Extinction Of Predator Population Research Articles

A Predator–Prey System with a Modified Leslie–Gower and Prey Stage Structure Scheme in Deterministic and Stochastic Environments

The evolution of the population ecosystem is closely related to resources and the environment. Assuming that the environmental capacity of a predator population is positively correlated with the number of prey, and that the prey population has a sheltered effect, we investigated a predator–prey model with a juvenile–adult two-stage structure. The dynamical behaviour of the model was examined from two distinct environmental perspectives, deterministic and stochastic, respectively. For the deterministic model, the conditions for the existence of equilibrium points were obtained by comprehensive use of analytical and geometric methods, and the local and global asymptotic stability of each equilibrium point was discussed. For the stochastic system, the effect of noise intensity on the long-term dynamic behavior of the population was investigated. By constructing appropriate Lyapunov functions, the criteria that determined the extinction of the system and the ergodic stationary distribution were given. Finally, through concrete examples and numerical simulations, the understanding of the dynamic properties of the model was deepened. The results show that an improvement in the predator living environment would lead to the decrease in the prey population, while more prey shelters could lead to the decline or even extinction of predator populations.

Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

A Stochastic Holling-Type II Predator-Prey Model with Stage Structure and Refuge for Prey

In this paper, we study a stochastic Holling-type II predator-prey model with stage structure and refuge for prey. Firstly, the existence and uniqueness of the global positive solution of the system are proved. Secondly, the stochastically ultimate boundedness of the solution is discussed. Next, sufficient conditions for the existence and uniqueness of ergodic stationary distribution of the positive solution are established by constructing a suitable stochastic Lyapunov function. Then, sufficient conditions for the extinction of predator population in two cases and that of prey population in one case are obtained. Finally, some numerical simulations are presented to verify our results.

Acaricides sublethal effects are more harmful to predatory mite Phytoseiulus macropilis Banks (Acari: Phytoseiidae) than to the pest Tetranychus urticae Koch (Acari: Tetranychidae)

To evaluate the lethal and sublethal effect of the abamectin and dimethoate acaricides on the predator P. macropilis and its prey T. urticae. Scope: Lethal and sublethal effect of acaricides on P. macropilis and T. urticae. Methodology: The lethal and sublethal effect of the abamectin and dimethoate acaricides on the predator P. macropilis and its prey T. urticae was determined in laboratory experiments. Main results: T. urticae was 2.6-fold and 4.2-fold more tolerant than P. macropilis to abamectin and dimethoate, respectively. The instantaneous rate of increase of prey and predator decreased linearly with increasing concentrations of both acaricides. However, the instantaneous rate of increase of the predator population decreased more rapidly than that of the pest, resulting in extinction of predator populations, whereas the pest population persisted. Conclusions: Farmers may achieve better control by not spraying acaricides, but managing the populations of this predator in the field using natural enemy conservation techniques.

On a predator-prey system interaction under fluctuating water level with nonselective harvesting

Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.

Modeling the plankton–fish dynamics with top predator interference and multiple gestation delays

Many prey organisms have developed defense mechanisms against predation. If the predator can encounter in a limited spatial domain, the feeding rates reflect interference between predators and the corresponding functional response depends on both predator and prey densities. In this manuscript, an attempt has been made to understand the role of top predator interference and gestation delays on the dynamics of a three-species food chain model involving intermediate and top predators population. Interaction between the prey and an intermediate predator follows the Monod–Haldane functional response, while that between the top predator and its prey depends on Beddington–DeAngelis-type functional response. Analytically, we study the essential mathematical features such as boundedness, stability and direction of bifurcating periodic solution around the coexisting equilibrium for the model system. Numerically, we study the Hopf and transcritical bifurcations scenarios with respect to inhibitory effect of phytoplankton against zooplankton and death rate of fish population for the non-delayed system. Further, we study the stability behavior of the delayed model system. Model system exhibits irregular behavior when the interference is high or gestation period is larger than its critical value. Further, the system shows extinction of predators with the increase in inhibitory effect. Stability domain plots with respect to different important system parameters for non-delayed system and delay parameters for delayed system give a significant impact to study the stability of the different equilibrium points and bifurcation scenarios of both non-delayed and delayed systems. Our results point out the complexity of three-way interactions between phytoplankton, zooplankton and fish population in marine environment and highlight the role of predator interference and gestation delays in exhibiting the chaotic dynamics and extinction of predator population.