IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v246y2012icp1-10.html
   My bibliography  Save this article

Effect of population size in a predator–prey model

Author

Listed:
  • Campillo, F.
  • Lobry, C.

Abstract

We consider a hybrid version of the basic predator–prey differential equation model: a pure jump stochastic model for the prey variable x coupled with a differential equation model for the predator variable y. This hybrid model is derived from the classical birth and death process. The model contains a parameter ω which represents the number of individuals for one unit of prey: x=1 corresponds to ω individual prey. It is shown by the mean of simulations and explained by a mathematical analysis based on a result from the singular perturbation theory – the so-called theory of Canards – that qualitative properties of the model like persistence or extinction are dramatically sensitive to ω. For instance, in our example, if ω=107 we have extinction and if ω=108 we have persistence. This means that we must be very cautious when we use continuous variables in place of discrete ones in dynamic population modeling even when we use stochastic differential equations in place of deterministic ones.

Suggested Citation

  • Campillo, F. & Lobry, C., 2012. "Effect of population size in a predator–prey model," Ecological Modelling, Elsevier, vol. 246(C), pages 1-10.
    • Handle: RePEc:eee:ecomod:v:246:y:2012:i:c:p:1-10
    DOI: 10.1016/j.ecolmodel.2012.07.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380012003432
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2012.07.015?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. Wade, M.J. & Harmand, J. & Benyahia, B. & Bouchez, T. & Chaillou, S. & Cloez, B. & Godon, J.-J. & Moussa Boudjemaa, B. & Rapaport, A. & Sari, T. & Arditi, R. & Lobry, C., 2016. "Perspectives in mathematical modelling for microbial ecology," Ecological Modelling, Elsevier, vol. 321(C), pages 64-74.
    2. Fowler, A.C. & Winstanley, H.F., 2018. "Microbial dormancy and boom-and-bust population dynamics under starvation stress," Theoretical Population Biology, Elsevier, vol. 120(C), pages 114-120.
    3. Fritsch, Coralie & Harmand, Jérôme & Campillo, Fabien, 2015. "A modeling approach of the chemostat," Ecological Modelling, Elsevier, vol. 299(C), pages 1-13.
    4. Chapwanya, Michael & Dumani, Phindile, 2023. "Spatio-temporal dynamics of microbial population under nutrient-limiting conditions," Applied Mathematics and Computation, Elsevier, vol. 456(C).

    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:246:y:2012:i:c:p:1-10. 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.