中文摘要：

系统总结了城市异速标度研究的学术源流、量纲困境和现状特征,重点探讨了城市化异速标度分析的前景和意义。异速标度是城市研究的基本理论方法之一,该方法起源于20世纪50年代的生物学和一般系统论。由于量纲难题,城市异速分析经过一段时间的研究热潮之后趋于冷落;由于分维概念的引入,异速标度关系摆脱了量纲困境;由于相关领域的推动,城市异速分析方法复兴。异速生长和异速标度分析在城市形态、城市生态、城市性态、城市动态以及城市体系等诸多领域都有应用。如今,异速生长正在与分形和自组织网络理论相互融合,发展成为基于一般标度律的城市过程和格局的集成分析方法。由于城市化与城市形态、城市体系等方面的密切相关,异速标度分析极有前景的一个发展方向可能是城市化研究。城市化异速分析可望将不同类型的城市异速标度研究成果组织成一个完整的逻辑框架。

英文摘要：

The allometric scaling analysis in urban studies originated from biology and general system theory. At first, it was employed to analyze the allometric relation between urban and rural population associated with urbanization. Before long, the studies on the scaling relation between urban area and population became the mainstream of the allometric analysis. The chief aim is to reveal the relationship between size and shape of cities. But a dimension conundrum arose. Urban area can be regarded as a 2-D measurement, and urban population used to be treated as a 3-D measurement. Thus, according to the principle of dimensional consistency, the scaling exponent of urban area and population should be 2/3. However, it does not conform to reality. Then, urban population was treated as a 2-D measurement. If this was true, the allometric scaling exponent should equal 1. However, this does not yet tally with the actual situation. Geographers and city scientists were placed in a dilemma whether to treat urban population size as a 2-D or a 3-D measurement because the observed scaling exponent values always come between 2/3 and 1. The geographical students failed to extricate themselves from the theoretical predicament before the introduction of the concept of fractional dimension. The rapid rise of fractal geometry and complexity theory results in the rejuvenation of alloemetric analysis of cities associated with scaling law. Now, allometry has been applied to urban form, urban ecology, urbanism, urban dynamics, and urban systems. All of the applications are the bases of studies on urbanization. One of the most significant research directions of allometry in urban studies in future may be the allometric scaling analysis in urbanization.