Climate models can correctly simulate the continuum of global-average temperature variability

Climate records exhibit scaling behavior with large exponents, resulting in larger fluctuations at longer timescales. It is unclear whether climate models are capable of simulating these fluctuations, which draws into question their ability to simulate such variability in the coming decades and centuries. Using the latest simulations and data syntheses, we find agreement for spectra derived from observations and models on timescales ranging from interannual to multimillennial. Our results confirm the existence of a scaling break between orbital and annual peaks, occurring around millennial periodicities. That both simple and comprehensive ocean-atmosphere models can reproduce these features suggests that long-range persistence is a consequence of the oceanic integration of both gradual and abrupt climate forcings. This result implies that Holocene low-frequency variability is partly a consequence of the climate system's integrated memory of orbital forcing. We conclude that climate models appear to contain the essential physics to correctly simulate the spectral continuum of global-mean temperature; however, regional discrepancies remain unresolved. A critical element of successfully simulating suborbital climate variability involves, we hypothesize, initial conditions of the deep ocean state that are consistent with observations of the recent past.

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.

Irrigated areas grow faster than the population

Unfolding regularities between population and irrigated agriculture might increase our capacity to predict their coevolution and better ensure food security and environmental welfare. Here I use three different data sets with detailed information at the national level for ~70% of the countries of Africa, Asia, the Americas, and Europe between 1950 and 2017 to show that irrigated areas might grow disproportionally for a given increase in population, e.g., with β > 1. The results are robust across continents, time series, population cut-offs, and variations in the area accounted for irrigation by official institutions and independent scholars. This systematic pattern suggests the existence of an underlying law driving the growth rate of irrigated areas that transcends local particularities and can be well approximated by a power function of population, specially in the case of the Americas, Asia, and Europe. Nonlinearities derived from the open-ended growth rate of irrigated areas should be taken into consideration when designing irrigation policies in order to avoid unexpected environmental costs.

Large cities get more for less: Water footprint efficiency across the US

Many urban indicators and functional citywide properties have been shown to scale with population due to agglomeration effects. We hypothesize that scaling relations may also exist for water-related urban indicators such as the water footprint. The water footprint is an indicator of water use that measures humans' appropriation of freshwater resources. We analyze the scaling of the water footprint for 65 mid- to large-sized US cities using both empirical estimates and a social interaction network model of city functioning. The network model is used to explain the presence of any scaling exponent in the empirical estimates of the urban water footprint by linking to previous theories of urban scaling. We find that the urban water footprint tends to approximately show sublinear scaling behavior with both population and gross domestic product. Thus, large cities tend to be more water footprint efficient and productive than mid-sized cities, where efficiency and productivity are quantified, in a broad sense, as deviations from a linear scaling exponent. We find the sublinear scaling may be linked to changes in urban economic structure with city size, which lead to large cities shifting water intensive economic activities to less populated regions. In addition, we find that green water contributes to the scaling both positively by transferring the dependence of food consumption on population into the water footprint and negatively by increasing heterogeneity. Overall, the proposed scaling relations allow for the comparison of water footprint efficiency and productivity of cities. Comparing these properties and identifying deviations from the expected behavior has implications for water resources and urban sustainability.

Urbanism and the division of labour in the Roman Empire

One of the hallmarks of human agglomeration is an increase in the division of labour, but the exact nature of this relationship has been debated among anthropologists, sociologists, economists, and historians and archaeologists. Over the last decade, researchers investigating contemporary urban systems have suggested a novel explanation for the links between the numbers of inhabitants in settlements and many of their most important characteristics, which is grounded in a view of settlements as social networks embedded in built environments. One of the remarkable aspects of this approach is that it is not based on the specific conditions of the modern world (such as capitalism or industrialization), which raises the issue of whether the relationships observed in contemporary urban systems can also be detected in pre-modern urban or even non-urban systems. Here, we present a general model for the relationship between the population and functional diversity of settlements, where the latter is viewed as an indicator of the division of labour. We then explore the applicability of this model to pre-modern contexts, focusing on cities in the Roman Empire, using estimates of their numbers of inhabitants, numbers of documented professional associations, and numbers of recorded inscriptions to develop an index of functional diversity. Our results are consistent with theoretical expectations, adding further support to the view that urban systems in both contemporary and pre-modern contexts reflect a common set of generative processes.

Hierarchical Scaling in Systems of Natural Cities

Hierarchies can be modeled by a set of exponential functions, from which we can derive a set of power laws indicative of scaling. The solution to a scaling relation equation is always a power law. The scaling laws are followed by many natural and social phenomena such as cities, earthquakes, and rivers. This paper reveals the power law behaviors in systems of natural cities by reconstructing the urban hierarchy with cascade structure. Cities of the U.S.A., Britain, France, and Germany are taken as examples to perform empirical analyses. The hierarchical scaling relations can be well fitted to the data points within the scaling ranges of the number, size and area of the natural cities. The size-number and area-number scaling exponents are close to 1, and the size-area allometric scaling exponent is slightly less than 1. The results show that natural cities follow hierarchical scaling laws very well. The principle of entropy maximization of urban evolution is then employed to explain the hierarchical scaling laws, and differences entropy maximizing processes are used to interpret the scaling exponents. This study is helpful for scientists to understand the power law behavior in the development of cities and systems of cities.

Universal scaling laws in metro area election results

We explain the anomaly of election results between large cities and rural areas in terms of urban scaling in the 1948–2016 US elections and in the 2016 EU referendum of the UK. The scaling curves are all universal and depend on a single parameter only, and one of the parties always shows superlinear scaling and drives the process, while the sublinear exponent of the other party is merely the consequence of probability conservation. Based on the recently developed model of urban scaling, we give a microscopic model of voter behavior in which we replace diversity characterizing humans in creative aspects with social diversity and tolerance. The model can also predict new political developments such as the fragmentation of the left and the immigration paradox.

Unveiling relationships between crime and property in England and Wales via density scale-adjusted metrics and network tools

Scale-adjusted metrics (SAMs) are a significant achievement of the urban scaling hypothesis. SAMs remove the inherent biases of per capita measures computed in the absence of isometric allometries. However, this approach is limited to urban areas, while a large portion of the world's population still lives outside cities and rural areas dominate land use worldwide. Here, we extend the concept of SAMs to population density scale-adjusted metrics (DSAMs) to reveal relationships among different types of crime and property metrics. Our approach allows all human environments to be considered, avoids problems in the definition of urban areas, and accounts for the heterogeneity of population distributions within urban regions. By combining DSAMs, cross-correlation, and complex network analysis, we find that crime and property types have intricate and hierarchically organized relationships leading to some striking conclusions. Drugs and burglary had uncorrelated DSAMs and, to the extent property transaction values are indicators of affluence, twelve out of fourteen crime metrics showed no evidence of specifically targeting affluence. Burglary and robbery were the most connected in our network analysis and the modular structures suggest an alternative to "zero-tolerance" policies by unveiling the crime and/or property types most likely to affect each other.

Generic patterns in the evolution of urban water networks: Evidence from a large Asian city

We examine high-resolution urban infrastructure data using every pipe for the water distribution network (WDN) and sanitary sewer network (SSN) in a large Asian city (≈4 million residents) to explore the structure as well as the spatial and temporal evolution of these infrastructure networks. Network data were spatially disaggregated into multiple subnets to examine intracity topological differences for functional zones of the WDN and SSN, and time-stamped SSN data were examined to understand network evolution over several decades as the city expanded. Graphs were generated using a dual-mapping technique (Hierarchical Intersection Continuity Negotiation), which emphasizes the functional attributes of these networks. Network graphs for WDNs and SSNs are characterized by several network topological metrics, and a double Pareto (power-law) model approximates the node-degree distributions of both water infrastructure networks (WDN and SSN), across spatial and hierarchical scales relevant to urban settings, and throughout their temporal evolution over several decades. These results indicate that generic mechanisms govern the networks' evolution, similar to those of scale-free networks found in nature. Deviations from the general topological patterns are indicative of (1) incomplete establishment of network hierarchies and functional network evolution, (2) capacity for growth (expansion) or densification (e.g., in-fill), and (3) likely network vulnerabilities. We discuss the implications of our findings for the (re-)design of urban infrastructure networks to enhance their resilience to external and internal threats.

Population-Area Relationship for Medieval European Cities

Medieval European urbanization presents a line of continuity between earlier cities and modern European urban systems. Yet, many of the spatial, political and economic features of medieval European cities were particular to the Middle Ages, and subsequently changed over the Early Modern Period and Industrial Revolution. There is a long tradition of demographic studies estimating the population sizes of medieval European cities, and comparative analyses of these data have shed much light on the long-term evolution of urban systems. However, the next step-to systematically relate the population size of these cities to their spatial and socioeconomic characteristics-has seldom been taken. This raises a series of interesting questions, as both modern and ancient cities have been observed to obey area-population relationships predicted by settlement scaling theory. To address these questions, we analyze a new dataset for the settled area and population of 173 European cities from the early fourteenth century to determine the relationship between population and settled area. To interpret this data, we develop two related models that lead to differing predictions regarding the quantitative form of the population-area relationship, depending on the level of social mixing present in these cities. Our empirical estimates of model parameters show a strong densification of cities with city population size, consistent with patterns in contemporary cities. Although social life in medieval Europe was orchestrated by hierarchical institutions (e.g., guilds, church, municipal organizations), our results show no statistically significant influence of these institutions on agglomeration effects. The similarities between the empirical patterns of settlement relating area to population observed here support the hypothesis that cities throughout history share common principles of organization that self-consistently relate their socioeconomic networks to structured urban spaces.

Rural to Urban Population Density Scaling of Crime and Property Transactions in English and Welsh Parliamentary Constituencies

Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, finding that scaling models based on population density provided a far superior framework to traditional population scaling. We found four types of scaling: i) non-urban scaling in which a single power law explained the relationship between the metrics and population density from the most rural to heavily urban environments, ii) accelerated scaling in which high population density was associated with an increase in the power-law exponent, iii) inhibited scaling where the urban environment resulted in a reduction in the power-law exponent but remained positive, and iv) collapsed scaling where transition to the high density environment resulted in a negative scaling exponent. Urban scaling transitions, when observed, took place universally between 10 and 70 people per hectare. This study significantly refines our understanding of urban scaling, making clear that some of what has been previously ascribed to urban environments may simply be the high density portion of non-urban scaling. It also makes clear that some metrics undergo specific transitions in urban environments and these transitions can include negative scaling exponents indicative of collapse. This study gives promise of far more sophisticated scale adjusted metrics and indicates that studies of urban scaling represent a high density subsection of overall scaling relationships which continue into rural environments.

Urban Scaling of Cities in the Netherlands

We investigated the socioeconomic scaling behavior of all cities with more than 50,000 inhabitants in the Netherlands and found significant superlinear scaling of the gross urban product with population size. Of these cities, 22 major cities have urban agglomerations and urban areas defined by the Netherlands Central Bureau of Statistics. For these major cities we investigated the superlinear scaling for three separate modalities: the cities defined as municipalities, their urban agglomerations and their urban areas. We find superlinearity with power-law exponents of around 1.15. But remarkably, both types of agglomerations underperform if we compare for the same size of population an agglomeration with a city as a municipality. In other words, an urban system as one formal municipality performs better as compared to an urban agglomeration with the same population size. This effect is larger for the second type of agglomerations, the urban areas. We think this finding has important implications for urban policy, in particular municipal reorganizations. A residual analysis suggests that cities with a municipal reorganization recently and in the past decades have a higher probability to perform better than cities without municipal restructuring.

The Non-linear Health Consequences of Living in Larger Cities

Urbanization promotes economy, mobility, access, and availability of resources, but on the other hand, generates higher levels of pollution, violence, crime, and mental distress. The health consequences of the agglomeration of people living close together are not fully understood. Particularly, it remains unclear how variations in the population size across cities impact the health of the population. We analyze the deviations from linearity of the scaling of several health-related quantities, such as the incidence and mortality of diseases, external causes of death, wellbeing, and health care availability, in respect to the population size of cities in Brazil, Sweden, and the USA. We find that deaths by non-communicable diseases tend to be relatively less common in larger cities, whereas the per capita incidence of infectious diseases is relatively larger for increasing population size. Healthier lifestyle and availability of medical support are disproportionally higher in larger cities. The results are connected with the optimization of human and physical resources and with the non-linear effects of social networks in larger populations. An urban advantage in terms of health is not evident, and using rates as indicators to compare cities with different population sizes may be insufficient.

Scale-Adjusted Metrics for Predicting the Evolution of Urban Indicators and Quantifying the Performance of Cities

More than a half of world population is now living in cities and this number is expected to be two-thirds by 2050. Fostered by the relevancy of a scientific characterization of cities and for the availability of an unprecedented amount of data, academics have recently immersed in this topic and one of the most striking and universal finding was the discovery of robust allometric scaling laws between several urban indicators and the population size. Despite that, most governmental reports and several academic works still ignore these nonlinearities by often analyzing the raw or the per capita value of urban indicators, a practice that actually makes the urban metrics biased towards small or large cities depending on whether we have super or sublinear allometries. By following the ideas of Bettencourt et al. [PLoS ONE 5 (2010) e13541], we account for this bias by evaluating the difference between the actual value of an urban indicator and the value expected by the allometry with the population size. We show that this scale-adjusted metric provides a more appropriate/informative summary of the evolution of urban indicators and reveals patterns that do not appear in the evolution of per capita values of indicators obtained from Brazilian cities. We also show that these scale-adjusted metrics are strongly correlated with their past values by a linear correspondence and that they also display crosscorrelations among themselves. Simple linear models account for 31%-97% of the observed variance in data and correctly reproduce the average of the scale-adjusted metric when grouping the cities in above and below the allometric laws. We further employ these models to forecast future values of urban indicators and, by visualizing the predicted changes, we verify the emergence of spatial clusters characterized by regions of the Brazilian territory where we expect an increase or a decrease in the values of urban indicators.

The Influence of Drivers and Barriers on Urban Adaptation and Mitigation Plans-An Empirical Analysis of European Cities

Cities are recognised as key players in global adaptation and mitigation efforts because the majority of people live in cities. However, in Europe, which is highly urbanized and one of the most advanced regions in terms of environmental policies, there is considerable diversity in the regional distribution, ambition and scope of climate change responses. This paper explores potential factors contributing to such diversity in 200 large and medium-sized cities across 11 European countries. We statistically investigate institutional, socio-economic, environmental and vulnerability characteristics of cities as potential drivers of or barriers to the development of urban climate change plans. Our results show that factors such as membership of climate networks, population size, GDP per capita and adaptive capacity act as drivers of mitigation and adaptation plans. By contrast, factors such as the unemployment rate, warmer summers, proximity to the coast and projected exposure to future climate impacts act as barriers. We see that, overall, it is predominantly large and prosperous cities that engage in climate planning, while vulnerable cities and those at risk of severe climate impacts in the future are less active. Our analysis suggests that climate change planning in European cities is not proactive, i.e. not significantly influenced by anticipated future impacts. Instead, we found that the current adaptive capacity of a city significantly relates to climate planning. Along with the need to further explore these relations, we see a need for more economic and institutional support for smaller and less resourceful cities and those at high risk from climate change impacts in the future.

Settlement scaling and increasing returns in an ancient society

A key property of modern cities is increasing returns to scale-the finding that many socioeconomic outputs increase more rapidly than their population size. Recent theoretical work proposes that this phenomenon is the result of general network effects typical of human social networks embedded in space and, thus, is not necessarily limited to modern settlements. We examine the extent to which increasing returns are apparent in archaeological settlement data from the pre-Hispanic Basin of Mexico. We review previous work on the quantitative relationship between population size and average settled area in this society and then present a general analysis of their patterns of monument construction and house sizes. Estimated scaling parameter values and residual statistics support the hypothesis that increasing returns to scale characterized various forms of socioeconomic production available in the archaeological record and are found to be consistent with key expectations from settlement scaling theory. As a consequence, these results provide evidence that the essential processes that lead to increasing returns in contemporary cities may have characterized human settlements throughout history, and demonstrate that increasing returns do not require modern forms of political or economic organization.

Superlinear and sublinear urban scaling in geographical networks modeling cities

Using a geographical scale-free network to describe relations between people in a city, we explain both superlinear and sublinear allometric scaling of urban indicators that quantify activities or performances of the city. The urban indicator Y(N) of a city with the population size N is analytically calculated by summing up all individual activities produced by person-to-person relationships. Our results show that the urban indicator scales superlinearly with the population, namely, Y(N)∝N(β) with β>1, if Y(N) represents a creative productivity and the indicator scales sublinearly (β<1) if Y(N) is related to the degree of infrastructure development. These results coincide with allometric scaling observed in real-world urban indicators. We also show how the scaling exponent β depends on the strength of the geographical constraint in the network formation.