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A New Law of Intercity Mobility

A group of network researchers proposes a "radiation model" of migration that more accurately predicts patterns of commuting, disease spread, and more.


The reigning model of intercity mobility, used to predict patterns of movement from commuting to the spread of infectious disease, is called the "gravity law." It was developed in the early 1940s by a Harvard lecturer named George Zipf and is, of course, based on Newton's law, which says gravitational force increases when the mass of two objects is great and the distance between them is minimal.

In that same spirit, Zipf's "gravity law" of mobility assumed that movement between two cities would be most frequent when their populations were large and their separation small. In reality, however, the "gravity law" doesn't do a great job estimating the intercity movement it was intended to predict. While Zipf's law frowns on the notion that people travel frequently between distant cities, recent research on so-called "super-commuters," outlined by our own Richard Florida, shows that a considerable subset of urban populations is actually willing to commute quite far.

The "gravity law" has several other limitations, most of which should be obvious to even the most dimwitted individual with an advanced dual degree in complex network mathematics and physics, and suffice it to say these setbacks have inspired other researchers to look for a better one. In a paper published online in the journal Nature in late February, an international group of researchers from Northeastern, M.I.T., and the University of Padua, in Italy, outline a model of mobility that performs better than the "gravity law" in head-to-head contests.

The "radiation model," as the new idea is called, makes several assumptions the gravity model does not. For starters, it downplays the distance between two cities and emphasizes not only the cities themselves but the density of the areas surrounding them. That enables the model to estimate the number of jobs in a region more accurately. It also accounts a bit more for actual human behavior: while the radiation model presumes that people choose a job based on a balance of proximity and benefits, it recognizes that they're willing to make long commutes if few jobs in their region satisfy their requirements.

As a result, the radiation model out-predicts the "gravity law" in direct competition. As an example, the researchers looked at mobility between two pairs of counties in Utah and Alabama. Both counties of origin had similar populations, as did both destination counties, and both pairs are more or less equidistant from one another. Actual Census data shows that 44 people make the commute in Utah, while six do in Alabama.

Since the pairs of counties are about the same size and distance apart, the "gravity law" treats them as equals. Sure enough, it predicts that only one commuter will make the trek in each place. The "radiation model," on the other hand, is able to take into account the fact that population density is very low in Utah compared to the national average, which means work opportunities close to home may be harder to come by. As a result it predicts a considerably more accurate 66 commuters in Utah and two in Alabama: 

Another example centers on trips made from New York. Once again the "gravity law" (middle panel, below) overestimates local movement and underestimates long- and even medium-distance movement. The "radiation model" (bottom panel) provides a "more realistic approximation to the observed commuting patterns" from the Census (top), the researchers demonstrate:

The researchers believe the increased accuracy of the radiation model will enhance all sorts of predictions about mobility. They conclude (citations removed for readability):

In summary, the superior performance of the radiation model can significantly improve the accuracy of predictive tools in all areas affected by mobility and transport processes, from epidemiology and spreading processes to urban geography and flow of resources in economics. The parameter-free modelling platform we introduced can predict commuting and transport patterns even in areas where such data are not collected systematically, as it relies only on population densities, which is relatively accurately estimated throughout the globe.

Top image credit: Andrew F. Kazmierski/

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