Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society's predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, ␤, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have ␤ Ϸ1.2 >1 (increasing returns), whereas those accounting for infrastructure display ␤ Ϸ0.8 <1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which ␤<1. Finally, we explore possible consequences of these scaling relations by deriving growth equations, which quantify the dramatic difference between growth fueled by innovation versus that driven by economies of scale. This difference suggests that, as population grows, major innovation cycles must be generated at a continually accelerating rate to sustain growth and avoid stagnation or collapse. population ͉ sustainability ͉ urban studies ͉ increasing returns ͉ economics of scale H umanity has just crossed a major landmark in its history with the majority of people now living in cities (1, 2). The present worldwide trend toward urbanization is intimately related to economic development and to profound changes in social organization, land use, and patterns of human behavior (1, 2). The demographic scale of these changes is unprecedented (2, 3) and will lead to important but as of yet poorly understood impacts on the global environment. In 2000, Ͼ70% of the population in developed countries lived in cities compared with Ϸ40% in developing countries. Cities occupied a mere 0.3% of the total land area but Ϸ3% of arable land. By 2030, the urban population of developing countries is expected to more than double to Ϸ4 billion, with an estimated 3-fold increase in occupancy of land area (3), whereas in developed countries it may still increase by as much as 20%. Paralleling this global urban expansion, there is the necessity for a sustainability transition (4-6) toward a stable total human population, together with a rise in living standards and the establishment of long-term balances between human development needs and the planet's environmental limits (7). Thus, a major challenge worldwide (5, 6) is to un...

With urban population increasing dramatically worldwide, cities are playing an increasingly critical role in human societies and the sustainability of the planet. An obstacle to effective policy is the lack of meaningful urban metrics based on a quantitative understanding of cities. Typically, linear per capita indicators are used to characterize and rank cities. However, these implicitly ignore the fundamental role of nonlinear agglomeration integral to the life history of cities. As such, per capita indicators conflate general nonlinear effects, common to all cities, with local dynamics, specific to each city, failing to provide direct measures of the impact of local events and policy. Agglomeration nonlinearities are explicitly manifested by the superlinear power law scaling of most urban socioeconomic indicators with population size, all with similar exponents (1.15). As a result larger cities are disproportionally the centers of innovation, wealth and crime, all to approximately the same degree. We use these general urban laws to develop new urban metrics that disentangle dynamics at different scales and provide true measures of local urban performance. New rankings of cities and a novel and simpler perspective on urban systems emerge. We find that local urban dynamics display long-term memory, so cities under or outperforming their size expectation maintain such (dis)advantage for decades. Spatiotemporal correlation analyses reveal a novel functional taxonomy of U.S. metropolitan areas that is generally not organized geographically but based instead on common local economic models, innovation strategies and patterns of crime.

Much research has suggested that night-time light (NTL) can be used as a proxy for a number of variables, including urbanization, density, and economic growth. As governments around the world either collect census data infrequently or are scaling back the amount of detail collected, alternate sources of population and economic information like NTL are being considered. But, just how close is the statistical relationship between NTL and economic activity at a fine-grained geographical level? This paper uses a combination of correlation analysis and geographically weighted regressions in order to examine if light can function as a proxy for economic activities at a finer level. We use a fine-grained geo-coded residential and industrial full sample micro-data set for Sweden, and match it with both radiance and saturated light emissions. We find that the correlation between NTL and economic activity is strong enough to make it a relatively good proxy for population and establishment density, but the correlation is weaker in relation to wages. In general, we find a stronger relation between light and density values, than with light and total values. We also find a closer connection between radiance light and economic activity, than with saturated light. Further, we find the link between light and economic activity, especially estimated by wages, to be slightly overestimated in large urban areas and underestimated in rural areas.

Over the last few decades, in disciplines as diverse as economics, geography and complex systems, a perspective has arisen proposing that many properties of cities are quantitatively predictable due to agglomeration or scaling effects. Using new harmonized definitions for functional urban areas, we examine to what extent these ideas apply to European cities. We show that while most large urban systems in Western Europe (France, Germany, Italy, Spain, UK) approximately agree with theoretical expectations, the small number of cities in each nation and their natural variability preclude drawing strong conclusions. We demonstrate how this problem can be overcome so that cities from different urban systems can be pooled together to construct larger datasets. This leads to a simple statistical procedure to identify urban scaling relations, which then clearly emerge as a property of European cities. We compare the predictions of urban scaling to Zipf's law for the size distribution of cities and show that while the former holds well the latter is a poor descriptor of European cities. We conclude with scenarios for the size and properties of future pan-European megacities and their implications for the economic productivity, technological sophistication and regional inequalities of an integrated European urban system.

Invention has been commonly conceptualized as a search over a space of combinatorial possibilities. Despite the existence of a rich literature, spanning a variety of disciplines, elaborating on the recombinant nature of invention, we lack a formal and quantitative characterization of the combinatorial process underpinning inventive activity. Here, we use US patent records dating from 1790 to 2010 to formally characterize invention as a combinatorial process. To do this, we treat patented inventions as carriers of technologies and avail ourselves of the elaborate system of technology codes used by the United States Patent and Trademark Office to classify the technologies responsible for an invention's novelty. We find that the combinatorial inventive process exhibits an invariant rate of ‘exploitation’ (refinements of existing combinations of technologies) and ‘exploration’ (the development of new technological combinations). This combinatorial dynamic contrasts sharply with the creation of new technological capabilities—the building blocks to be combined—that has significantly slowed down. We also find that, notwithstanding the very reduced rate at which new technologies are introduced, the generation of novel technological combinations engenders a practically infinite space of technological configurations.

Rapid advances in artificial intelligence (AI) and automation technologies have the potential to significantly disrupt labor markets. While AI and automation can augment the productivity of some workers, they can replace the work done by others and will likely transform almost all occupations at least to some degree. Rising automation is happening in a period of growing economic inequality, raising fears of mass technological unemployment and a renewed call for policy efforts to address the consequences of technological change. In this paper we discuss the barriers that inhibit scientists from measuring the effects of AI and automation on the future of work. These barriers include the lack of high-quality data about the nature of work (e.g., the dynamic requirements of occupations), lack of empirically informed models of key microlevel processes (e.g., skill substitution and human–machine complementarity), and insufficient understanding of how cognitive technologies interact with broader economic dynamics and institutional mechanisms (e.g., urban migration and international trade policy). Overcoming these barriers requires improvements in the longitudinal and spatial resolution of data, as well as refinements to data on workplace skills. These improvements will enable multidisciplinary research to quantitatively monitor and predict the complex evolution of work in tandem with technological progress. Finally, given the fundamental uncertainty in predicting technological change, we recommend developing a decision framework that focuses on resilience to unexpected scenarios in addition to general equilibrium behavior.

Understanding cities is central to addressing major global challenges from climate change to economic resilience. Although increasingly perceived as fundamental socio-economic units, the detailed fabric of urban economic activities is only recently accessible to comprehensive analyses with the availability of large datasets. Here, we study abundances of business categories across US metropolitan statistical areas, and provide a framework for measuring the intrinsic diversity of economic activities that transcends scales of the classification scheme. A universal structure common to all cities is revealed, manifesting self-similarity in internal economic structure as well as aggregated metrics (GDP, patents, crime). We present a simple mathematical derivation of the universality, and provide a model, together with its economic implications of open-ended diversity created by urbanization, for understanding the observed empirical distribution. Given the universal distribution, scaling analyses for individual business categories enable us to determine their relative abundances as a function of city size. These results shed light on the processes of economic differentiation with scale, suggesting a general structure for the growth of national economies as integrated urban systems.

No abstract