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Researchers create first large-scale model of human mobility that incorporates human motive; population distribution rather than size

Researchers from MIT, Northeastern University and Italy’s University of Padua have identified an underlying flaw in the “gravity law”—a statistical formula used in modeling the movement of people and goods between cities, states or countries. The gravity law, which measures the “attraction” between two places, assumes that the number of trips between two cities is dependent on population size and the distance between the cities. However, the researchers found that distance between two cities is far less important than the population size in the area surrounding them.

The team has now created a model that takes human motives into account rather than simply assuming that a larger city attracts commuters. They then tested their “radiation model” on five types of mobility studies and compared the results to existing data. In each case, the radiation model’s predictions were far more accurate than the gravity model’s, which are sometimes off by an order of magnitude. A paper on their work is published in the journal Nature.

Introduced in its contemporary form in 1946, but with roots that go back to the eighteenth century, the gravity law is the prevailing framework with which to predict population movement, cargo shipping volume and inter-city phone calls, as well as bilateral trade flows between nations. Despite its widespread use, it relies on adjustable parameters that vary from region to region and suffers from known analytic inconsistencies. Here we introduce a stochastic process capturing local mobility decisions that helps us analytically derive commuting and mobility fluxes that require as input only information on the population distribution.

The resulting radiation model predicts mobility patterns in good agreement with mobility and transport patterns observed in a wide range of phenomena, from long-term migration patterns to communication volume between different regions. Given its parameter-free nature, the model can be applied in areas where we lack previous mobility measurements, significantly improving the predictive accuracy of most of the phenomena affected by mobility and transport processes.

—Simini et al.

The gravity law states that the number of people in a city who will commute to a larger city is based on the population of the larger city. (The larger the population of the big city, the more trips the model predicts.) The number of trips will decrease as the distance between cities grows. One obvious problem with this model is that it will predict trips to a large city without taking into account that the population size of the smaller city places a finite limit on how many people can possibly travel.

The new radiation model accounts for this and other limitations of the gravity model by focusing on the population of the surrounding area, which is defined by the circle whose center is the point of origin and whose radius is the distance to the point of attraction, usually a job. It assumes that job availability is proportional to the population size of the entire area and rates a potential job’s attractiveness based on population density and travel distance. (People are willing to accept longer commutes in sparsely populated areas that have fewer job opportunities.)

To demonstrate the radiation model’s accuracy in predicting the number of commuters, the researchers selected two pairs of counties in Utah and Alabama, each with a set of cities with comparable population sizes and distances between them. In this instance, the gravity model predicts that one person will commute between each set of cities. But according to census data, 44 people commuted in Utah and six in the sparsely populated area of Alabama. The radiation model predicts 66 commuters in Utah and two in Alabama, a result well within the acceptable limit of statistical error, González says.

The co-authors also tested the model on other indices of connectedness, including hourly trips measured by phone data, commuting between US counties, migration between US cities, intercity telephone calls made by 10 million anonymous users in a European country, and the shipment of goods by any mode of transportation among U.S. states and major metropolitan areas. In all cases, the model’s results matched existing data.

Resources

  • Filippo Simini, Marta C. González, Amos Maritan & Albert-László Barabási (2012) A universal model for mobility and migration patterns. Nature doi:10.1038/nature10856

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