The European Physical Journal Special Topics

, Volume 223, Issue 11, pp 2065–2085 | Cite as

Human population and atmospheric carbon dioxide growth dynamics: Diagnostics for the future

  • A.D. Hüsler
  • D. Sornette
Part of the following topical collections:
  1. Dynamic Systems: From Statistical Mechanics to Engineering Applications


We analyze the growth rates of human population and of atmospheric carbon dioxide by comparing the relative merits of two benchmark models, the exponential law and the finite-time-singular (FTS) power law. The later results from positive feedbacks, either direct or mediated by other dynamical variables, as shown in our presentation of a simple endogenous macroeconomic dynamical growth model describing the growth dynamics of coupled processes involving human population (labor in economic terms), capital and technology (proxies by CO2 emissions). Human population in the context of our energy intensive economies constitutes arguably the most important underlying driving variable of the content of carbon dioxide in the atmosphere. Using some of the best databases available, we perform empirical analyses confirming that the human population on Earth has been growing super-exponentially until the mid-1960s, followed by a decelerated sub-exponential growth, with a tendency to plateau at just an exponential growth in the last decade with an average growth rate of 1.0% per year. In contrast, we find that the content of carbon dioxide in the atmosphere has continued to accelerate super-exponentially until 1990, with a transition to a progressive deceleration since then, with an average growth rate of approximately 2% per year in the last decade. To go back to CO2 atmosphere contents equal to or smaller than the level of 1990 as has been the broadly advertised goals of international treaties since 1990 requires herculean changes: from a dynamical point of view, the approximately exponential growth must not only turn to negative acceleration but also negative velocity to reverse the trend.


European Physical Journal Special Topic Population Growth Rate Exponential Model Carbon Dioxide Emission Average Growth Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Akaev, V. Sadovnichy, A. Korotayev, Eur. Phys. J. Special Topics 205, 355 (2012)CrossRefADSGoogle Scholar
  2. 2.
    J.M. Barnola, M. Anklin, J. Porcheron, D. Raynaud, J. Schwander, B. Stauffer, Tellus B 47(1–2), 264 (1995)CrossRefADSGoogle Scholar
  3. 3.
    R. Biggs, S.R. Carpenter, W.A. Brock, Proc. Natl. Acad. Sci. USA 106(3), 826 (2009)CrossRefADSGoogle Scholar
  4. 4.
    J.G. Canadell, C. Le Quere, M.R. Raupach, C.B. Field, E.T. Buitenhuis, P. Ciais, T.J. Conway, N.P. Gillett, R.A. Houghton, G. Marland, Proc. Natl. Acad. Sci. 104(47) 18866 (2007)CrossRefADSGoogle Scholar
  5. 5.
    M.R. Chertow, J. Industr. Ecol. 4(4), 13 (2000)CrossRefGoogle Scholar
  6. 6.
    C.W. Cobb, P.H. Douglas, Amer. Econ. Rev. 18(1), 139 (1928)Google Scholar
  7. 7.
    V. Dakos, M. Scheffer, E.H. van Nes, V. Brovkin, V. Petoukhov, H. Held, Proc. Natl. Acad. Sci. USA 105(38), 14308 (2008)CrossRefADSGoogle Scholar
  8. 8.
    J.M. Drake, B.D. Griffen, Nature 456(September), 456 (2010)CrossRefADSGoogle Scholar
  9. 9.
    T. Garrett, Climatic Change 104(3), 437 (2011)CrossRefGoogle Scholar
  10. 10.
    S. Gluzman, D. Sornette, Phys. Rev. E 6601(016134), U315 (2002)MathSciNetGoogle Scholar
  11. 11.
    N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Perseus Publishing, 1992)Google Scholar
  12. 12.
    A. Goriely, J. Differen. Eqns. 161(2), 422 (2000)MathSciNetCrossRefzbMATHADSGoogle Scholar
  13. 13.
    C.A.S. Hall, J.W. Day, Jr., Amer. Scientist 97, 230 (2009)CrossRefGoogle Scholar
  14. 14.
    K. Ide, D. Sornette, Physica A 307(1–2), 63 (2002)MathSciNetCrossRefzbMATHADSGoogle Scholar
  15. 15.
    A. Johansen, D. Sornette, Physica A: Stat. Mech. Appl. 294(3-4), 465 (2001)CrossRefzbMATHADSGoogle Scholar
  16. 16.
    A. Korotayev, J. World-Syst. Res. 11(1), 79 (2005)Google Scholar
  17. 17.
    A. Korotayev, A.S. Malkov, D. Khaltourina, Introduction to Social Macrodynamics: Secular Cycles and Millennial Trends (URSS, 2006)Google Scholar
  18. 18.
    M. Kremer, Q. J. Econ. 108, 681 (1993)CrossRefGoogle Scholar
  19. 19.
    D.H. Meadows, The Limits to Growth; a Report for the Club of Rome’s Project on the Predicament of Mankind (Universe Books, 1972)Google Scholar
  20. 20.
    Organisation for Economic Co-operation and Development, World Energy Outlook 2011Google Scholar
  21. 21.
    R. Pielke, T. Wigley, C. Green, Nature 452(7187), 531 (2008)CrossRefADSGoogle Scholar
  22. 22.
    M.R. Raupach, J.G. Canadell, C. Le Quéré, Biogeosci. Discuss. 5(4), 2867 (2008)CrossRefADSGoogle Scholar
  23. 23.
    J. Rockstrom, W. Steffen, K. Noone, A. Persson, F.S. Chapin, E.F. Lambin, T.M. Lenton, M. Scheffer, C. Folke, H.J. Schellnhuber, B. Nykvist, C.A. de Wit, T. Hughes, S. van der Leeuw, H. Rodhe, S. Sorlin, P.K. Snyder, R. Costanza, U. Svedin, M. Falkenmark, L. Karlberg, R.W. Corell, V.J. Fabry, J. Hansen, B. Walker, D. Liverman, K. Richardson, P. Crutzen, J.A. Foley, Nature 461(7263), 472 (2009)CrossRefADSGoogle Scholar
  24. 24.
    D. Romer, Advanced Macroeconomics, 2nd ed. (McGraw-Hill/Irwin, 2000)Google Scholar
  25. 25.
    Royal Society and the US National Academy of Sciences, Climate Change: Evidence & CausesGoogle Scholar
  26. 26.
    S.G. Sammis, D. Sornette, Proc. Natl. Acad. Sci. USA 99(Supp1), 2501 (2002)CrossRefADSGoogle Scholar
  27. 27.
    M. Scheffer, J. Bascompte, W.A. Brock, V. Brovkin, S.R. Carpenter, V. Dakos, H. Held, E.H. van Nes, M. Rietkerk, G. Sugihara, Nature 461(7260), 53 (2009)CrossRefADSGoogle Scholar
  28. 28.
    D. Sornette, Proc. Natl. Acad. Sci. USA 99(Supp1), 2522 (2002)CrossRefADSGoogle Scholar
  29. 29.
    D. Sornette, Why Stock Markets Crash (Critical Events in Complex Financial Systems), (Princeton University Press, 2003)Google Scholar
  30. 30.
    D. Sornette, Critical Phenomena in Natural Sciences: Chaos, Fractals, Self-organization and Disorder: Concepts and Tools (Springer Series in Synergetics), 2nd ed. (Springer, 2006)Google Scholar
  31. 31.
    P.A. Stephens, W.J. Sutherland, R.P. Freckleton, Oikos 87, 185 (1999)CrossRefGoogle Scholar
  32. 32.
    S.A. Umpleby, Population Env. 11(3), 159 (1990)CrossRefGoogle Scholar
  33. 33.
    P.-F. Verhulst, Mém. de l’Academie Royale des Sci. et Belles-Lettres de Bruxelles 18, 1 (1845)Google Scholar
  34. 34.
    P.-F. Verhulst, Mém. de l’Academie Royale des Sci. et Belles-Lettres de Bruxelles 20, 1 (1847)Google Scholar
  35. 35.
    H. von Foerster, P.M. Mora, L.W. Amiot, Science 132(3436), 1291 (1960)CrossRefADSGoogle Scholar
  36. 36.
    P.E. Waggoner, J.H. Ausubel, Proc. Natl. Acad. Sci. USA 99(12), 7860 (2002)CrossRefADSGoogle Scholar
  37. 37.
    S.R. Weart, The Discovery of Global Warming: Revised and Expanded Edition (New Histories of Science, Technology, and Medicine) (Harvard University Press, revised and expanded edition, 2008)Google Scholar
  38. 38.
    V.I. Yukalov, E.P. Yukalova, D. Sornette, Physica D 238, 1752 (2009)MathSciNetCrossRefzbMATHADSGoogle Scholar
  39. 39.
    V.I. Yukalov, E.P. Yukalova, D. Sornette, Eur. Phys. J. Special Topics 205, 313 (2012)CrossRefADSGoogle Scholar
  40. 40.
    V.I. Yukalov, E.P. Yukalova, D. Sornette, Physica D 241, 1270 (2012)CrossRefzbMATHADSGoogle Scholar
  41. 41.
    V.I. Yukalov, E.P. Yukalova, D. Sornette, Int. J. Bifurc. Chaos 24(2), 1450021 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  1. 1.Department of ManagementTechnology and Economics, ETH ZurichZurichSwitzerland
  2. 2.Swiss Finance Institute c/o University of GenevaGeneva 4Switzerland

Personalised recommendations