Water Week

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Analysis of “metabolism” of cities shows big cities just get richer; rich cities get bigger; and superlinear boom followed by a bust

Posted by waterweek on 26 September 2007

With help from their collaborators at Arizona State University, Tempe, and Dresden University of Technology in Germany, West and Bettencourt tracked down all sorts of information about the “metabolism” of cities, including the number of gasoline stations and laundries, electrical power usage and the total wages earned. Their database, assembled with the aid of the internet from hundreds of cities across the US, Europe and China, is the first important outcome of the project. It was reported in Proceedings of the National Academy Of Sciences, vol104, P 7301

Team plotted each variable:“The type of data they obtained would not have been possible to get 20 years ago,” says Sidney Redner, a physicist from Boston University who has written on migration to and from cities. The team plotted each variable versus city population and looked for an overarching pattern. “When I started, I thought everything would be like biology,” says West.

What if – cities followed biological laws:If cities followed biological laws, he reasoned, their metabolism per capita ought to slow down as they get bigger, and the scaling should follow a power law. “Had we seen quarter powers, we would have said, ‘Fantastic! Cities are just big biological organisms’,” West says. “But it just wasn’t true.” Instead, they found that the variables fell into two distinct groups .

• Quantities related to a city’s infrastructure, such as the number of gas stations and the length of paved roads, did scale “sublinearly”, meaning that the larger the city, the less of these were required per capita; but

• measures of economic output and innovation – the number of patents, total wages, GDP, even the pace of walking – scaled “superlinearly”, showing increasing returns with size.

Growth may accelerate out of control: “The scaling laws say that on average as a city grows you can predict its output and input, its energy consumption, its wealth creation, its level of crime,” says Bettencourt. The results suggest that bigger cities have a faster pace of life, fuelled by wealth and new ideas. It’s a phenomenon that has no biological counterpart, says West, but it fits with the common perception of the big city.

No no maximum per capita income: What’s more, the consequences for growth over time are clear. While biological organisms have a built-in mechanism for keeping their size under control, cities may not, which means their growth can accelerate out of control. indeed, Bettencourt and West’s work strongly suggests that there is no maximum per capita income; big cities just get richer, and rich cities get bigger.

Major implications for urban sustainabilityThis has major implications for urban sustainability. The researchers have shown in their models…

• if sublinear growth dominates, a city’s population will gradually approach its optimum size and then stabilise; By contrast;

• a city growing superlinearly has no maximum size, so in theory its population can keep growing infinitely. Of course, no real city can sustain such growth, so any superlinear boom must be followed by a bust. New York is a perfect example. Throughout its history, West says, the city has experienced waves of accelerating growth:

• from 1800 to 1850, from 1860 to 1890, from 1900 to 1920, from 1930 to 1940 and from 1950 to 1960. (After 1960, the pattern was harder to discern.)

• Each boom was followed by a bust, and the cycles are getting shorter; in fact, they are getting too short for the decennial census to track.

Proceedings of the National Academy Of Sciences, vol104, P 7301 New Scientist, 26/5/2007, p.50


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