IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v216y2008i2p89-101.html
   My bibliography  Save this article

Nonlinearities in mathematical ecology: Phenomena and models

Author

Listed:
  • Svirezhev, Yuri M.

Abstract

Presented is a critical survey of canonical nonlinear models in theoretical population ecology, namely single-species population, prey–predator, competition, migration within a metapopulation, and trophic chains. Various nonlinear effects, like hysteresis, structural instability, dissipative structures, dynamic chaos, etc., do exist in these models, but the problem how to detect these phenomena in real ecosystems is not yet solved. In the mathematics of nonlinear models, the central question is whether the simplest, i.e., Volterra-type, nonlinearity is sufficient to reproduce a variety of nonlinear phenomena in a given model or we need a more sophisticated formalism. Examples are considered where the Volterra models fail. Although fundamental physical principles, like, e.g., the mass conservation law, should work in ecology too, the ecological origin of the models often causes mathematical effects which are distinct from those in theoretical physics. For example, the trophic-chain model does reveal a kind of chaotic behaviour, but the “ecological strange attractor” occupies an intermediate position between Lorenz's and Feigenbaum's attractors; moreover, the phase volume of our system contracts, hence the system is dissipative (like a Lorenz's one) in spite of its matter conservation property. Nevertheless, when applied properly, physical concepts, like, e.g., the thermodynamic notion of exergy, give better insight both to the patterns of nonlinear ecosystem behaviour and to comparison of the patterns.

Suggested Citation

  • Svirezhev, Yuri M., 2008. "Nonlinearities in mathematical ecology: Phenomena and models," Ecological Modelling, Elsevier, vol. 216(2), pages 89-101.
  • Handle: RePEc:eee:ecomod:v:216:y:2008:i:2:p:89-101
    DOI: 10.1016/j.ecolmodel.2008.03.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380008001270
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ecolmodel.2008.03.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rossi, Federico & Liveri, Maria Liria Turco, 2009. "Chemical self-organization in self-assembling biomimetic systems," Ecological Modelling, Elsevier, vol. 220(16), pages 1857-1864.
    2. Rayfield, Bronwyn & Moilanen, Atte & Fortin, Marie-Josée, 2009. "Incorporating consumer–resource spatial interactions in reserve design," Ecological Modelling, Elsevier, vol. 220(5), pages 725-733.
    3. Semenov, Alexander V. & Franz, Eelco & van Bruggen, Ariena H.C., 2010. "COLIWAVE a simulation model for survival of E. coli O157:H7 in dairy manure and manure-amended soil," Ecological Modelling, Elsevier, vol. 221(4), pages 599-609.
    4. Lischke, Heike & Löffler, Thomas J., 2017. "Finding all multiple stable fixpoints of n-species Lotka–Volterra competition models," Theoretical Population Biology, Elsevier, vol. 115(C), pages 24-34.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:216:y:2008:i:2:p:89-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.