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The Origins of Scaling in Cities

Cities are perhaps the ultimate expression of human sociality displaying at once humanity’s greatest achievements and some of its most difficult challenges. Despite the increasing importance of cities in human societies our ability to understand them scientifically, and manage them in practice, has remained unsatisfactorily limited. The greatest difficulties to any scientific approach to cities have resulted from their many interdependent facets, as social, economic, infrastructural and spatial complex systems, which exist in similar but changing forms over a huge range of scales. Here, I show how cities may evolve following a small set of basic principles that operate locally and can explain how cities change gradually from the bottom-up. As a result I obtain a theoretical framework that derives the general open-ended properties of cities through the optimization of a set of local conditions. This framework is used to predict, in a unified and quantitative way, the average social, spatial and infrastructural properties of cities as a set of scaling relations that apply to all urban systems, many of which have been observed in nations around the world. Finally, I compare and contrast the structure and dynamics of cities to those of other complex systems that share some analogous properties.

 

The Origins of Scaling in Cities
Lúis M. A. Bettencourt

SFI-WP 12-09-014

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Keystones in a Tangled Bank

In the past decade, ecologists have increasingly applied complex network theory (1, 2) to ecological interactions, both in entire food webs (3) and in networks representing ecological interactions, especially those between plants and their animal pollinators or seed dispersers (4). How important are individual species to the maintenance of such ecological networks? On page 1489 of this issue, Stouffer et al. (5) analyze terrestrial, freshwater, and marine food webs to infer the contributions of individual species to network stability. In a related field study on page 1486 of this issue, Aizen et al. (6) explore plant and pollinator webs on a landscape scale. Using a different field study design, Pocock et al. (7) recently focused on a local community in which several webs of different kinds of interactions and organisms form a composite network.

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Evolutionary Conservation of Species’ Roles in Food Webs

Studies of ecological networks (the web of interactions between species in a community) demonstrate an intricate link between a community’s structure and its long-term viability. It remains unclear, however, how much a community’s persistence depends on the identities of the species present, or how much the role played by each species varies as a function of the community in which it is found. We measured species’ roles by studying how species are embedded within the overall network and the subsequent dynamic implications. Using data from 32 empirical food webs, we find that species’ roles and dynamic importance are inherent species attributes and can be extrapolated across communities on the basis of taxonomic classification alone. Our results illustrate the variability of roles across species and communities and the relative importance of distinct species groups when attempting to conserve ecological communities.

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