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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., Competing Interests: The authors have declared that no competing interests exist.

Urban areas consume more than 66% of the world's energy and generate more than 70% of global greenhouse gas emissions. With the world's population expected to reach 10 billion by 2100, nearly 90% of whom will live in urban areas, a critical question for planetary sustainability is how the size of cities affects energy use and carbon dioxide (CO2) emissions. Are larger cities more energy and emissions efficient than smaller ones? Do larger cities exhibit gains from economies of scale with regard to emissions? Here we examine the relationship between city size and CO2 emissions for U.S. metropolitan areas using a production accounting allocation of emissions. We find that for the time period of 1999-2008, CO2 emissions scale proportionally with urban population size. Contrary to theoretical expectations, larger cities are not more emissions efficient than smaller ones.

The factors that account for the differences in the economic productivity of urban areas have remained difficult to measure and identify unambiguously. Here we show that a microscopic derivation of urban scaling relations for economic quantities vs. population, obtained from the consideration of social and infrastructural properties common to all cities, implies an effective model of economic output in the form of a Cobb-Douglas type production function. As a result we derive a new expression for the Total Factor Productivity (TFP) of urban areas, which is the standard measure of economic productivity per unit of aggregate production factors (labor and capital). Using these results we empirically demonstrate that there is a systematic dependence of urban productivity on city population size, resulting from the mismatch between the size dependence of wages and labor, so that in contemporary US cities productivity increases by about 11% with each doubling of their population. Moreover, deviations from the average scale dependence of economic output, capturing the effect of local factors, including history and other local contingencies, also manifest surprising regularities. Although, productivity is maximized by the combination of high wages and low labor input, high productivity cities show invariably high wages and high levels of employment relative to their size expectation. Conversely, low productivity cities show both low wages and employment. These results shed new light on the microscopic processes that underlie urban economic productivity, explain the emergence of effective aggregate urban economic output models in terms of labor and capital inputs and may inform the development of economic theory related to growth.

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.

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, beta, that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have beta approximately 1.2 >1 (increasing returns), whereas those accounting for infrastructure display beta approximately 0.8 <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 beta<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.

We propose a dedicated research effort on the determinants of settlement persistence in the ancient world, with the potential to significantly advance the scientific understanding of urban sustainability today. Settlements (cities, towns, villages) are locations with two key attributes: They frame human interactions and activities in space, and they are where people dwell or live. Sustainability, in this case, focuses on the capacity of structures and functions of a settlement system (geography, demography, institutions) to provide for continuity of safe habitation. The 7,000-y-old experience of urbanism, as revealed by archaeology and history, includes many instances of settlements and settlement systems enduring, adapting to, or generating environmental, institutional, and technological changes. The field of urban sustainability lacks a firm scientific foundation for understanding the long dure' e, relying instead on narratives of collapse informed by limited case studies. We argue for the development of a new interdisciplinary research effort to establish scientific understanding of settlement and settlement system persistence. Such an effort would build upon the many fields that study human settlements to develop new theories and databases from the extensive documentation of ancient and premodern urban systems. A scientific foundation will generate novel insights to advance the field of urban sustainability. [ABSTRACT FROM AUTHOR]

The peoples of southern Mesoamerica, including the Classic period Maya, are often claimed to exhibit a distinct type of spatial organization relative to contemporary urban systems. Here, we use the settlement scaling framework and properties of settlements recorded in systematic, full-coverage surveys to examine ways in which southern Mesoamerican settlement systems were both similar to and different from contemporary systems. We find that the population-area relationship in these settlements differs greatly from that reported for other agrarian settlement systems, but that more typical patterns emerge when one considers a site epicenter as the relevant social interaction area, and the population administered from a given center as the relevant interacting population. Our results imply that southern Mesoamerican populations mixed socially at a slower temporal rhythm than is typical of contemporary systems. Residential locations reflected the need to balance energetic and transport costs of farming with lower-frequency costs of commuting to central places. Nevertheless, increasing returns in activities such as civic construction were still realized through lower-frequency social mixing. These findings suggest that the primary difference between low-density urbanism and contemporary urban systems lies in the spatial and temporal rhythms of social mixing. [ABSTRACT FROM AUTHOR]