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Open study published in Chaos, Solitons & Fractals proposes a non-linear rate feedback equation to explain 12,000 years of human growth and simulates, in an extreme scenario, how environmental crises could rapidly reduce the global population by 2064.
The global population decline could occur rapidly if environmental crises imposed severe limits on Earth, indicates a new mathematical model published in Chaos, Solitons & Fractals. In the worst simulated scenario, humanity would be halved by around 2064.
Population decline appears as an extreme scenario, not as a prediction
The study was developed by Alessio Zaccone and Kostya Trachenko, from Queen Mary University of London. The central proposal is a non-linear mathematical equation, called the rate feedback model, capable of bringing together 12,000 years of human population growth in a single framework.
The research applies to demography a framework originally developed in another field: the physics of disordered materials, such as glasses and amorphous solids. The so-called Trachenko-Zaccone equation seeks to describe changes in population pace using a single parameter.
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The most sensitive point of the analysis lies in the hypothetical future scenarios. The current global trajectory, within the model, remains relatively stable and does not indicate imminent collapse. Population decline only arises when the calculation imposes a strong environmental or social rupture.
Model connects slow growth, industrial explosion, and recent stabilization
The equation was compared with population data from different historical eras, from the Neolithic phase to the modern period. The result reproduced varied patterns, including phases of slow growth, intense accelerations, and the more moderate regime observed since around 1970.
Unlike classical models, which usually treat growth as exponential or logistic, the new framework naturally alternates between distinct regimes. Thus, the explosive expansion of the industrial era and the more gentle recent growth appear as parts of the same dynamic.
The study also revisits the prediction of Heinz von Foerster and collaborators, made in 1960, according to which the world population would mathematically tend to infinity around 2026. The global reduction in fertility rates has diverted this predicted trajectory.
Worst-case scenario reduces Earth’s sustainable capacity
In the most provocative simulation, crises such as climate collapse, pandemics, conflicts, or resource shortages would abruptly reduce the planet’s sustainable capacity to about 2 billion people. In this conservative worst-case hypothesis, the population decline would be accelerated on a global scale, in a few years.
The authors emphasize that the exercise should not be read as a prediction. It shows the sensitivity of population dynamics to sudden changes. The contribution of the model lies in offering a unique mathematical language to explore stabilization, uncontrolled growth, or sudden collapse.
