On measure problems in allometric analysis of cities -- How to correctly understand the law of allometric growth

TL;DR

This paper clarifies the correct understanding of allometric growth in urban analysis, emphasizing that average measures are not universally applicable and that allometric relationships are independent of such averages.

Contribution

It corrects misconceptions by explaining that allometric relationships in urban growth are independent of average measures and provides a proper theoretical understanding.

Findings

Average measures cannot be universally applied to allometric relationships.

Allometric relationships are derived independently of average measures.

The allometric scaling exponent equals the ratio of related growth rates.

Abstract

The law of allometric growth originated from biology has been widely used in urban research for a long time. Some conditional research conclusions based on biological phenomena have been erroneously transmitted in the field of urban geography, leading to some misunderstandings. One of the misunderstandings is that allometric analysis must be based on average measure. The aim of this paper is at explaining how to correctly understand the law of urban allometric growth by means of the methods of literature analysis and mathematical analysis. The results show the average measures cannot be applied to all types of allometric relationships, and the allometric relationships based on average measures cannot be derived from a general principle. Whether it is an empirical model or a theoretical model of allometric growth, its generation and derivation are independent of the average measures. Conclusions can be reached that the essence of allometric growth lies in that the ratio of two related general relative growth rates is a constant, and this constant represents the allometric scaling exponent and fractal dimension ratio. The average measures are helpful to estimate the allometric scaling exponent value which accords with certain theoretical expectations more effectively.