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Introduction to Urban Science Evidence and Theory of Cities as Complex Systems

Bettencourt, Luís M. A.
MIT Press: London, 2021
ISBN 9780262046008 (hb)
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Reviewed by Bernardo Alves Furtado
Institute for Applied Economic Research (Ipea)

Cover of book

With this book, Bettencourt promises to establish a theory of urban sciences. His goal is to understand the "fundamental processes at work" in cities (p.18). Moreover, he proposes to use this knowledge to generate "useful and falsifiable predictions" (p.28). Although this challenge may seem grand and unreachable from the first few pages of the reading, at the end, he delivers. Gathering models, findings, pieces of evidence from a wide range of disciplines, from paramount authors, and from the most varied empirical databases, he accumulates formulations and reasoning to build up a cohesive picture that stands on a sound mathematical support.

Bettencourt actually presents works from urban sociologists, historians and architects (Jacobs 1961; Lynch 1984; Mumford 1961), but also from a plethora of economic, geographic and spatial analysts, from Thünen (Thünen 1826), Christäller (Christaller 1826), Alonso (Alonso 1964) and the Muth-Mills synthesis (Brueckner 1987), to the core-periphery model (Fujita, Krugman & Venables 1999), or the diversity of urban systems (Black & Herderson 1999). These names (along with Glaser, Batty, Puga, Benenson, Wirth, or Pumain, to name a few of the references) are familiar for those into urban studies. The added-value comes from the detailed discussion provided by archaeologists, evolutionary biologists, demographers, anthropologists, and physicists. All contributions framed within great thinkers such as Alfred Marshall, Paul Samuelson, Herbert Simon, Paul Anderson, Durkheim or, Bettencourt's co-worker, Geoffrey West (and collaborators, especially, José Lobo (Lobo et al. 2020) and Deborah Strumsky (Bettencourt et al. 2007).

However, the book is not just talk and prose. It is woven with empirical evidence, as suggested by the subtitle: "Evidence and Theory of Cities as Complex Systems". The book examines old, very old, to recent and projected data, including general (like Our World in Data), selected (OECD), and national sources. It also brings census data from India, England, Scotland, and Wales, South Africa, Brazil, Mexico, and more.

All chapters contain reviewed models and ideas, evidence and theoretical advances. However, the heart of the proposed theory can be found in chapter 3: "Complex Networks and Urban Scaling". Before that, in chapters 1 and 2, Bettencourt explores the triumph of the cities (Glaeser 2012), as the necessary place where collective actions, such as Politics, occur. He argues that cities benefit from increasing returns due to interdependence and connectivity of its population, allowing them to produce "positive-sum gains" (Glaeser 2012) (p. 400). He also explains that in cities "the whole [actually] becomes not only more than but very different from the sum of its parts (Anderson 1972, p. 395)". Bettencourt therefore conceptualizes cities as "interdependent socioeconomic and spatial (infrastructural) networks that coevolve to support each other" (p. 70).

The evidence presented in chapter 3 (see the references in pp.79-80, Table 3.2) indicates that city populations have three scaling regimes. The structural and spatial needs (such as highways or metro lines, and sanitation networks) scale sublinearly, resulting in savings as city size increases. Social and informational features, on the other hand, benefit from network effects and scale superlinearly leading to more than doubling of specialization, diversity, and production when the city doubles its size. Unfortunately, the same applies for poverty, crime and violence. Basic needs of the population, such as housing or jobs, scale linearly.

Overall, Bettencourt develops his arguments through four consecutive parts to establish "a self-consistent spatial equilibrium between socioeconomic interactions and movement costs that derives quantitative predictions for urban scaling exponents and prefactors" (p. 85). He starts with a simple model to demonstrate the need to balance cost of movement across space and friction against the benefits of connectivity. The four principles that guides his reasoning involve (a) the role of urban areas as places for encounter and opportunities, (b) the incremental need for connections in urban networks (streets/highways) as the city grows, (c) the physical human constrains — the fact that time and mobility of individuals is finite and bounded —, and (d) the relevance of social interactions for socioeconomic output.

The construction of the equations that support the theory are derived from these principles as well as the definitions of some control parameters (D and Hm). Hm is a fractal dimension, with values ranging from 0 (representing a point) to 2, covering the full extent of a city (see also Figure 3.8, p. 90). D is the number of dimensions, with a value of 2 representing a plane. For simplicity, the prediction exponent parameters in the book are set to D=2 and Hm=1, although the generalization to other values is also present.

Urban scaling suggests that, on average, land area (A) of a city is proportional to its population with a prefactor (a) and an exponent (α), such that A=αNα. Bettencourt (p. 99) also provides the expected equation (and parameter estimates) for network volume (An=A0NN), with an estimate of N=5/6, for the special cases of D and Hm, network length, interactions per capita, social (economic) outputs, power dissipation; and land rents.

Chapter 4 illustrates and expands the findings through a series of examples of scaling, as well as when and why results deviate from the expected. Specifically, Section 4.2.2 (pp. 169ss) discusses population dynamics and emerging inequalities. The author brings selection effects from evolutionary theory to show that when group-level growth rates are higher than the rest within heterogeneous population, inequality at the city level rises. This sets the scenario for the neighborhood discussion of Chapter 6.

Chapter 5 explores the positive impacts of larger city size as places richer in diversity (and its measurement). The goal of the chapter is to understand the mechanisms that sustain this diversity. The debate includes background on the effects of culture (and subculture), specialization, and division of labor. A richer connected space—due to similar reasons—also generates higher congestion, pollution, and social challenges. Certainly, "[b]efore differences between individuals become 'useful', a certain amount of accident, unconventionality, and experimentation is certainly tolerated or even encouraged" (p. 222).

Chapter 6 focuses on the role of neighborhood effects and their relevance as places of opportunities within cities. Neighborhoods offer essential services, such as housing, sanitation, and healthcare, as well as jobs, education, social networking. The formation of neighborhoods results from a combination of choice (where you want to live) and necessity (where you can live) (Furtado 2009). This spatial selection creates both benefits and drawbacks. Bettencourt's proposal is to quantify the mechanisms behind this spatial selection. The neighborhood is the place where (essential, cohesive, communal) local information is available.

Chapter 7 examines ancient urban (and tribal) settlements to demonstrate the application of the theory. A threshold idea for urban settlements is also presented, based on ethnographic analysis and the concept of scalar stress (Johnson 2009). The pre-Hispanic civilizations are noted for developing urban systems that evolved independently from those in Europe and elsewhere.

Chapter 8 characterizes the open-endedness of cities as components of integrated urban systems. Bettencourt revisits demography and the "laws" of geography to demonstrate that cities are essentially part of a (national) system. They compose flows which are not necessarily symmetric, although dependent from one another. These asymmetries contain information that can be measured (Chapter 9). He also dwells on the dynamics of urban, rural, migration, and vital rates to reflect on the need of adjustments on the current scholarship.

In Chapter 9, Bettencourt investigates the relationship between information, its codification in institutions, and learning. He begins by revisiting models of endogenous growth and macroeconomics (Jones & Romer 2010). He then demonstrates the correlation between urbanization and economic growth. He uses the concept of fitness from evolutionary dynamics and the Price equation (Andersen 2004) to calculate the weights that break down the contributions of different individuals to growth. This enables him to describe the variation of economic output as a function of contributions from urban/rural migration, cities, firms, and individuals (equation 9.28, p. 381). Ultimately, the decision-making process of each individual is captured by the exact specification of their actions (wijlk), which are based on knowledge and information available within his or her local socioeconomic environment. In Section 9.3 (pp. 385ss) Bettencourt delves into the statistical mechanics of growth and information.

Chapter 9 is crucial to comprehending the concept of learning within city interactions. It encompasses both redundant and synergistic information. Redundancy occurs when multiple agents have access to non-exclusive information, like the tacit knowledge to operate a machine. On the other hand, synergy arises from complementary information that creates new possibilities when combined in an organized manner. The chapter also highlights the findings of Ostrom (2009), who outlines the conditions needed for the emergence of collective organization (and institutions).

Bettencourt emphasizes that the proposed theory is general and reflects average trends, rather than being specific to a single city. Policymakers looking for concrete solutions or step-by-step guides will be disappointed by this book. However, Bettencourt does provide insights into how individuals, firms and institutions can take action to drive development and address inequalities. Specifically by providing access to opportunities at the neighborhood level, promoting connectivity, reducing barriers to local information, and including diversity among households. The goal is to make information synergistic, rather than redundant.

Computational social scientists and urban researchers can leverage the insights from this book in a number of ways. Bettencourt's exploration of urban scaling as a predictive tool provides a theoretical foundation that can be used to structure the analysis of specific city and urban systems. The decomposition of the formulation to the level of individuals, households, and neighborhoods offers the application of the concept of human agency to agent-based modeling. This can serve as a basis of comparison across scales, allowing modelers to see if their behavioral processes average to the expected values. By providing both a theoretical foundation and the potential for data-driven validation, the book offers a dual engine for advancing our understanding of cities and urban systems.

In conclusion, "Introduction to Urban Science" is a comprehensive and insightful examination of the interplay between population and urban scaling, while showcasing early models across disciplines, traditions, and (guess?) scales. The book sheds light on the importance of processes (at the local level) in the formation and persistence of cities as open-ended systems with asymmetric flow. Bettencourt emphasizes the role of spatial sorting and selection in the creation of both innovation and inequalities. Inequalities that reside in people, but also in a relevant manner in neighborhoods. Overall, the book is definitely worth reading for anyone interested in gaining a deeper understanding of the complex dynamics of cities and their citizens.


ALONSO W. (1964). Location and Land Use: Toward a General Theory of Land Rent, Hamburg (New York): New Jersey: Prentice Hall.

ANDERSEN E. S. (2004). Population thinking, Price’s equation and the analysis of economic evolution, Evolutionary and Institutional Economics Review, 1, 127–148.

ANDERSON W. (1972). More Is Different, Science, 177, 393–396.

BETTENCOURT J., L. M.J. Lobo, and D. Strumsky (2007). Invention in the city: Increasing returns to patenting as a scaling function of metropolitan size, Research Policy, 36(1), 107–120.

BLACK M., and A. Henderson (1999). A theory of urban growth, Journal of Political Economy, 107(2), 252–284.

BRUECKNER W. (1987). 'The structure of urban equilibria: a unified treatment of the Muth-Mills model.' In Handbook of Regional and Urban Economics, Elsevier Science Publishers B.V.

CHRISTALLER W. (1966). Central Places in Southern Germany, Hamburg (New York): New Jersey: Prentice Hall.

FUJITA M. Krugman, and A. Venables (1999). The Spatial Economy: Cities, Regions and International Trade, Hamburg (New York): New Jersey: Prentice Hall.

FURTADO B. A. (2009). Modeling social heterogeneity, neighborhoods and local influences on urban real estate prices: spatial dynamic analyses in the Belo Horizonte metropolitan area, Brazil. Netherlands Geographical Studies ISSN 0169-4839, Utrecht, The Netherlands: Faculteit Geowetenschappen Universiteit Utrecht.

GLAESER E. L., L. M.J. Lobo, and D. Strumsky (2012). Triumph of the City: How Our Greatest Invention Makes Us Richer, Smarter, Greener, Healthier, and Happier. New York, NY: Penguin Books.

JACOBS J. (1961). The Death and Life of Great American Cities. Cities, 21(2), 13–25.

JOHNSON G. A., (1982). “Organizational structure and scalar stress, Theory and Explanation in Archaeology, 36(1), p. 389–421, Academic Press, 1982.

JONES C. I., and P. M. Romer (2010). The new Kaldor facts: ideas, institutions, population, and human capital, American Economic Journal: Macroeconomics, 2(1), 224–245.

LOBO J., L. M. Bettencourt, M. E. Smith, and S. Ortman (2020). Settlement scaling theory: Bridging the study of ancient and contemporary urban systems, Urban Studies, 57(4), 731–747.

LYNCH K. (1984). Good City Form, Cambridge, MA: The MIT press.

MUMFORD K. (1961). The City in History: Its Origins, Its Transformations, and Its Prospects, Houghton Mifflin Harcourt.

OSTROM E. (2004). A general framework for analyzing sustainability of social-ecological systems, Science, 325(5939), 419–422.

THUNEN J. H. v. (1966). Der Isolierte Staat, Hamburg (New York): Pergamon Press, 1826. 3.