Global population: from Super-Malthus behavior to Doomsday criticality

Abstract

AbstractThe report discusses global population changes from the Holocene beginning to 2023, via two Super Malthus (SM) scaling equations. SM-1 is the empowered exponential dependence: $$P\left(t\right)={P}_{0}exp{\left[\pm \left(t/\tau \right)\right]}^{\beta }$$ P t = P 0 e x p ± t / τ β , and SM-2 is the Malthus-type relation with the time-dependent growth rate $$r(t)$$ r ( t ) or relaxation time τ$$(t)=1/r(t)$$ ( t ) = 1 / r ( t ) : $$P\left(t\right)={P}_{0}exp\left(r\left(t\right)\times t\right)={P}_{0}exp\left[\tau \left(t\right)/t\right]$$ P t = P 0 e x p r t × t = P 0 e x p τ t / t . Population data from a few sources were numerically filtered to obtain a 'smooth' dataset, allowing the distortions-sensitive and derivative-based analysis. The test recalling SM-1 equation revealed the essential transition near the year 1970 (population: ~ 3 billion): from the compressed exponential behavior ($$\beta >1)$$ β > 1 ) to the stretched exponential one ($$\beta <1$$ β < 1 ). For SM-2 dependence, linear changes of $$\tau \left(T\right)$$ τ T during the Industrial Revolutions period, since ~ 1700, led to the constrained critical behavior $$P\left(t\right)={P}_{0}exp\left[b{\prime}t/\left({T}_{C}-t\right)\right]$$ P t = P 0 e x p b ′ t / T C - t , where $${T}_{C}\approx 2216$$ T C ≈ 2216 is the extrapolated year of the infinite population. The link to the 'hyperbolic' von Foerster Doomsday equation is shown. Results are discussed in the context of complex systems physics, the Weibull distribution in extreme value theory, and significant historic and prehistoric issues revealed by the distortions-sensitive analysis.