Discovering the laws of urbanisation

In 2012 the world's population exceeded 7 billion, and since 2008 the number of individuals living in urban areas has surpassed that of rural areas. This is the result of an overall increase of life expectancy in many countries that has caused an unprecedented growth of the world's total population during recent decades, combined with a net migration flow from rural villages to urban agglomerations. While it is clear that the rate of natural increase and migration flows are the driving forces shaping the spatial distribution of population, a general consensus on the mechanisms that characterise the urbanisation process is still lacking. Here we present two fundamental laws of urbanisation that are quantitatively supported by empirical evidence: 1) the number of cities in a country is proportional to the country's total population, irrespective of the country's area, and 2) the average distance between cities scales as the inverse of the square root of the country's population density. We study the spatio-temporal evolution of population considering two classes of models, Gravity and Intervening Opportunities, to estimate migration flows and show that they produce different spatial patterns of cities.