IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i7p1065-d379051.html
   My bibliography  Save this article

Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans

Author

Listed:
  • Yuri V. Tyutyunov

    (Southern Scientific Centre of the Russian Academy of Sciences (SSC RAS), Chekhov Street, 41, Rostov-on-Don 344006, Russia)

  • Anna D. Zagrebneva

    (Faculty of IT Systems and Technologies, Don State Technical University (DSTU), Gagarin Square, 1, Rostov-on-Don 344000, Russia)

  • Andrey I. Azovsky

    (Faculty of Biology, Lomonosov Moscow State University (MSU), Leninskie Gory, 1-12, Moscow 119991, Russia
    Shirshov Institute of Oceanology, Russian Academy of Sciences, Nakhimovskiy Prospekt, 36, Moscow 117218, Russia)

Abstract

A simple mathematical model capable of reproducing formation of small-scale spatial structures in prey–predator system is presented. The migration activity of predators is assumed to be determined by the degree of their satiation. The hungrier individual predators migrate more frequently, randomly changing their spatial position. It has previously been demonstrated that such an individual response to local feeding conditions leads to prey–taxis and emergence of complex spatiotemporal dynamics at population level, including periodic, quasi-periodic and chaotic regimes. The proposed taxis–diffusion–reaction model is applied to describe the trophic interactions in system consisting of benthic diatom microalgae and harpacticoid copepods. The analytical condition for the oscillatory instability of the homogeneous stationary state of species coexistence is given. The model parameters are identified on the basis of field observation data and knowledge on the species ecology in order to explain micro-scale spatial patterns of these organisms, which still remain obscure, and to reproduce in numerical simulations characteristic size and the expected lifetime of density patches.

Suggested Citation

  • Yuri V. Tyutyunov & Anna D. Zagrebneva & Andrey I. Azovsky, 2020. "Spatiotemporal Pattern Formation in a Prey-Predator System: The Case Study of Short-Term Interactions Between Diatom Microalgae and Microcrustaceans," Mathematics, MDPI, vol. 8(7), pages 1-15, July.
  • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1065-:d:379051
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/7/1065/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/8/7/1065/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Banerjee, Malay & Pal, Swadesh & Roy Chowdhury, Pranali, 2022. "Stationary and non-stationary pattern formation over fragmented habitat," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Yuri V. Tyutyunov, 2023. "Spatial Demo-Genetic Predator–Prey Model for Studying Natural Selection of Traits Enhancing Consumer Motility," Mathematics, MDPI, vol. 11(15), pages 1-18, August.
    3. Vitaly G. Il’ichev & Dmitry B. Rokhlin, 2023. "Paradoxes of Competition in Periodic Environments: Delta Functions in Ecological Models," Mathematics, MDPI, vol. 12(1), pages 1-12, December.

    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:gam:jmathe:v:8:y:2020:i:7:p:1065-:d:379051. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.