Stabilizing ecosystem dynamics: The toxicity effect on an ecosystem in the presence of self-defence

Abstract

One of the important problems in environmental biology is the effect of toxins on the ecosystems focusing on trophic interactions with the planning of self-defence. This study presents a new eco-toxicant dynamical model to describe the interactions between prey, middle predator, and top predator. In this model, the Lotka-Volterra is used to devour the prey by the middle predator, which is affected by surrounding toxins. The middle predators, in turn, are subject to predation by top predators with Holling-IV functional. However, they spread toxins as a way of defensive strategy. The dynamic behavior of the proposed system is extensively explored by analyzing the boundedness of solutions and equilibrium points, followed by analyzing their stability under various ecological conditions. This study also contributes to a refined understanding of the trophic interplay under toxic stress. Determining key factors that lead to the systems’ stability by exploiting the variation in parameter space is a primary objective. Important parameter ranges that potentially determine the stabilities of parameters used in the models are identified. These variations vital factors for stabilizing the ecosystem correspond to environmental toxicity levels and the extent to which species positively or negatively interact. These theoretical results are supported by numerical simulations which provide insights into the complex interactions of the ecosystem under the influence of toxic. It is also supported by a practical comprehensive model of an aquatic ecosystem that focuses on the lionfish species due to its importance in affecting the parrotfish and the moray eel given its predatory tendencies and associated toxicity.