A universal model for mobility and migration patterns

Introduced in its contemporary form by George Kingsley Zipf in 1946, but with roots that go back to the work of Gaspard Monge in the 18th century, the gravity law is the prevailing framework to predict population movement, cargo shipping volume, 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 phenomena affected by mobility and transport processes.

💡 Research Summary

The paper critically examines the long‑standing gravity model of human mobility, which predicts the flow Tᵢⱼ between two locations i and j as a product of source and destination populations raised to adjustable exponents and a distance‑decay function f(rᵢⱼ). The authors enumerate six fundamental shortcomings of this approach: (i) lack of a rigorous derivation, (ii) reliance on up to nine tunable parameters, (iii) inability to predict flows where prior traffic data are missing, (iv) systematic empirical mismatches (e.g., two US counties with similar populations and distances exhibit an order‑of‑magnitude difference in commuting), (v) the unphysical divergence of flows as destination population grows, and (vi) deterministic nature that cannot capture stochastic fluctuations.

To overcome these issues, the authors propose a stochastic, first‑principles “radiation model”. The model is built on two intuitive steps reflecting job‑search behavior: (1) each region with population n generates n / n_jobs job opportunities, each assigned a random benefit z drawn from a distribution p(z); (2) an individual selects the closest job whose benefit exceeds the best offer in the home region, thereby prioritizing proximity over higher wages. By applying this decision rule to all individuals proportionally to local population, the model yields an analytical expression for the average commuting flux:

 Tᵢⱼ = Tᵢ · mᵢ nⱼ /