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

César Antonio Sepúlveda-Quiroz, Luis Miguel Valenzuela (), Gamaliel Blé, Rafael Martínez-García, Carlos Alfonso Álvarez-González and Antioco López-Molina
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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
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

Mathematics, 2024, vol. 12, issue 21, 1-16

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.

Keywords: global stability; cannibal; Hopf bifurcation; coexistence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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