UC Irvine

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 ≤D. With coefficient values P(t) = 3.83 × 109/[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 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. © 2013 Elsevier Inc.