Global population crisis scenarios predicted by the most general dynamic model

TL;DR

This paper introduces a comprehensive nonlinear differential equation model that captures the entire history of global population growth and predicts future scenarios, including potential population decline due to resource limits.

Contribution

It presents a unified nonlinear dynamic model that encompasses all known growth regimes and offers predictive capabilities for future population scenarios.

Findings

The model reproduces historical growth patterns from Neolithic to present.

It predicts a possible global population halving by 2064 due to resource depletion.

Different growth regimes are special cases of the general nonlinear model.

Abstract

We show that a simple nonlinear differential equation (originally studied in the physics of disordered systems) is able to mathematically describe the global population growth over the past 12000 years. Different regimes of population growth since the early Neolithic until today are shown to be all solutions to the same nonlinear differential equation in its various limits. These also include the well-known Malthus (exponential) and Verhulst (logistic) growth regimes, as well as von Foerster's ``doomsday'' formula. All these limits correspond to neglecting higher-order terms in a more general nonlinear dynamic model described by the proposed nonlinear differential equation. While the older models may provide valid fittings to limited time intervals in the global population growth curve in time, their clearly approximate nature prevents them from being predictive over longer periods of time. The proposed comprehensive solution of the proposed model is instead well suited to provide predictions for future scenarios. These include halving of the global population as early as 2064 due to resource depletion, if the effect of the Earth's limited carrying capacity were to set in today.