Institute of High Pressure Physics

In the globalized world of the 21st century, a reliable description of the evolution of the world's population is becoming increasingly important. A critical analysis of the literature on the subject shows that the problem of the world population continues to become one of the most important cognitive challenges.

A recent publication by A. A. Sojecka and A. Drozd-Rzoska “Global Population: From Super-Malthus Behavior to Judgment Day Criticality” [Scientific Reports 14 (2024) 9853] https://doi.org/10.1038/s41598-024-60589-3, presents a novel model analysis of the evolution of the global population using a methodology originally developed by Aleksandra Drozd-Rzoska for the dynamics of complex soft matter systems, in particular for subcooled liquids, glasses, and supercritical fluids.

This paper discusses global population changes from the Holocene onset (10 000 BC) to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence:

P(t)=P₀exp[+/-(t/t)]^b,

and SM-2 includes the time-dependent growth rate r(t) or relaxation time t(t) = 1/r(t):

P(t)=P₀exp[r(t)xt) = P₀exp[t/t(t)].

Global population data from a few sources were numerically filtered to obtain a 'smooth, analytic' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential crossover transformation near the year 1970 (population: ~3 billion): from the compressed exponential behavior (b>1) to the stretched exponential one (b<1). For SM-2 dependence, linear changes of t(T) during the Industrial Revolutions period, since the year ~1700, led to the constrained critical behavior P(t)=P₀exp[b't/T_C-t)], where T_C ~ 2216 is is the extrapolated year of the infinite population. The link to the famous 'hyperbolic, Doomsday' equation [von Foerster et al. Science 132 (1960) 1291] is shown.

The results are discussed by recalling: *the complex systems physics; *the Weibull distribution in extreme value theory; *the significant historical and prehistoric issues revealed by distortion-sensitive analysis. The importance of the reliable determination of global population changes for effective global management in the globalized world is stressed.

The paper also indicates that global population changes can be non-monotonic, which yields a significant problem in long-term deterministic forecasting. It introduces an innovative way of data analysis sensitive to subtle deviations from model relations related to the 'bottom-up' methodology, which has hardly been used so far. Global population forecasting till the year 2100 is given.