Effect of Additional Food on Predator–prey Interactions With Water-Level Fluctuation

Abstract

Significant variations of the water-level of the lake can have a strong impact on the persistence of species. Indeed, when the water-level is low, during the autumn, the contact between the predator and the prey is more frequent, and the predation increases. Conversely, when the water-level is high, in the spring, it is more difficult for the predator to find a prey and the predation decreases. In this paper, we consider a seasonally varying predator–prey model to study the influence of water-level variations on the interaction between two species of fishes in an artificial lake. A seasonal variation of the water-level is introduced in the predation rate. The predator population is provided some additional food apart from the focal prey, and follows logistic growth in the absence of prey population. As control upon the over predation, the predator population is harvested. Sensitivity analysis shows that the biomass of predator population is highly sensitive to the additional food and water variations. In the absence of additional food, our results show bursting patterns of fishes whereas positive periodic solution arises if the additional food is available in sufficient amount. The positive periodic solution is shown to be globally stable. Higher values of water-level fluctuations induce double periodic oscillations. Our findings show that providing additional food source to the generalist predator together with water-level fluctuations exerts a strong influence on the interaction between fishes.

A nonautonomous model for the effect of rarity value on the dynamics of a predator–prey system with variable harvesting

“…The benefit of considering the above forms of q(t) and l(t) is that these time dependent parameters q(t) and l(t) have high and low seasons both in the periods where sin(𝜔t) is positive and negative, respectively [52,53]. Here, the parameters q 1 (0 < q 1 < q) and l 1 (0 < l 1 < l) decide the strength of seasonal forcing in q(t) and l(t), respectively.…”

“…We consider the sinusoidal forms of $$$ q(t) $$$ and $$$ l(t) $$$: $$$$ q(t)&amp;amp;amp;#x0003D;q&amp;amp;amp;#x0002B;{q}_1\sin \left(\omega t\right),l(t)&amp;amp;amp;#x0003D;l&amp;amp;amp;#x0002B;{l}_1\sin \left(\omega t\right). $$$$ The benefit of considering the above forms of $$$ q(t) $$$ and $$$ l(t) $$$ is that these time dependent parameters $$$ q(t) $$$ and $$$ l(t) $$$ have high and low seasons both in the periods where $$$ \sin \left(\omega t\right) $$$ is positive and negative, respectively [52, 53]. Here, the parameters $$$ {q}_1\kern0.1em \left(0&amp;amp;lt;{q}_1&amp;amp;lt;q\right) $$$ and $$$ {l}_1\kern0.1em \left(0&amp;amp;lt;{l}_1&amp;amp;lt;l\right) $$$ decide the strength of seasonal forcing in …”

A systematic study of autonomous and nonautonomous predator–prey models for the combined effects of fear, refuge, cooperation and harvesting

“…Let c denotes the degree of hunting cooperation among the predator species. By considering Michaelis-Menten type harvesting, several researchers have showed that harvesting of species has a strong impact on the population dynamics [ 57 , 58 ]. Here, we introduce nonlinear harvesting of predators by the term where q is the catching capability coefficient, E is the effort applied to harvest the predators, and and are positive constants.…”

Dynamics of a generalist predator–prey system with harvesting and hunting cooperation in deterministic/stochastic environment

“…The role of harvesting in a disease-dominated predator-prey system was explored by Sk and Pal [6]. Sarkar et al [13] investigated the impact of additional foods in a predator-prey system within aquatic ecosystems, considering nonlinear harvesting of predators alongside water level fluctuations.…”