Skip to main content
SpringerLink
Log in

Dynamics of Niche Construction in Models “Consumers–Renewable Resource” and “Consumers–Predators–Renewable Resource”

  • Conference paper
  • First Online:
New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 90))

  • 811 Accesses

Abstract

In this chapter a question of “how much over-consumption a renewable resource can tolerate” is addressed using mathematical models, where a consumer population compete for the common resource, can contribute to resource restoration, and is subject to attacks of predators. The bifurcation analysis of the systems shows that well-adapted predators can keep the system in a stable equilibrium even for “strong” prey over-consumption, when the initial system of resource–consumer goes to extinct. It means that predators may extend the domain of the total system coexistence.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Andronov, A., Leontovich, E., Gordon, I., & Maier, A. (1973). Qualitative theory of second-order dynamic systems. N.-Y.-Toronto: Wiley.

    MATH  Google Scholar 

  2. Bautin, N., & Leontovich, E. (1976). Methods and techniques for qualitative analysis of dynamical systems on the plane. Moscow: Nauka.

    Google Scholar 

  3. Bazykin, A.D. (2000). Nonlinear dynamics of interacting populations. World scientific series on Nonlinear Science, Ser. A (Vol. 11). Singapore: Word Scientific.

    Google Scholar 

  4. Berezovskaya, F. (1979). Non-hyperbolic equilibrium of a planar system of ordinary differential equation. Analysis by Newton diagram method. PhD Dissertation. Institute of Mathematics, Ukraine Acad. Sci.

    Google Scholar 

  5. Berezovskaya, F. S., Novozhilov, A. S., & Karev, G. P. (2007). Population models with singular equilibrium. Mathematical Biosciences, 208(1), 270–299.

    Article  MathSciNet  MATH  Google Scholar 

  6. Brauer, F., & Castillo-Chavez, C. (2001). Mathematical models in population biology and epidemiology. New York: Berlin, Heidelberg, Hong Kong, London, Milan, Paris, Tokyo: Springer.

    Google Scholar 

  7. Grinnell, J. (1917). The niche-relationships of the California thrasher. The Auk, 34(4), 427.

    Article  Google Scholar 

  8. Hardin, G. (1968). The tragedy of the commons. Science, 162(5364), 1243–8.

    Google Scholar 

  9. Hooper, D. U., Chapin, F. S., III, Ewel, J. J., Hector, A., Inchausti, P., Lavorel, S., et al. (2005). Effects of biodiversity on ecosystem functioning: A consensus of current knowledge. Ecological Monographs, 75(1), 3–35.

    Article  Google Scholar 

  10. Kareva, I., Berezovskaya, F., & Castillo-Chavez, C. (2012). Transitional regimes as early warning signals in resource dependent competition models. Mathematical Biosciences, 240, 114–123.

    Article  MathSciNet  MATH  Google Scholar 

  11. Kareva, I., Berezovskaya, F., & Karev, G. (2013). Mixed strategies and natural selection in resource allocation. Mathematical Biosciences and Engineering, 10(5&6), 1561–1586.

    Article  MathSciNet  MATH  Google Scholar 

  12. Kareva, I., Morin, B., & Karev, G. (2012). Preventing the tragedy of the commons through punishment of over-consumers and encouragement of under-consumers. Bulletin of Mathematical Biology, 75, 565–588.

    Article  MathSciNet  Google Scholar 

  13. Krakauer, D. C., Page, K. M., & Erwin, D. H. (2009). Diversity, dilemmas, and monopolies of niche construction. The American Naturalist, 173(1), 26–40.

    Article  Google Scholar 

  14. Kuznetsov, Y. (1998). Elements of applied bifurcation theory. New York: Springer.

    MATH  Google Scholar 

  15. Odling-Smee, F. J., Laland, K. N., & Feldman, M. W. (2003). Niche construction: The neglected process in evolution, Ser. Monographs in Population Biology, 37. Princeton University Press.

    Google Scholar 

  16. Odum, E. (1971). Fundamentals in ecology (3rd ed.). Philadelphia: Saunders.

    Google Scholar 

  17. Post, D. M., Conners, M. E., & Goldberg, D. S. (2000). Prey preference by a top predator and the stability of linked food chains. Ecology, 81, 8–14.

    Article  Google Scholar 

  18. Volterra, V. (1931). Le¸cons sur la Th’eorie Math’ematique de la Lutte pour la Vie. Paris: Gauthier-Villare.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Howard University, Washington, DC, 20059, USA

    Faina S. Berezovskaya

  2. National Centre for Biotechnology Information, Bethesda, MD, 20894, USA

    Georgiy P. Karev

Authors
  1. Faina S. Berezovskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Georgiy P. Karev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Faina S. Berezovskaya .

Editor information

Editors and Affiliations

  1. Dept of Mathematics & Computer Sciences, Virginia State University, Petersburg, Virginia, USA

    Bourama Toni

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Berezovskaya, F.S., Karev, G.P. (2014). Dynamics of Niche Construction in Models “Consumers–Renewable Resource” and “Consumers–Predators–Renewable Resource”. In: Toni, B. (eds) New Frontiers of Multidisciplinary Research in STEAM-H (Science, Technology, Engineering, Agriculture, Mathematics, and Health). Springer Proceedings in Mathematics & Statistics, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-07755-0_8

Download citation

Publish with us

Policies and ethics

Search

Navigation