A city, just like a person, grows and changes over time. Yet unlike, say, your closest friend, its evolution is subject to millions of independent decisions made by those who dwell within the urban frontier. A new study from a group of environmental scientists suggests the demographic changes taking place in cities depend on two important forces: memory of the recent past and the influence of other nearby cities. After comparing Spanish and American cities, the researchers discovered cities in Spain have both shorter memories and smaller spheres of influence.

“A countless number of degrees of freedom is involved in a city’s evolution, that is, a host of individual contributions, involving millions of people acting on their own free will,” note the researchers, who hail from universities in Spain, Switzerland, and Argentina, in their published research. “Devising a unified theory constitutes a formidable challenge.”

Currently, slightly more than half of the earth’s population lives in urban areas, according to the United Nations, yet this is forecast to increase to 66 percent by 2050. Understanding the economic and ecologic sustainability of such a rapid growth rate is important and justifies the development of “quantitative unified theories of urban living,” according to the authors of the current study. And so they have developed a series of algorithms to analyze demographic patterns in order to assess the “collective coherence” of an environment… and predict its future.

Spanish and American Cities Under the Lens

The researchers have applied their algorithms to cities in Spain and the United States. They used demographic data from the Spanish National Institute for Statistics (INE) for the period 1900-2011, and from the U.S. Census Office between 1830 and the year 2000. Their results show that Spanish cities demonstrate a 15-year-old memory and interact with other cities within a span of 80 km (about 50 miles), while the corresponding figures for American cities are 25 years and 200 km (about 125 miles).

What a "15-year-old memory" would mean is this: The number of people who move to another city in one year is directly related to the number of people who did so the previous year. However, this correlation tails off as time goes by — specifically, after 15 years the correlation drops to half. (The memory number, then, represents a sort of "half-life.")

"This implies that a decision as personal as whether to move house or emigrate also depends on how many people did the same the year before independently, people that in reality you have never even met!" said Dr. Alberto Hernando, of the Lausanne Federal Institute of Technology and lead author of the study.

The "memories" of separate cities, according to the algorithms, also take into account events such as wars or economic recessions/depressions, which can generate "post-traumatic amnesia" that remains etched on its population. The point is that within a city economic downturns do not only impact individual people who may be directly harmed by a crisis, but they impact the collective behavior of society as well.

The study also suggests an individual city's growth is determined by how its neighbors develop, with a different "sphere of influence" for each country. Like people, cities are part of a social network with their futures linked to those who surround them.

While the authors say their empirical findings are relevant to understanding a country "at a collective macroscopic level," they also believe their study is simply a start and much more extensive research is needed to reach a final formula determining how cities evolve. Ultimately, the researchers conclude there’s a “more coherent evolution in U.S. cities” compared to Spain.

Source: Hernando A, Hernando R, Plastino A, Zambrano E. Memory-endowed US cities and their demographic interactions. J.R. Soc. Interface. 2015.