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Mathematics
Article . 2024 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Mathematics
Article . 2024
Data sources: DOAJ
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Mathematical Model to Study the Effect of Refuge on Cannibalism in Atractosteus tropicus

Authors: César Antonio Sepúlveda-Quiroz; Luis Miguel Valenzuela; Gamaliel Blé; Rafael Martínez-García; Carlos Alfonso Álvarez-González; Antioco López-Molina;

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

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.

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Keywords

coexistence, QA1-939, Hopf bifurcation, cannibal, global stability, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
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