The growth equation of cities

Area of Science:

• Urban Science
• Complex Systems Science
• Computational Social Science

Background:

• Understanding urban population evolution and hierarchy is crucial for urban studies.
• Zipf's law has been the dominant model for city size distribution, but recent studies question its universality.
• Existing models fail to adequately explain city population fluctuations and the rise and fall of urban systems.

Purpose of the Study:

• To introduce a novel stochastic equation for modeling city population growth.
• To analyze the impact of interurban migratory shocks on urban dynamics.
• To provide a more accurate model for city population distribution and hierarchy.

Main Methods:

• Empirical analysis of recent population datasets from Canada, France, the UK, and the USA.
• Development of a stochastic equation based on observed urban growth patterns.
• Testing the model's predictions against empirical data and established laws like Zipf's law.

Main Results:

• The model demonstrates that rare, large interurban migratory shocks significantly influence city population growth.
• The proposed equation predicts a complex, non-universal shape for city population distribution, indicating Zipf's law is not generally applicable.
• The model accurately predicts temporal variations in city hierarchy, aligning with empirical observations.

Conclusions:

• The study introduces a robust model for city population dynamics, emphasizing the role of rare events.
• Findings challenge the universal applicability of Zipf's law, suggesting a more intricate urban organization.
• The research offers valuable insights for urban planning and understanding the evolution of complex systems.