Effects Of Refuge Research Articles

Dynamical behavior of a discrete-time predator–prey system incorporating prey refuge and fear effect

This paper explores the effects of fear and refuge in a discrete-time two species predator–prey model. The fraction of prey that seeks refuge is assumed to be proportional to the amount of predators. The local stability of the corresponding fixed points is analyzed. The conditions of flip bifurcation and Neimark–Sacker bifurcation at the positive fixed point are described. The sufficient conditions for the positive fixed point to be globally asymptotically stable are derived in this article. Utilization of hybrid control strategy stabilizes the system’s chaotic nature. Finally, the paper supports the theoretical analysis with a numerical simulation that demonstrates the intricate nature of the system. It is observed that both fear effect and prey refuge can destabilize or stabilize the system depending on the value of handling time. Also, fear effect can restore stability in the system that exhibits chaos due to a high prey growth rate.

A discrete-time dynamical model of prey and stage-structured predator with juvenile hunting incorporating negative effects of prey refuge

This paper examines a discrete predator–prey model that incorporates prey refuge and its detrimental impact on the growth of the prey population. Age structure is taken into account for predator species. Furthermore, juvenile hunting along with its negative effects in the form of prey counterattack is considered. This paper provides a comprehensive analysis of the existence and stability conditions pertaining to all possible fixed points of this system. The impact of the parameters reflecting prey growth and prey refuge is thoroughly discussed. This paper delves into the occurrence of the Neimark–Sacker bifurcation and period-doubling bifurcation, specifically in relation to the parameters associated with prey growth rate and prey refuge. Numerous numerical simulations are presented in order to validate the theoretical findings.

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

Study on dynamic behavior of two fishery harvesting models: effects of variable prey refuge and imprecise biological parameters

Study on dynamic behavior of two fishery harvesting models: effects of variable prey refuge and imprecise biological parameters

A generalist predator–prey system with the effects of fear and refuge in deterministic and stochastic environments

In the present study, we investigate the dynamics of a generalist predator–prey system by considering that the fear of predators suppresses the birth rate and enhances the intraspecies competition of the prey species. Also, we assume that a constant proportion of the prey population is taking refuge, which results in a reduction in the predation pressure. We consider Cosner functional response to describe the interactions between prey and predator species. We rigorously analyze the proposed model analytically as well as numerically. We see that the system exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle–node, Hopf and transcritical bifurcations with varying degrees of fear, on the prey’s reproduction and intraspecies competition, induced by the predator species. The emergence of multistability scenarios in the system is also stimulated by the birth rate of prey species and the growth in predator species due to the additional food sources. We modify our proposed model to its stochastic counterpart by considering the impact of environmental white noises on the natural death rates of both prey and predator species. The simulation results for the stochastic system demonstrate that the fluctuations in the densities of prey and predator populations due to stochastic perturbations are highly sensitive to the intensities of the environmental noises. Additionally, we find that the stochastic system showcases noise-induced transitions whenever the deterministic system exhibits bistability.

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.

Small‐scale habitat complexity preserves ecosystem services on coral reefs

AbstractCoral reef habitat quality is declining in many locations because of heatwaves (coral bleaching) and other disturbances. Reef‐building corals provide refuge from predation, so declining complexity restricts the transfer of energy to upper trophic levels.We use a size‐based ecosystem model to test systematically the effects of refuge at specific sizes and the impacts of distributions of refuges that vary in size. Outcomes are assessed in terms of ecosystem service provision.Simulations indicate that refuge sheltering fish between 5 and 10 cm in length enhances fish biomass and fisheries productivity, for example, increasing herbivore biomass by up to 80%.We identify and present a range of refuge profiles that can theoretically improve ecosystem service provision by as much as sixfold. Profiles where refuge availability decreases with increasing fish size consistently outrank other designs.Synthesis and application: These results highlight how critical small‐scale refuge is for coral reefs, and how we might design artificial reefs to maximise service provision.

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.

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

In the present study, we investigate the roles of fear, refuge and hunting cooperation on the dynamics of a predator–prey system, where the predator population is subject to harvesting at a nonlinear rate. We also focus on the effects of seasonal forcing by letting some of the model parameters to vary with time. We rigorously analyze the autonomous and nonautonomous models mathematically as well as numerically. Our simulation results show that the birth rate of prey and the fear of predators causing decline in it, and harvesting of predators first destabilize and then stabilize the system around the coexistence of prey and predator; if the birth rate of prey is very low, both prey and predator populations extinct from the ecosystem, and for a range of this parameter, only the prey population survive. The fear of predators responsible for increase in the intraspecific competition among the prey species and the refuge behavior of prey have tendency to stabilize the system, whereas the cooperative behavior of predators during the hunting time destroys stability in the ecosystem. Numerical investigations of the seasonally forced model showcase the appearances of periodic solution, higher periodic solutions, bursting patterns and chaotic dynamics.

Dynamical System Analysis of the Prey-predator Interactions involving Prey Refuge and Herd Behaviors in Preys

By employing a prey refuge mechanism, more preys can be protected from predation. Prey species are also better protected from predation when they congregate in herds. However, what if the prey refuge and herd behavior mechanisms were combined in a system? To investigate this phenomenon, we consider two different prey-predator systems with prey refuge capacity. The first system is a simple prey-predator with prey refuge, whereas the second system considers prey refuge and prey herd behavior mechanisms. Using these models, we explore how different prey refuge strategies affect species interactions in both systems. To accomplish this, we use theoretical techniques (e.g., computing steady states and performing the stability analysis) and numerical bifurcation analysis to demonstrate various dynamical behaviors of these two prey-predator systems. Once prey refuge is treated as a bifurcation parameter, we observe the occurrence of supercritical Hopf and transcritical bifurcations in both systems. Furthermore, we explore the dynamic effects of prey refuge and predator handling time on species population interactions: our findings reveal that using both prey refuge and herd behavior as escape strategies; it is possible to dilute the predation pressure and ensure species biodiversity.

A delay nonautonomous model for the effects of fear and refuge on predator–prey interactions with water-level fluctuations

The interaction of prey (small fish) and predator (large fish) in lakes/ ponds at temperate and tropical regions varies when water level fluctuates naturally during seasonal time. We relate the perceptible effect of fear and anti-predator behavior of prey with the water-level fluctuations and describe how these are influenced by the seasonal changing of water level. So, we consider these as time-dependent functions to make the system more realistic. Also, we incorporate the time-dependent delay in the negative growth rate of prey in predator–prey model with Crowley–Martin-type functional response. We clearly provide the basic dynamics of the system such as positiveness, permanence and nonpersistence. The existence of positive periodic solution is studied using Continuation theorem, and suffiecient conditions for globally attractivity of positive periodic solution are also derived. To make the system more comprehensive, we establish numerical simulations, and compare the dynamics of autonomous and nonautonomous systems in the absence as well as the presence of time delay. Our results show that seasonality and time delay create the occurrence of complex behavior such as prevalence of chaotic disorder which can be potentially suppressed by the cost of fear and prey refuge. Also, if time delay increases, then system leads a boundary periodic solution. Our findings assert that the predation, fear of predator and prey refuge are correlated with water-level variations, and give some reasonable biological interpretations for persistence as well as extinction of species due to water-level variations.

Dynamics of an infected prey–generalist predator system with the effects of fear, refuge and harvesting: deterministic and stochastic approach

Dynamics of an infected prey–generalist predator system with the effects of fear, refuge and harvesting: deterministic and stochastic approach

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.

A patchy predator-prey model with effect of prey refuge and migration

In this paper, a patchy predator-prey model with the effect of prey refuge and migration is proposed. The effect of prey refuge and migration on the dynamical behaviors of the proposed model is investigated by applying an analytical approach. The results show the stabilizing and destabilizing effects of prey refuge and migration are observed under some certain conditions. For the effect of prey refuge, the destabilizing impact is found in heterogeneous predation model with Holling II type functional response. For the effect of migration, the dynamical consequences is bistable while the level of prey refuge is less than a threshold value. The destabilizing effect is firstly observed theoretically when the attack rates of predators is proportional to the migration ratio.

A nonautonomous model for the effects of refuge and additional food on the dynamics of phytoplankton-zooplankton system

In this paper, a mathematical model for the interacting dynamics of phytoplankton-zooplankton is proposed. The phytoplankton have the ability to take refuge and release toxins to avoid over predation by zooplankton. The zooplankton are provided some additional food to persist in the system. The phytoplankton are assumed to be affected directly by external toxic substances whereas zooplankton are affected indirectly by feeding on the affected phytoplankton. We incorporate seasonal variations in the model, assuming the level of nutrients, refuge and the rate of toxins released by phytoplankton as functions of time. Our results show that when high toxicity and refuge cause extinction of zooplankton, providing additional food supports the survival of zooplankton population and controls the phytoplankton population. Prey refuge and additional food have stabilizing effects on the system; higher values of the former results in extinction of zooplankton whereas phytoplankton disappear for larger values of the latter. Seasonality in nutrients level and toxins released by phytoplankton generate higher periodic solutions while time-dependent refuge of phytoplankton causes the occurrence of a period-three solution. The possibility of finding additional food for zooplankton may push back the ecosystem to a simple stable state from a complex dynamics.

The effects of simple density-dependent prey diffusion and refuge in a predator-prey system

We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: (1) prey spread follows a nonlinear diffusion rule, (2) preys have a refuge zone (sometimes called “protection zone”) where predators cannot enter, (3) predators move following linear diffusion. We present a bifurcation analysis for the system that shows the existence of positive solutions at the steady state. We complement the theoretical results with numerical computations and compare our results with those obtained in the case of having linear diffusion for the prey movement. Our results show that both models, with linear and nonlinear diffusion for the prey, have the same bifurcation point and the positive solution curves are virtually the same in a neighborhood of this point, but they get drastically different as the bifurcation parameter approaches zero.

A delay non-autonomous model for the combined effects of fear, prey refuge and additional food for predator

In this paper, we investigate the combined effects of fear, prey refuge and additional food for predator in a predator–prey system with Beddington type functional response. We observe oscillatory behaviour of the system in the absence of fear, refuge and additional food whereas the system shows stable dynamics if anyone of these three factors is introduced. After analysing the behaviour of system with fear, refuge and additional food, we find that the system destabilizes due to fear factor whereas refuge and additional food stabilize the system by killing persistent oscillations. We extend our model by considering the fact that after sensing the chemical/vocal cue, prey takes some time for assessing the predation risk. The delayed system shows chaotic dynamics through multiple stability switches for increasing values of time delay. Moreover, we see the impact of seasonal change in the level of fear on the delayed as well as non-delayed system.

Combining refuges with transgenic insect releases for the management of an insect pest with non-recessive resistance to Bt crops in agricultural landscapes

Reinforcing the high-dose/refuge strategy with releases of transgenic insects has been suggested as a method for simultaneously managing agricultural pest populations and resistance to transgenic crops. Theoretical and empirical studies have shown that these approaches can work when deployed against closed populations and the assumptions of the HDR strategy are met. However, field-evolved resistance is often linked to non-recessive resistance or refuge non-compliance, and pest management regimes are likely to take place at the landscape-level. It is therefore important to understand how effective such strategies are when resistance is non-recessive, and how they could be employed in agricultural landscapes. We developed a spatially-explicit model to investigate the efficacy of strategies combining refuges with transgenic insect releases to manage a pest with non-recessive resistance in agricultural landscapes. We compared two release strategies, area-wide releases and localised releases targeted at population hotspots, and analysed the effects of refuge and release parameters on population and resistance dynamics. Area-wide releases reliably achieved landscape-level pest eradication. Localised releases also eradicated the pest when low release thresholds were combined with high release ratios, and maintained the pest at low densities when insufficient to achieve extinction. Reinforcing refuges with localised releases also greatly enhanced the probability of resistance extinction. However, when resistance remained in the population, localised releases prevented resistance from reaching fixation rather than greatly delaying or reversing resistance evolution. Our work indicates that combining refuges with simple release policies is effective for landscape-level pest suppression when the HDR assumptions are violated, but more nuanced release strategies may be required to enhance the benefits to resistance management.

Effect of fear on prey-predator dynamics: Exploring the role of prey refuge and additional food.

The effect of induced fear in the prey due to the presence of a predator can alone develop anti-predator resistance to such an extent that it might reduce the prey reproduction in a significant amount. As fear can perceptibly affect the densities of the terrestrial vertebrates, here we investigate the cost of fear on a Holling type II predator-prey model associated with prey refuge and additional food to the predator. We evidently provide conditions on the existence and stability of equilibria as well as the occurrence of the Hopf bifurcation. Besides, we study how the presence of fear re-calibrates the effects of prey refuge and additional food in terms of quality and quantity on the system dynamics. We observe that the effect of fear not only reduces the predator density but also considerably drives the system toward stability. All the results presented here are mainly analytical but to make it more comprehensive, we perform numerical simulation. Moreover, to show the vast applicability of our results, we compare it with a few other models according to the presence of fear, refuge, and additional food.

Training fish for restocking: refuge and predator training in the hatchery has limited benefits for a marine fish.

Large numbers of hatchery-reared fish are released in stocking programmes; however, success is limited by high mortality. Predation is seen as the main cause of deaths but might be reduced by training fish before release to avoid predators and/or use refuge. In this study on a potential restocking species, yellowfin bream Acanthopagrus australis, the effects of predator training and refuge on the behaviour of fish in the hatchery were tested. In the first experiment, juvenile bream were exposed to predatory mangrove jack (Lutjanus argentimaculatus) fed exclusively on bream flesh while housed in tanks with and without refuge. Predator training altered fish behaviour when fish were re-exposed to predators, but the effects were subtle and varied between groups of fish. In contrast, refuge created strong and consistent changes in behaviour, significantly slowing down the amount of time that fish took to consume food. A second experiment focused on the effects of refuge. Bream were trained to use artificial seagrass or house bricks as refuge and then exposed to mangrove jacks in a laboratory predation experiment. When refuge was available, fish significantly slowed down their feeding rate. There was a small, transient increase in survival for fish given seagrass refuges, but this was irrespective of whether the bream were trained to use refuge. The results of this study indicate that the use of refuge may be innate and the benefits of refuge may be available to naive hatchery-reared fish or fish trained to use refuge shortly before release. This suggests that there is potential to improve post-release survival of fingerlings without time-consuming and expensive hatchery training.