Buildings as Species: Competition and Scaling Rules in Cities

TL;DR

This paper models urban buildings as ecological species, revealing how competition and spatial distribution follow power-law behaviors and bifurcate into different predation regimes, informing urban spatial dynamics.

Contribution

It introduces a novel ecological framework for analyzing building competition in cities using the convex hull as a species definition, uncovering power-law distributions and bifurcations in spatial coexistence.

Findings

Perimeter distribution follows a power-law beyond a critical density.

Species coexistence probability bifurcates with building number.

Two predation regimes influence spatial homogeneity and diversity.

Abstract

We look at buildings' competition over space in cities through the lens of ecology. Adopting the convex hull of the building's footprint perimeter as a definition of species yields parallels to forest trees' competition, which we expound on. Their perimeter distribution $p(r)$ follows a power-law behavior beyond a critical threshold of the density of the built environment. In this regime, the species coexistence likelihood $p(d)$, where $d$ is the distance to the nearest competitor, which we define to be a building with a larger $r$, bifurcates with the buildings' number $n$. This reveals two different predation laws: a vicious predatory one which is linked spatial homogeneity and segregation, as opposed to another favoring spatial diversity and intermixing between species.