Evolutionary Model of the City Size Distribution

Joachim Kaldasch

doi:10.1155/2014/498125

Abstract

An evolutionary model of the city size distribution is presented that explains the size of a city from the reproduction process and the migration of humans between cities. The model suggests that the city size distribution is a lognormal distribution with a power law tail in agreement with empirical results and computer simulations. The main idea of the model is that the competition between cities in the migration process is the origin of Gibrat's law. While growth rate fluctuations generate the lognormal branch of the size distribution, the power law tail for large cities is caused by a small mean growth rate.

Highlights

The paper aims at deriving the size distribution of cities from the idea that the evolution of a city is a self-organized process
An evolutionary model of the city size distribution is presented that explains the size of a city from the reproduction process and the migration of humans between cities
The model suggests that the city size distribution is a lognormal distribution with a power law tail in agreement with empirical results and computer simulations

Summary

Introduction

The paper aims at deriving the size distribution of cities from the idea that the evolution of a city is a self-organized process. The presented evolutionary theory goes beyond previous research by deriving Gibrat’s law from the main two processes governing the population size of a city: the reproduction of humans and their migration between cities. The dynamics of self-organized systems is governed by positive feedback processes [26, 27] Both the reproduction of humans and their migration are self-amplifying processes, while the migration flow is shown to be the result of an evolutionary competition between cities. A model of the self-organized evolution of cities is established . It allows the derivation of the empirically found city size distribution. The relation of the model to Zipf ’s law is discussed in the conclusion

The Model

Conclusion

Replacement Process

Power Law Distribution of the City Size

Zipf’s Law