Abstract
Abstract Up to 1900, world population growth over 1500 years fitted the quasi-hyperbolic format P ( t ) = a /( D − t ) M , but this fit projected to infinite population around 2000. The recent slowdown has been fitted only by iteration of differential equations. This study fits the mean world population estimates from CE 400 to present with “tamed quasi-hyperbolic function” P ( t ) = A /[ln( B + e ( D − t )/ τ )] M , which reverts to P = a /( D − t ) M when t . With coefficient values P ( t ) = 3.83 × 10 9 /[ln(1.28 + e (1980 − t)/22.9 )] 0.70 , the fit is within ± 9%, except in 1200–1400, and projects to a plateau at 10.2 billion. An interaction model of population, Earth's carrying capacity and technological–organizational skills is proposed. It can be approximately fitted with this P ( t ) and an analogous equation for carrying capacity.
Highlights
Fifty years ago, Science published a study with the provocative title “Doomsday: Friday 13 November, A.D. 2026” [1]
The smoothness of world population growth curve since CE 400, with a single inflection point around 2000, suggests that stable long-term factors may be at work, rather than accumulation of random developments
Eq (1) can be derived from interaction between these exponential growths when they reciprocally enhance their rate “constants” [4]. Such interaction might be assumed because more people means more potential innovators, and higher technological–organizational skills increase Earth's carrying capacity and make a larger population possible
Summary
Science published a study with the provocative title “Doomsday: Friday 13 November, A.D. 2026” [1] It fitted world population during the previous two millennia with P = 179 × 109/(2026.9−t)0.99. The smoothness of world population growth curve since CE 400, with a single inflection point around 2000, suggests that stable long-term factors may be at work, rather than accumulation of random developments. This underlying basis for quasi-hyperbolic pattern and later slowdown needs elaboration. A modified explicit equation is proposed, which fits the mean world population estimates from CE 400 to present and to foreseeable future This “tamed quasi-hyperbolic function” fits approximately an interaction model of population, Earth's
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