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. 2021 May 20;16(5):e0247214.
doi: 10.1371/journal.pone.0247214. eCollection 2021.

Footprints to singularity: A global population model explains late 20th century slow-down and predicts peak within ten years

Christopher Bystroff  1
Affiliations

Footprints to singularity: A global population model explains late 20th century slow-down and predicts peak within ten years

Christopher Bystroff. PLoS One. .

Abstract

Projections of future global human population are traditionally made using birth/death trend extrapolations, but these methods ignore limits. Expressing humanity as a K-selected species whose numbers are limited by the global carrying capacity produces a different outlook. Population data for the second millennium up to the year 1970 was fit to a hyper-exponential growth equation, where the rate constant for growth itself grows exponentially due to growth of life-saving technology. The discrepancies between the projected growth and the actual population data since 1970 are accounted for by a decrease in the global carrying capacity due to ecosystem degradation. A system dynamics model that best fits recent population numbers suggests that the global biocapacity may already have been reduced to one-half of its historical value and global carrying capacity may be at its 1965 level and falling. Simulations suggest that population may soon peak or may have already peaked. Population projections depend strongly on the unknown fragility or robustness of the Earth's essential ecosystem services that affect agricultural production. Numbers for the 2020 global census were not available for this study.

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Conflict of interest statement

The author has declared that no competing interests exist. Salary was provided by RPI, NIH and Grantham Foundation. The donors, Grantham Foundation and NIH, do not have any competing interest in this work.

Figures

Fig 1
Fig 1
(a) World4, a system dynamics model that reproduces world population numbers up to 2010 and projects forward. Stocks (rectangles) and flows (solid arrows) form two interacting closed systems, one for Technology and one for Environment. Input variables (ovals) are colored and grouped by function. Output variables (white) are the global carrying capacity (CC) and population. Dashed lines indicate variable dependencies. (b) World4 simulations superposed on 20th century population numbers (thick cyan line) and UN population projections [11] (dashed blue line is the median projection and light blue are 95% confidence region). The program hyperfit carried out 1 million World4 simulations using randomly selected parameters from ranges listed in Table 1. Shown are the 184 trajectories that deviate from 1970–2010 population data by less than rms 0.5e8. Simulations are colored by their E0 value (total ecosystem size in gha, see inset). Counterintuitively, a low E0 means a higher population is sustainable. Double-headed arrows indicate 80% confidence ranges for peak date, peak height and 2060 population.
Fig 2
Fig 2. Feedback.
(a) Ignorance feeds back in a positive way to rewilding. Rewilding increases ecosphere. Ecosphere feeds back negatively to obsolescence. Obsolescence increases ignorance. (b) Exponential decrease of both ecosphere (pE) by domestication and ignorance (pI) by learning, results in a switch, first in ignorance then in ecosphere. Inset: undamped Lotke-Volterra oscillation.
Fig 3
Fig 3. Least-squares fits to years 1970–2010 are non-linearly correlated in the space of the four variables (E0, a, u and v) that effect only recent population data, as shown using hyperfit.
For example, as seen in (a), the best-fit setting for v (ecosystem-dependent obsolescence of technology) goes down as we increase the setting for a (ecosystem fragility). Each image is a projection of minimum values of residuals from the 4D space to 2D spaces (a) a, v, (b) a, E0, (c) E0, v. (d) A plot of five trajectories using optimal and suboptimal values, demonstrating the effect of choice of E0 (total ecosystem size) on growth rate (1960–2000) and on the position of the population peak, ignoring other parameters. A hypothesized infinite ecosystem, E0 = ∞ (black), leads to massive overestimate of growth rate. E0 = 0.800e10 (green) or E0 = 0.750e10 (orange) overestimates growth rate and predicts a later peak. E0 = 0.695e10 (cyan) is optimal and predicts a 2020 peak. E0 = 0.600e10 (magenta) underestimates growth and predicts that we are past the peak. Thick blue line is population data up to 2010. 2020 population numbers are not available.
Fig 4
Fig 4. Half-Earth scenarios.
Population projections for conservation efforts with various % enforcement, length of phase-in period and the % of ecosphere to be preserved, as compared to a BAU scenario. Dotted line is the present year, 2020.
Fig 5
Fig 5. Plot of Eq 10, the ecosphere component of the carrying capacity for humans.
Increasing values of a move the curve to the right, meaning ecosystem services are more fragile with respect to the ecosphere.
See this image and copyright information in PMC

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