IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v222y2011i3p598-605.html
   My bibliography  Save this article

Deterministic approach to the study of the interaction predator–prey in a chemostat with predator mutual interference. Implications for the paradox of enrichment

Author

Listed:
  • Cabrera F, María I.

Abstract

Our understanding of predator–prey systems has progressed in recent decades mainly due to the ability to test models in chemostats. This study aimed to develop a deterministic model using differential equations to reproduce the dynamics of the interaction of a predator and a prey in a two stage chemostat focusing in the proposed previous prey dependent model of Fussmann et al. (2000) [Fussmann, G.F., Ellner, S.P., Shertzer, K.W., Hairston Jr., N.G., 2000. Crossing the Hopf bifurcation in a live predator–prey system. Science 290, 1358–1360]. The main problem with that model, but parameterized with the values obtained in this study (particularly the concentration of nutrient), was that the temporal trajectory of both the prey and the predator showed very high peaks that eventually led to the extinction of predator in all cases. In the same way the experimental time series obtained in this study does not exhibit the behavior predicted by the model of Fussman et al. On the contrary, as prey density increases, the system actually becomes more stable. Finally, the model that best explained the behavior of the predator and prey in the chemostat, at medium to high dilution rates, was the ratio dependent (algae–nitrogen) model with mutual interference measured in the chemostat (rotifer–alga) and that incorporated the age structure of the predator. Qualitative analysis of the dynamic behavior enabled evaluation of coexistence at equilibrium, coexistence on limit cycles, extinction of the predator or extinction of both populations.

Suggested Citation

  • Cabrera F, María I., 2011. "Deterministic approach to the study of the interaction predator–prey in a chemostat with predator mutual interference. Implications for the paradox of enrichment," Ecological Modelling, Elsevier, vol. 222(3), pages 598-605.
    • Handle: RePEc:eee:ecomod:v:222:y:2011:i:3:p:598-605
    DOI: 10.1016/j.ecolmodel.2010.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380010004795
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2010.09.008?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.

    References listed on IDEAS

    as
    1. Edward McCauley & Roger M. Nisbet & William W. Murdoch & Andre M. de Roos & William S. C. Gurney, 1999. "Large-amplitude cycles of Daphnia and its algal prey in enriched environments," Nature, Nature, vol. 402(6762), pages 653-656, December.
    2. Harmand, J. & Godon, J.J., 2007. "Density-dependent kinetics models for a simple description of complex phenomena in macroscopic mass-balance modeling of bioreactors," Ecological Modelling, Elsevier, vol. 200(3), pages 393-402.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jian, Fuji & Jayas, Digvir S. & White, Noel D.G. & Smith, E.A., 2008. "Numerical analysis and parameter estimation technique for insect population redistribution models," Ecological Modelling, Elsevier, vol. 211(1), pages 47-56.
    2. Ginzburg, Lev R. & Jensen, Christopher X.J. & Yule, Jeffrey V., 2007. "Aiming the “unreasonable effectiveness of mathematics” at ecological theory," Ecological Modelling, Elsevier, vol. 207(2), pages 356-362.
    3. 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.
    4. Morozov, Andrew & Sen, Moitri & Banerjee, Malay, 2012. "Top-down control in a patchy environment: Revisiting the stabilizing role of food-dependent predator dispersal," Theoretical Population Biology, Elsevier, vol. 81(1), pages 9-19.
    5. Nisbet, Roger M. & Martin, Benjamin T. & de Roos, Andre M., 2016. "Integrating ecological insight derived from individual-based simulations and physiologically structured population models," Ecological Modelling, Elsevier, vol. 326(C), pages 101-112.
    6. Vanoverbeke, Joost, 2008. "Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia," Ecological Modelling, Elsevier, vol. 216(3), pages 385-401.

    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:222:y:2011:i:3:p:598-605. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.