  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.
