IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i21p3380-d1509299.html
   My bibliography  Save this article

Mathematical Model to Study the Effect of Refuge on Cannibalism in Atractosteus tropicus

Author

Listed:
  • César Antonio Sepúlveda-Quiroz

    (Laboratorio de Fisiología en Recursos Acuáticos, División Académica de Ciencias Biológicas, UJAT, Carretera Villahermosa–Cárdenas Km 0.5, Villahermosa C.P. 86039, Tabasco, Mexico
    Tecnológico Nacional de México-Instituto Tecnológico de Villahermosa, Carretera Villahermosa-Frontera, Km 3.5, Ciudad Industrial, Villahermosa C.P. 86010, Tabasco, Mexico)

  • Luis Miguel Valenzuela

    (División Académica Multidisciplinaria de Jalpa de Méndez, UJAT, Carretera Nacajuca–Jalpa de Méndez, R/a Rivera Alta, Jalpa de Méndez C.P. 86205, Tabasco, Mexico)

  • Gamaliel Blé

    (División Académica de Ciencias Básicas, UJAT, Km 1, Carretera Cunduacán–Jalpa de Méndez, Cunduacán C.P. 86690, Tabasco, Mexico)

  • Rafael Martínez-García

    (Laboratorio de Fisiología en Recursos Acuáticos, División Académica de Ciencias Biológicas, UJAT, Carretera Villahermosa–Cárdenas Km 0.5, Villahermosa C.P. 86039, Tabasco, Mexico)

  • Carlos Alfonso Álvarez-González

    (Laboratorio de Fisiología en Recursos Acuáticos, División Académica de Ciencias Biológicas, UJAT, Carretera Villahermosa–Cárdenas Km 0.5, Villahermosa C.P. 86039, Tabasco, Mexico)

  • Antioco López-Molina

    (División Académica Multidisciplinaria de Jalpa de Méndez, UJAT, Carretera Nacajuca–Jalpa de Méndez, R/a Rivera Alta, Jalpa de Méndez C.P. 86205, Tabasco, Mexico)

Abstract

Cannibalism is a behavior that different species of fish exhibit in the early stages of their life, and it has been widely reported. In Tabasco, Mexico, the ancestral species Atractosteus tropicus is farmed, which is a freshwater fish with a high nutritional and economic value. This species exhibits high cannibalistic behavior both in its larval and juvenile stages, which considerably decreases its production. Therefore, strategies have been developed to mitigate the effects of this behavior. One of them is the placement of shelters (rocks and artificial vegetation), which allow the vulnerable population to protect themselves from cannibals. The goal of this work is to study the effect of shelters on the cannibalistic behavior of the A. tropicus population through a mathematical model. The population is divided into two classes, the vulnerable population (prey) and the cannibal population (predator). Moreover, a system of ordinary differential equations is established, which is analyzed, and sufficient conditions for the coexistence of the two species are shown. Numerical simulations show coexistence by varying levels of refuge. The results obtained in this work can be applied to other populations that exhibit cannibalistic behavior.

Suggested Citation

  • César Antonio Sepúlveda-Quiroz & Luis Miguel Valenzuela & Gamaliel Blé & Rafael Martínez-García & Carlos Alfonso Álvarez-González & Antioco López-Molina, 2024. "Mathematical Model to Study the Effect of Refuge on Cannibalism in Atractosteus tropicus," Mathematics, MDPI, vol. 12(21), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:21:p:3380-:d:1509299
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/21/3380/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/21/3380/
    Download Restriction: no
    ---><---

    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:12:y:2024:i:21:p:3380-:d:1509299. 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.