城市增长方程 (Nature, 19 November 2020, VOL 587, ISSUE 7834)

城市科学寻求理解和解释在世界主要城市系统中观察到的规律。对城市人口演变进行建模是该科学和所有城市研究的核心。从数量上说，最根本的问题是了解城市人口的分层组织和特大城市的统计数据。

最初人们认为该规律是一个被称为齐普夫定律的普遍原理；但最近的实证研究对该模型的有效性提出了质疑。一个理论模型必须能够解释相对频繁的城市和文明的兴衰，虽然进行了诸多尝试，但这些基本问题尚未得到令人满意的答案。

研究组引入了一个用于建模城市人口增长的随机方程，根据对最新数据集（针对加拿大、法国、英国和美国）的实证分析而构建。该模型揭示了罕见但大规模的城际迁移冲击是如何主导城市增长的。

该方程预测了城市人口分布的复杂形状，并表明由于有限时间效应，齐普夫定律通常不成立，这也意味着城市的组织更加复杂。与观察结果一致，它还预测了城市分层结构中存在的多重时间变化。

研究结果强调了罕见事件在复杂系统的演进中，以及在城市规划中（更实际的层面）的重要性。

▲ Abstract

The science of cities seeks to understand and explain regularities observed in the world’s major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most fundamental problem is to understand the hierarchical organization of city population and the statistical occurrence of megacities. This was first thought to be described by a universal principle known as Zipf’s law; however, the validity of this model has been challenged by recent empirical studies. A theoretical model must also be able to explain the relatively frequent rises and falls of cities and civilizations, but despite many attempts these fundamental questions have not yet been satisfactorily answered. Here we introduce a stochastic equation for modelling population growth in cities, constructed from an empirical analysis of recent datasets (for Canada, France, the UK and the USA). This model reveals how rare, but large, interurban migratory shocks dominate city growth. This equation predicts a complex shape for the distribution of city populations and shows that, owing to finite-time effects, Zipf’s law does not hold in general, implying a more complex organization of cities. It also predicts the existence of multiple temporal variations in the city hierarchy, in agreement with observations. Our result underlines the importance of rare events in the evolution of complex systems and, at a more practical level, in urban planning.

2020--The growth equation of cities--Nature（2020 Nov; 587(7834)397-401）.pdf