A mathematical model for captive fish with cannibalism

Abstract

A mathematical model is analyzed for a population of fish exhibiting cannibalism during its larval stage. The population is divided into three classes (vulnerable, cannibals, and non-vulnerable). It is assumed that initially, the entire population is vulnerable, and as they develop, individuals transition into one of the other classes. In addition, the interaction between the non-vulnerable and the cannibals is a predator-prey relationship with a Beddington-DeAngelis functional response. The global stability of the equilibrium point is demonstrated and numerical simulations show how food quality influences the cannibalistic behaviour of the population and its survival. Furthermore, it is shown that the solutions fit the data obtained experimentally for \textit{Atractosteus tropicus} in its larval state. This model can be adapted for other fish species that exhibit cannibalism.