Prey Fear Research Articles

Local and global dynamics of a prey–predator system with fear, Allee effect, and variable attack rate

Fear prompts prey to adopt risk-averse behaviors, such as reduced foraging activity, increased vigilance, and avoidance of areas with high predator presence, which affects its reproduction. In a real scenario, a population requires a minimum density to avoid extinction, known as an Allee threshold. In light of these biological factors, we propose a predator–prey model with (i) a fear effect in a prey population, (ii) an Allee effect in a predator population, and (iii) a non-constant attack rate that modifies the functional response. We ensured the non-negativity and boundedness of the solutions and examined the local and global stability status for each existing steady state solutions. We investigated some deep dynamical properties of the system by varying different parameters, such as cost of fear in prey and strength of the Allee effect in predators and their mortality rate. In codimension one bifurcations, we observed saddle node, Hopf, homoclinic, and coalescence of two limit cycles. Additionally, codimension two bifurcations were observed, including Bautin and Bogdanov Takens bifurcations. To provide a clearer understanding of these bifurcations, we conducted biparametric analysis involving the fear and Allee parameters, as well as the fear parameter and predator mortality rate. Our investigation shows that cost of fear and strength of Allee strongly influences the survival status of the predator. Furthermore, bistability and tristability reveal that the survival and extinction of predator are dependent on the initial population level. Numerical simulations and graphical illustrations are provided to support and validate our theoretical findings.

Catastrophic and noncatastrophic population crashes in a bitrophic system with dynamic additional food provision to cooperative predators.

In this article we contemplate the dynamics of an additional food-provided prey-predator system. We assume that the behavior of cooperative predators induces fear in prey, which radically affects the prey's birth and death rates. We observe that the structural instability imposed by strong cooperative hunting among predators goes away with higher intensities of fear levels affecting the prey's reproductive output and mortality. High levels of prey refuge are not conducive to the survival of predators. In such a situation, adequate supply of high-quality additional food is favorable regarding the persistence and stability of the system. Interestingly, the system potentially exhibits two stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including saddle-node and backward bifurcations, and associated hysteresis effects with prey refuge along with additional food quantity and quality. In the stochastic environment, the system experiences critical transitions through bifurcation-induced tipping events with time-varying additional food for predators. Enhanced disturbance events promote noise-induced switching and tipping events. Finally, our investigation explores whether impending population crashes resulting from the variability of additional food quantity and quality can reliably be predicted using early warning signals in the context of redshifted noise. Overall, our results may provide insights for finding control strategies in the context of community ecology.

Complex dynamical study of a delayed prey–predator model with fear in prey and square root harvesting of both species

In the current study, the dynamics of predator-prey systems under the influence of fear effect on the reproduction of prey population and harvesting on both species has been proposed. Assessing the dynamics of the system with the combined influence of fear and harvesting for various values of n is our central objective. We present comprehensive mathematical findings that cover fundamental dynamical features, the presence of positive equilibria, and the stability of all equilibria. Hopf-bifurcating periodic solutions have been demonstrated to emerge around the positive equilibrium point, and the direction of the Hopf-bifurcating limit cycle is determined using the first Lyapunov coefficient. Furthermore, in two-parameter space, we have seen that the system experiences the Bogdanov-Takens bifurcation. Moreover, we have included predator gestation delay and noticed some chaotic dynamics in the system. In addition, we run through numerical simulations to numerically validate our mathematical findings. The article is concluded with a conclusion at the end.

Prey fear of a specialist predator in a tri-trophic food web can eliminate the superpredator

We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

Stability Analysis of a Prey-Predator Model with Prey Refuge and Fear of Adult Predator

This paper is concerned with a Holling-II stage-structured predator-prey system in which predators are divided into an immature and mature predators. The aim is to explore the impact of the prey's fear caused by the dread of mature predators in a prey-predator model including intraspecific competitions and prey shelters. The theoretical study includes the local and global stability analysis for the three equilibrium points of the system and shows the prey's fear may lead to improving the stability at the positive equilibrium point. A numerical analysis is given to ensure the accuracy of the theoretical outcomes and to testify the conditions of stability of the system near the non-trivial equilibrium points.

Complex dynamical behaviour of a delayed prey-predator model with square root functional response in presence of fear in the prey

ABSTRACT Recently, by studying some field experimental data and research articles it has been observed that due to predation, predators not only affect prey by direct killing, but they also induce the predation fear in prey which reduces its reproduction rate. The grouping behaviour of animals is one of the most important and interesting phenomena in the field of population dynamics. As a result of prey-predator forming groups, many authors have considered different functional responses in their proposed models. In reality, the amount of biomass converted into the predator due to the prey consumption is not instantaneous. To incorporate the gestation delay in this paper we have proposed and analysed a delayed prey-predator model with square root functional response and fear effect in the prey. We have discussed the qualitative analysis of solutions of the considered model in presence and absence of delay. Moreover, the transcritical bifurcation, Hopf bifurcation with it’s direction and the impact of the fear effect on both populations are studied here. Finally, some numerical simulations through graphical illustrations are carried out to support the analytical results.. i

Phenotypically Determined Liver Dysfunction in a Wistar Rat Model of Post-Traumatic Stress Disorder.

The extraordinary situation of the 2019–2022 pandemic caused a dramatic jump in the incidence of post-traumatic stress disorder (PTSD). PTSD is currently regarded not only as a neuropsychiatric disorder, but also as a comorbidity accompanied by cardiovascular diseases, circulatory disorders, liver dysfunction, etc. The relationship between behavioral disorders and the degree of morphofunctional changes in the liver remains obscure. In this study, PTSD was modeled in sexually mature male Wistar rats using predatory stress induced by a prey’s fear for a predator. Testing in an elevated plus maze allowed the rat population to be divided into animals with low-anxiety (LAP) and high-anxiety (HAP) phenotypes. It was found that morphofunctional analysis of the liver, in contrast to its biochemical profiling, provides a clearer evidence that predatory stress induces liver dysfunction in rats of both phenotypes. This may indicate a decrease in the range of compensatory adaptive reactions in stressed animals. However, in HAP rats, the level of morphofunctional abnormalities in the mechanisms responsible for carbohydrate-fat, water-electrolyte and protein metabolism in the liver testified the prenosological state of the organ, while further functional loading and resulting tension of the regulatory systems could lead to homeostatic downregulation. Meanwhile, the liver of LAP animals was only characterized by insignificant diffuse changes. Thus, we demonstrate here a link between behavioral changes and the degree of morphofunctional transformation of the liver.

Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response

This paper investigates the dynamics of a discrete fractional prey-predator system. The prey-predator interaction is modelled using the square root functional response, which appropriately models systems in which the prey exhibits a strong herd structure, implying that the predator generally interacts with the prey along the herd's outer corridor. Some recent field experiments and studies show that predators affect prey by directly killing and inducing fear in prey, reducing prey species' reproduction rate. Considering these facts, we propose a mathematical model to study herd behaviour and fear effect in the prey-predator system. We show algebraically equilibrium points and their stability condition. Condition for Neimark-Sacker bifurcation, Flip bifurcation and Fold bifurcation are given. Phase portraits and bifurcation diagrams are portraits that depict the model's behaviour based on some hypothetical data. Numerical simulations reveal the model's rich dynamics as a result of fear and fractional order.

Stability switching and chaos in a multiple delayed prey–predator model with fear effect and anti-predator behavior

Recent studies demonstrate that the density of prey population is not only affected by direct killing by the predator, but the fear in prey caused by predator also reduces it by cutting down the reproduction rate of prey community, and prey shows anti-predator behavior in response to this fear. In this study, we propose a prey–predator model with fear in prey due to predator and anti-predator behavior by prey against the predator with fear response delay and gestation delay. It is assumed that the predator consumes prey via simplified Holling Type-IV functional response. We evaluate the equilibrium points and study the local and global stability behavior of the system around them. It is observed that our system undergoes Hopf-bifurcation with respect to the fear parameter. Moreover, the system shows the attribute of bi-stability involving two stable equilibriums. Further, we study the dynamics of the delayed system by incorporating fear response delay and gestation delay. We observe that the delayed system suffers Hopf-bifurcation with respect to both delays. Using the normal form method and center manifold theory, the direction and stability of Hopf-bifurcation are studied. Chaotic behavior for delayed system is observed for large values of fear response delay. All these findings are supported by numerical simulation.

Modeling the Effect of Fear in a Prey–Predator System with Prey Refuge and Gestation Delay

Recently, some field experiments and studies show that predators affect prey not only by direct killing, they induce fear in prey which reduces the reproduction rate of prey species. Considering this fact, we propose a mathematical model to study the fear effect and prey refuge in prey–predator system with gestation time delay. It is assumed that prey population grows logistically in the absence of predators and the interaction between prey and predator is followed by Crowley–Martin type functional response. We obtained the equilibrium points and studied the local and global asymptotic behaviors of nondelayed system around them. It is observed from our analysis that the fear effect in the prey induces Hopf-bifurcation in the system. It is concluded that the refuge of prey population under a threshold level is lucrative for both the species. Further, we incorporate gestation delay of the predator population in the model. Local and global asymptotic stabilities for delayed model are carried out. The existence of stable limit cycle via Hopf-bifurcation with respect to delay parameter is established. Chaotic oscillations are also observed and confirmed by drawing the bifurcation diagram and evaluating maximum Lyapunov exponent for large values of delay parameter.

Impact of Predator Signals on the Stability of a Predator–Prey System: A Z-Control Approach

In contrast to long standing view on predator–prey interactions that predators have only direct effect on prey by killing, recent field experimentation on terrestrial vertebrates showed that indirect effect of predators’ fear may alter the behavioral changes on prey, including foraging and reproduction. Usually, prey perceive the signals from predators (chemical and/or vocal cues) and change their life-history and behavior to reduce the probability of being killed. Recently, Wang et al. (J Math Biol 73:1179–1204, 2016) proposed and analyzed a predator–prey model by considering the fear effect on prey population. They concluded that the model dynamics may exhibit both supercritical and subcritical Hopf bifurcation, while the classical predator–prey model exhibits only supercritical Hopf bifurcation. The cost of fear on prey may dramatically reduce foraging and reproduction, which may change the ecosystem stability. In the present investigation, we explore the possible applications of fear in prey due to predators’ signals and error based Z-control mechanism by manipulating the abundance of predator population. Our results suggest that by manipulating or controlling the abundance of predator one can achieve a desired prey population density. We also observe that Z-control mechanism has the property to produce a stable steady-state or a stable limit cycle by excluding the bi-stability situation as observed by Wang et al. We perform extensive numerical simulations to illustrate our analytical findings.