Effect Of Prey Refuge Research Articles

Plankton interaction model: Effect of prey refuge and harvesting

Abstract Harmful algal blooms are one of the major threats to aquatic ecosystem. Some phytoplankton species produce toxins during algal bloom and affect other aquatic species as well as human beings. Thus, for the conservation of aquatic habitat, it is much needed to control such phenomenon. In the present study, we propose a mathematical model of toxin-producing phytoplankton and zooplankton species, which follows the Holling Type III functional response. We consider the effect of prey refuge and harvesting on both the species. Boundedness of the proposed model, existence of equilibria, and their stability have been discussed analytically. We also discuss the optimal harvesting policy and existence of bionomic equilibrium. The numerical simulation has also been performed. We identify the control parameters that are responsible for the system dynamics of the model. The parameter prey refuge has a great impact on the dynamics of the model system. Higher value of prey refuge leads to the stable dynamics. Also, the growth rate of phytoplankton acts as a control parameter for the dynamics of the model. The higher value of growth rate of phytoplankton is responsible for oscillatory behavior.

KONTROL OPTIMAL MODEL LESLIE-GOWER DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PERLINDUNGAN PADA PREY

This paper studied the Leslie-Gower predator-prey model with the effects of prey refuge and linear harvesting on predator populations. Prey populations grow as a logistic model when there is no interaction with predators. The predator population is assumed to have economic value. Analysis of Bionomic and Harvesting Control have been studied further. The results showed that the protective effect of prey had an effect on harvesting activity in the population so that it affected profits in predatory harvests. Simulation of several calculations is given to purchase the analysis results

Effects of prey refuge and predator cooperation on a predator–prey system

ABSTRACT We develop and investigate a discrete-time predator–prey model with cooperative hunting among predators and a spatial prey refuge. The system can exhibit two positive equilibria if the magnitude of cooperation is large and the maximal reproduction number of predators is less than one. In such a scenario, the predator population may exhibit a strong Allee effect, and therefore the predator may survive if its density is above the threshold. When the positive equilibrium is unique, we prove that hunting cooperation can destabilize the equilibrium through a Neimark–Sacker bifurcation. Numerical findings indicate that a high degree of predator hunting cooperation can help rescue the predator population if the proportion of prey refuge is large, while hunting cooperation becomes destabilizing when the proportion of refuge is small. Despite hunting cooperation's destabilizing effect, it can facilitate predator persistence, particularly with a large proportion of prey refuge. Furthermore, there exists a wide parameter space where the predator–prey interaction may exhibit chaotic behaviour.

Effect of prey refuge in a three species food chain model with Beddington-DeAngelis functional response

Effect of prey refuge in a three species food chain model with Beddington-DeAngelis functional response

Neimark–Sacker Bifurcation of a Discrete-Time Predator–Prey Model with Prey Refuge Effect

In this paper, we deduce a predator–prey model with discrete time in the interior of R+2 using a new discrete method to study its local dynamics and Neimark–Sacker bifurcation. Compared with continuous models, discrete ones have many unique properties that help to understand the changing patterns of biological populations from a completely new perspective. The existence and stability of the three equilibria are analyzed, and the formation conditions of Neimark–Sacker bifurcation around the unique positive equilibrium point are established using the center manifold theorem and bifurcation theory. An attracting closed invariant curve appears, which corresponds to the periodic oscillations between predators and prey over a long period of time. Finally, some numerical simulations and their biological meanings are given to reveal the complex dynamical behavior.

Effects of prey refuge with Holling type IV functional response dependent prey predator model

ABSTRACT In the present study, we have proposed two mathematical models for predator-prey interactions incorporating prey refuge having significant role in curbing the dynamical behaviour of both the system of prey-predator interactions from both the ecological and mathematical point of view. Here one introduces the prey refuge which depends on the encounters between prey and predator with Holling type IV functional response. Intra-specific competition among predators in searching food is considered in the second model as an additional effect to the first one. After the formulation of the models, the points of equilibria with its stability are systematically analyzed and the existence of bifurcation at the points of equilibrium has been duly carried out through their graphical representations with appropriate discussion in order to validate the applicability of both the system under consideration. It is found that the Hopf bifurcation of both the systems, which is of sub-critical type. The predation rate bears an important role in changing the stability of predator-free equilibrium to co-existence equilibrium. It is also observed that the biomass of prey density increases and predator density decreases with respect to gradual increment of the coefficient of prey refuge. Existence of paradox of enrichments are examined as well in both the model system.

On optimal harvesting policy for two economically beneficial species mysida and herring: a clue for conservation biologist through mathematical model

ABSTRACT In this paper, we have studied the dynamics of two species, ecological model, considering two economically beneficial marine species herring (Clupea harengus) as predator and mysida (Hemimysis anomala) as its prey with Beddington–DeAngelis functional response, the effect of prey refuge and linear harvesting in both populations. The local and global stability of the equilibrium points has been established here. The axial equilibrium point goes through transcritical bifurcation depending on the harvesting effort of both species. The interior equilibrium point goes through super critical Hopf bifurcation depending on prey intrinsic growth rate. Additionally, we have determined the suitable value of the MSY policy for the harvesting and find suitable harvesting level using the optimal control theory, such that both the species persist simultaneously. Finally, numerical simulations have been performed to justify the theoretical findings. It is clear from the numerical simulations that the prey refuge and mutual interference between predators stabilized the unstable system to a stable one. This finding could give some clue to the experimental biologist and business personnel for making management decisions in controlling the harvesting strategies of the two economic beneficial fish populations, mysida and herring.

Contrasting effects of prey refuge on biodiversity of species

Abstract Refugia have been perceived as a major role in structuring species biodiversity, and understanding the impacts of this force in a community assembly with prey–predator species is a difficult task because refuge process can interact with different ecological components and may show counterintuitive effects. To understand this problem, we used a simple two-species model incorporating a functional response inspired by a Holling type-II equation and a prey refuge mechanism that depends on prey and predator population densities (i.e., density-dependent prey refuge). We then perform the co-dimension one and co-dimension two bifurcation analysis to examine steady states and its stability, together with the bifurcation points as different parameters change. As the capacity of prey refuge is varied, there occur critical values i.e., saddle-node and supercritical Hopf bifurcations. The interaction between these two co-dimension one bifurcations engenders distinct outcomes of ecological system such as coexistence of species, bistability phenomena and oscillatory dynamics. Additionally, we construct a parameter space diagram illustrating the dynamics of species interactions as prey refuge intensity and predation pressure vary; as the two saddle-node move nearer to one another, these bifurcations annihilate tangentially in a co-dimension two cusp bifurcation. We also realised several contrasting observations of refuge process on species biodiversity: for instance, while it is believed that some refuge processes (e.g., constant proportion of prey refuge) would result in exclusion of predator species, our findings show that density-dependent prey refuge is beneficial for both predator and prey species, and consequently, promotes the maintenance of species biodiversity.

Effect of predators' behavior on prey-predator interaction

In this paper, we study the effect of the behavior of predators on prey-predator interaction. We assume that there is one prey population that suffers from the fear of predators which could force it to move in to the refuge; and three are two predator populations, one of them is aggressive in its attack and the other one using sit-and-wait procedure, which is less aggressive. All the model’s equilibrium points have been found and their stability was established. The possibility of transcritical and Hopf bifurcation was also investigated and numerical simulations were given. The effect of prey refuge and fear also are detected. The cost of them is to allow the model to reach to double transcritical point. The effect of the competition between prey populations is to convert the model from the stable limit cycle to a spiral stable equilibrium point of afraid prey with predator. When it becomes large it converts the model to the stable trivial solution.

The effect of prey refuge on the dynamics of three species food web system

In this paper, a mathematical model is proposed to study the effect of prey refuge on the dynamics of three species food web system. The food web comprises of a single prey and two competing predators. The two predators predate their prey following Holling type II functional response. In this work we discussed boundedness of the system, existence condition of the equilibrium points and the Jacobean matrix is obtained by linearization techniques. The local stability of the equilibrium points was discussed by using Routh-Hurwitz criteria and the global stability of the equilibrium points by constructing suitable Lyapunov function. Numerical simulation is conducted to support the analytical result. Finally, the effect of prey refuge on the dynamics of one prey two predator was discussed based on the analytical and numerical simulation results. From the numerical simulations, it is found that the dynamical system is persistent for a small value of the refuge constant. However, an increase in the refuge constant leads to the extinction of one of the predator species.

Dynamics of Fractional Holling Type-II Predator-Prey Model with Prey Refuge and Additional Food to Predator

Prey refuge and additional food provided to predator help in balancing the population in ecology. In this paper, we have analysed a fractional Holling Type-II predator-prey model with prey refuge and additional food to predator. Existence and uniqueness of solution is established with the help of existing theory of fractional calculus. Sufficient conditions for existence and stability of equilibrium points are derived. Effect of prey refuge and quality of additional food to predator on balancing the population is crucially analyzed. Theoretical results are supported by numerical simulations.

Impact of fear effect exerted by Pterois volitans on a coral reef ecosystem with parrotfish refuge and harvesting of both fishes

The number of coral reefs around the world is slowly declining due to environmental and anthropogenic reason, and Pterois volitans also put extra stress on coral reefs by decreasing the number of herbivorous fishes (parrotfish). Moreover, uncontrolled growth of algae interrupts the growth of corals since corals and algae grow together on algal turf. Here Parrotfish also play an important role in the enhancement of corals by grazing. In this paper, parrotfish and P-volitans are taken as prey and predator, respectively, and the fear effect on the dynamics of the system is investigated. The effect of prey refuge is also shown. Constant harvesting policy for both fishes is included. Stable coexistence region for two parameter spaces: Hopf bifurcation and saddle-node bifurcation, is shown and formulated for the system. Numerical simulations are illustrated to verify the authenticity of the analytical calculations.

Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases. In the end, several numerical solutions are presented to check the analytical results.

Effect of Prey Refuge and Harvesting on Dynamics of Eco-epidemiological Model with Holling Type III

In this research, we formulate and analyze an eco-epidemiology model of the modified Leslie-Gower model with Holling type III by incorporating prey refuge and harvesting. In the model, we find at most six equilibrium where three equilibrium points are unstable and three equilibrium points are locally asymptotically stable. Furthermore, we find an interesting phenomenon, namely our model undergoes Hopf bifurcation at the interior equilibrium point by selecting refuge as the bifurcation parameter. Moreover, we also conclude that the stability of all populations occurs faster when the harvesting rate increases. In the end, several numerical solutions are presented to check the analytical results.

Supplement of Additional Food: Dynamics of Self-Competitive Prey–Predator System Incorporating Prey Refuge

This paper deals with the dynamics of a prey-dependent two-species model, associating the Holling type II response function. We incorporate the prey refuge to the system with additional food supplement to self-competitive predator. We have found three ecologically significant equilibrium points as well as discussed their stability, instability conditions. The obtained results suggest that the coexisting equilibrium point can go through a Hopf bifurcation for some suitable value of prey refuge. Numerical simulations are performed to support all the analytical findings and to investigate the effects of additional food and self-interactions among predators for various densities of prey refuge. It can be observed that additional food supports coexisting behavior while intraspecific competition does not enhance coexistence so much but reducing the predator population, supports a stable solution. Although a very strong prey refuge forces the predators to extinct in both cases. Moreover, a comparison of four food web models has been performed to elaborate significantly the effects of prey refuge, additional food, and self-competition, respectively, on the system dynamics. The results yield that the model can fairly illustrate a realistic environmental ecology of two interacting populations and may be useful for species conservation.

Stability analysis of a fractional-order predator\u2013prey model incorporating a constant prey refuge and feedback control

In this paper, a kind of fractional-order predator–prey (FOPP) model with a constant prey refuge and feedback control is considered. By analyzing characteristic equations, we carry out detailed discussion with respect to stability of equilibrium points of the considered FOPP model. Besides, the effects of prey refuge and feedback control are also studied by numerical analysis. Our study reveals that prey refuge and feedback control can be used to adjust the biomass of prey species and predator species such that prey species and predator species finally reach a better state level.

About the optimal harvesting of a fuzzy predator–prey system: a bioeconomic model incorporating prey refuge and predator mutual interference

To understand roles of fuzzy biological parameters, in this paper, we propose a fuzzy predator–prey harvesting model that incorporates both the effects of prey refuge and predator mutual interference. Using the triangular fuzzy numbers for the imprecise parameters, we first study the existence of the feasible equilibria and their global stability and then discuss the bionomic equilibrium and the possible optimal harvesting policy. Numerical simulations are carried out to illustrate our analytical results, based on which discussions and conclusions are made. They show that the fuzziness of biological parameters can greatly affect the dynamics of the ecological system.

Dynamical behavior of a generalized eco-epidemiological system with prey refuge

A generalized eco-epidemiological system with prey refuge is proposed in this paper. The saturation incidence kinetics and a generalized functional response are used to describe the contact process and the predation process, respectively. Based on mathematical issue, the local and global stability properties, Hopf bifurcation, and permanence of the dynamical system are investigated. Based on the ecological aspects, the impact of prey refuge on the dynamical consequences of the eco-epidemiological system and the mechanism of prey refuge are discussed. The results reveal that the stabilizing and destabilizing effects occur under some certain conditions. Based on epidemiological issue, the controlling strategies of the infectious disease are proposed. The results show that the prey refuge can control the spread of disease by the relative level of prey refuge. This study has resolved some basic and interesting issues for an eco-epidemiological system with a generalized response function and the effect of prey refuge.

食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响

PDF HTML阅读 XML下载 导出引用 引用提醒 食饵庇护所对斑块环境下Leslie-Gower捕食系统的影响 DOI: 10.5846/stxb201704130654 作者: 作者单位: 河南大学 数学与统计学院 应用数学研究所 作者简介: 通讯作者: 中图分类号: Q141 基金项目: 中国博士后科学基金项目（2017M612388）；国家自然科学基金项目（31200312）；河南大学科学基金项目（yqpy20140045） The effect of prey refuge in a patchy Leslie-Gower predation system Author: Affiliation: Henan UniversityInstitute of Applied Mathematics, School of Mathematics and Information Sciences, Fund Project: 摘要 | 图/表 | 访问统计 | 参考文献 | 相似文献 | 引证文献 | 资源附件 | 文章评论 摘要:建立了一个显式含有空间庇护所的两斑块Leslie-Gower捕食者-食饵系统。假设只有食饵种群在斑块间以常数迁移率迁移，且在每个斑块上食饵间的迁移比局部捕食者-食饵相互作用发生的时间尺度要快。利用两个时间尺度，可以构建用来描述所有斑块总的食饵和捕食者密度的综合系统。数学分析表明，在一定条件下，存在唯一的正平衡点，并且此平衡点全局稳定。进一步，捕食者的数量随着食饵庇护所数量增加而降低；在一定条件下，食饵的数量随着食饵庇护所数量增加先增加后降低，在足够强的庇护所强度下，两物种出现灭绝。对比以往研究，利用显式含有和隐含空间庇护所的数学模型所得结论不一致，这意味着在研究庇护所对捕食系统种群动态影响时，空间结构可能起着重要作用。 Abstract:Predation is a common and important species interaction in many ecological systems. Mathematical models are important and very useful tools to understand and analyze the dynamic behavior of the predator-prey systems. Classical predator-prey models such as the Lotka-Volterra model and Leslie-Gower model can be used in a homogeneous environment. However, in general, the environment is heterogeneous and this can be represented using a set of discrete patches connected by migration. In the simplest situation, the two patches predator-prey model is used, which is composed of the local population process and the dispersal from patch to patch. Prey escaping predation in space or time is widely observed. Spatial or temporal refuges are well-known examples of this class of mechanism. Most theoretical studies have focused on how refuges add stability to the system with predator-prey interactions. The role of spatial and temporal refuges on species coexistence in communities with intraguild predation has also been investigated. These studies have two characteristics. First, most of the research is based on the Lotka-Volterra framework, only a few on the Leslie-Gower framework. Second, the traditional way to model this is to modify the functional response of predators and consider prey refuges, implicitly. The prey refuge can positively affect the growth of prey and negatively that of predators, because the decrease of predation success can lead to the reduction of prey mortality. On the other hand, the hiding behavior of prey could be either advantageous or detrimental for the involved populations. For example, the prey population in the refuges has a low or even negative growth rate because they are rarely offered feeding or mating opportunities. That is, there is a different population structure between the prey refuge and the normal habitat patch. Therefore, it is more reasonable to consider prey refuge explicitly. Based on the above consideration, this paper proposes a Leslie-Gower predator-prey model incorporating the effect of prey refuge explicitly in a two-patch environment. We assume that the prey dispersal is at a constant migration rate and is faster than the local predator-prey interaction, while the predator cannot disperse between patches. Taking advantage of the two different time scales, we use aggregation methods to obtain a reduced (aggregated) model governing the total prey and predator densities. The mathematical analysis of the aggregated model shows that there exists a unique and globally stable positive equilibrium under a certain condition. Simple mathematical analysis shows that increasing the amount of refuge can increase predator densities. As far as the prey species is concerned, under a certain condition, there exists a threshold, such that, for the prey refuge smaller than this threshold, increasing the amount of prey refuge can increase the prey densities, and if the prey refuge is larger than this threshold, increasing the amount of prey refuge can decrease the prey densities. Furthermore, prey and predator will become extinct when the effect of prey refuge is strong enough. In contrast to previous research, the effects of refuges used by the prey are different in spatially implicit and spatially explicit models. The discrepancy suggests that the spatial structure is important when refuges are included. 参考文献 相似文献 引证文献

Complex dynamics generated by negative and positive feedback delays of a prey–predator system with prey refuge: Hopf bifurcation to Chaos

Various field and laboratory experiments show that prey refuge plays a significant role in the stability of prey–predator dynamics. On the other hand, theoretical studies show that delayed system exhibits a much more realistic dynamics than its non-delayed counterpart. In this paper, we study a multi-delayed prey–predator model with prey refuge. We consider modified Holling Type II response function that incorporates the effect of prey refuge and then introduce two discrete delays in the model system. A negative feedback delay is considered in the logistic prey growth rate to represent density dependent feedback mechanism and a positive feedback delay is considered to represent the gestation time of the predator. Our study reveals that the system exhibits different dynamical behaviors, viz., stable coexistence, periodic coexistence or chaos depending on the values of the delay parameters and degree of prey refuge. The interplay between two delays for a fixed value of prey refuge has also been determined. It is noticed that these delays work in a complementary fashion. In addition, using the normal form theory and center manifold argument, we derive the explicit formulae for determining the direction of the bifurcation, the stability and other properties of the bifurcating periodic solutions.