Global population: from Super-Malthus behavior to Doomsday criticality

Abstract

Abstract The 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

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