Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

Influence of technological progress and renewability on the sustainability of ecosystem engineers populations

Instituto de Fíısica de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil

Special Issues: Mathematical Methods in the Biosciences

Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human’s ecosystem engineering that has profoundly modified the world’s landscape. Despite the age-old concern that unchecked population and economic growth may be unsustainable, the prospect of societal collapse remains contentious today. Contrasting with the usual approach to modeling human-nature interactions, which are based on the Lotka-Volterra predator-prey model with humans as the predators and nature as the prey, here we address this issue using a discrete-time population dynamics model of ecosystem engineers. The growth of the population of engineers is modeled by the Beverton-Holt equation with a density-dependent carrying capacity that is proportional to the number of usable habitats. These habitats (e.g., farms) are the products of the work of the individuals on the virgin habitats (e.g., native forests), hence the denomination engineers of ecosystems to those agents. The human-made habitats decay into degraded habitats, which eventually regenerate into virgin habitats. For slow regeneration resources, we find that the dynamics is dominated by rounds of prosperity and collapse, in which the population reaches vanishing small densities. However, increase of the efficiency of the engineers to explore the resources eliminates the dangerous oscillatory patterns of feast and famine and leads to a stable equilibrium that balances population growth and resource availability. This finding supports the viewpoint of growth optimists that technological progress may avoid collapse.
  Article Metrics

Keywords discrete dynamical systems; human-nature dynamics; Beverton-Holt model; ecosystem engineers; population collapse

Citation: Guilherme M Lopes, José F Fontanari. Influence of technological progress and renewability on the sustainability of ecosystem engineers populations. Mathematical Biosciences and Engineering, 2019, 16(5): 3450-3464. doi: 10.3934/mbe.2019173


  • 1. T. R. Malthus, An essay on the theory of population, Oxford University Press, Oxford, 1798.
  • 2. D. H. Meadows, D. L. Meadows, J. Randers, et al., The Limits to Growth; A Report for the Club of Rome's Project on the Predicament of Mankind, Universe Books, New York, 1972.
  • 3. D. H. Meadows, J. Randers and D. L. Meadows, Limits To Growth: The 30-Year Update, Chelsea Green Publishing, Vermont, 2004.
  • 4. J. Randers, 2052: A Global Forecast for the Next Forty Years, Chelsea Green Publishing, Vermont, 2012.
  • 5. J. D. Murray, Mathematical Biology: I. An Introduction, 3 rd edition, Springer, New York, 2003.
  • 6. J. A. Brander and M. S. Taylor, The Simple Economics of Easter Island: A Ricardo-Malthus Model of Renewable Resource Use, Am. Econ. Rev., 88 (1998), 119–138.
  • 7. S. Motesharrei, J. Rivas and E. Kalnay, Human and nature dynamics (HANDY): Modeling inequality and use of resources in the collapse or sustainability of societies, Ecol. Econom., 101 (2014), 90–102.
  • 8. B. D. Smith, The Ultimate Ecosystem Engineers,Science, 315 (2007), 1797–1798.
  • 9. J. A. Tainter, The Collapse of Complex Societies, Cambridge University Press, Cambridge, UK, 1990.
  • 10. J. Diamond, Collapse: How Societies Choose to Fail or Succeed, Penguin Books, New York, 2005.
  • 11. C. G. Jones, J. H. Lawton and M. Shachak, Organisms as ecosystem engineers, Oikos, 69 (1994), 373–386.
  • 12. W. S. C. Gurney and J. H. Lawton, The population dynamics of ecosystem engineers, Oikos, 76 (1996), 273–283.
  • 13. J. P. Wright and C. G. Jones, The Concept of Organisms as Ecosystem Engineers Ten Years On: Progress, Limitations, and Challenges, Bioscience, 56 (2006), 203–209.
  • 14. K. Cuddington, W. G. Wilson and A. Hastings, Ecosystem Engineers: Feedback and Population Dynamics, Am. Nat., 173 (2009), 488–498.
  • 15. C. Franco and J. F. Fontanari, The spatial dynamics of ecosystem engineers, Math. Biosci., 292 (2017), 76–85.
  • 16. R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations, Blackburn Press, Caldwell, NJ, 1993.
  • 17. W. E. Ricker, Stock and Recruitment, J. Fish. Res. Bd. Canada, 11 (1954), 559–623.
  • 18. J. F. Fontanari, The Collapse of Ecosystem Engineer Populations, Mathematics, 6 (2018), 9.
  • 19. K. Kaneko, Overview of Coupled Map Lattices, Chaos, 2 (1992), 279–282.
  • 20. M. P. Hassell, H. N. Comins and R. M. May, Spatial structure and chaos in insect population dynamics, Nature, 353 (1991), 255–258.
  • 21. H. N. Comins, M. P. Hassell and R. M. May, The spatial dynamics of host-parasitoid systems, J. Anim. Ecol., 61 (1992), 735–748.
  • 22. L. A. D. Rodrigues, D. C. Mistro and S. Petrovskii, Pattern Formation, Long-Term Transients, and the Turing-Hopf Bifurcation in a Space- and Time-Discrete Predator-Prey System, Bull. Math. Biol., 73 (2011), 1812–1840.
  • 23. D. C. Mistro, L. A. D. Rodrigues and S. Petrovskii, Spatiotemporal complexity of biological invasion in a space- and time-discrete predator-prey system with the strong Allee effect, Ecol. Complex., 9 (2012), 16–32.
  • 24. A. A. Berryman and J. A. Millstein, Are ecological systems chaotic – And if not, why not? Trends Ecol. Evol., 4 (1989), 26–28.
  • 25. J. C. Sprott, Chaos and Time-Series Analysis, Oxford University Press, Oxford, 2003.
  • 26. J. F. Fontanari and F. A. Rodrigues, Influence of network topology on cooperative problem-solving systems, Theory Biosci., 135 (2016), 101–110.
  • 27. S. M. Reia and J. F. Fontanari, Effect of group organization on the performance of cooperative processes, Ecol. Complex., 30 (2017), 47–56.
  • 28. G. Basalla, The Evolution of Technology, Cambridge University Press, Cambridge, UK, 1989.
  • 29. F. Courchamp, J. Berec and J. Gascoigne, Allee effects in ecology and conservation, Oxford University Press, Oxford, 2008.
  • 30. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, Springer, New York, 2004.
  • 31. S. Strogatz, Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering, Westview Press, Boulder, 2001.
  • 32. P. Turchin, Evolution in population dynamics, Nature, 424 (2003), 257–258.
  • 33. A. Atkisson, Believing Cassandra: How to be an Optimist in a Pessimist's World, Earthscan/Routledge, New York, 2010.


Reader Comments

your name: *   your email: *  

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved