Is there enough fertile soil to feed a planet of growing cities?

TL;DR

This paper investigates whether current agricultural soil consumption scales sustainably with city growth, deriving a mathematical model to estimate the maximum population that can be fed and highlighting the importance of the scaling law exponent.

Contribution

It introduces a new population dynamics model based on a scaling law for soil consumption, providing a quantitative estimate of food sustainability limits for growing cities.

Findings

The asymptotic limit of the model defines the maximum sustainable population.

A small scaling law exponent is necessary for food sustainability.

The model's reliability is analyzed for major cities.

Abstract

We analyze a scaling law for the consumption of agricultural soil by cities. The nonlinear dependence of the size of the city on the number of inhabitants gives rise to an equation for population dynamics. We found the asymptotic limit of the solution for this equation, given by the carrying capacity in terms of number of inhabitants that can be fed. The carrying capacity as a function of the scaling law exponent is computed numerically, showing that the exponent must be very small to ensure a food sustainability. We suggest a bound for the value of this exponent and analyze the reliability of the scaling law for major cities.