Extended Data Fig. 3: Density function of the out-of-system growth rate.

Natural growth and out-of-system migrations include international migrations and exchanges with small towns. The data shown are for US cities in 2013–2017 (top) and French cities (bottom) in 2003–2008, compared to a normal distribution. We note that a power-law fit of the right or the left tail would lead to a Pareto exponent of β ≫ 1. For French cities, we extrapolated the 2003 population in each city from the 1999 and 2006 censuses to test our assumption on the period 2003–2008.