By: Dyrol Lumbard, Mathematical Institute, University of Oxford
How are people, infrastructure and economic activity organised and interrelated? It is an intractable problem with ever-changing infinite factors of history, geography, economy and culture. But a paper by Oxford Mathematician Hyejin Youn and colleagues suggests “a mathematical function common to all cities.”
Think of the city as an ecosystem, types of businesses as species interacting in that system. Ecosystems in the natural world often share common patterns in distributions of species. That got the researchers thinking. Maybe the same consistency arises in the city too. Only instead of the food web, it’s people and money and businesses that require one another. We usually think of cities as unique. London is very different from Moscow. But, it turns out, what governs the distribution of their resources stays the same across the board.
The team analysed more than 32 million establishments in U.S. metro regions. An establishment, the unit of analysis of their study, indicates “a single physical location where business is conducted”. When the team measured relative sizes of business types (e.g. agriculture, finance, and manufacturing) in each and every city, and compared these distributions among cities, the universal law is found: despite widely different mixes of types of businesses and across different-sized cities, the shape of these distributions was completely universal. Cities have their own underlying dynamics. It doesn’t matter where they are, how old they are and who is in charge.
This underlying pattern allowed researchers to build a stochastic model. As cities grow, the total number of establishments is linearly proportional to its population size (more people, more businesses). When an establishment is created it differentiates from any existing types with a probability which determines how diversified a city is given its size. This probability turns out to be inversely proportional to city size: the more businesses, the harder it is to differentiate them from existing businesses. This process, with further research, displays an open-ended, never-ending, albeit slowing, diversification of businesses in a statistically predictable way, constituting a human eco-system.
This article was first published on the website of the Mathematical Institute, University of Oxford, on 22 February 2016.