The dynamic of the geographical distribution of a population

Gustavo De Santis, University of Florence
Giambattista Salinari, University of Florence

The frequency distribution by population size of a set of geographical areas approaches a log-normal curve: we develop a theoretical framework to explain why this happens, and the reason is that a markovian process is in place. The population at time t+1 of each unit can be thought of as determined by the population of the same unit at time t plus a random component, distributed as a normal variable, whose parameters (mean and variance) depend on the population size of the unit at time t. In particular, the units with a larger starting population are characterized by a greater variance in their subsequent evolution. The model applies satisfactorily to the geographical distribution of virtually all European populations in several years, and using different units of analysis