Relative size measures of urban form based on allometric subtraction

Abstract

One of the most common relativization techniques in life sciences quantifies body condition based on residuals from the linear regression in the log–log plot of body mass against a linear measure of size. Given the network-based analogy between organisms and cities, the method is applied to comparative urban studies to formulate relativized allometric measures based on the allometry to size of metric and topological measures of street networks. The analysis of a sample of 70 cities from a confined region considered in three historical stages demonstrates that the more allometric scaling of a measure to size diverges from the linear, the more allometric measures show discrepancy to the existing relativization methods that are based on mean measures and ratios between measures. Allometric measures reflect the dynamics of specific regional samples of cities and therefore also differ from relativization methods that relate measures that grow exponentially with size against static theoretical yardsticks. The comparison involving two additional samples of cities from other regions suggests that the proposed allometric measures can be used to approximate size-invariant measures for cities with unknown allometry more reliably than existing relativization measures. The method can be applied to formulate relativized indices for any measure that displays allometry to size in various scales of the built environment.