Contrasting effects of prey refuge on biodiversity of species

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.

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.

A Leslie-Gower predator prey model with density dependent birth rate on prey species and prey refuge is proposed and studied in this paper. Sufficient condition which ensure the global stable of the positive equilibrium is obtained. Our study indicates density dependent birth rate of prey species has negative effect on the final density of both prey and predator species. Density dependent birth rate may lead to the Allee effect of prey species and enhance the extinction chance of the species. Numeric simulations are carried out to show the feasibility of the main results.

In this study, we have analyzed a mathematical model on predator–prey interactions incorporating prey refuge and additive Allee effect on the prey species. The various dynamical behaviors of the system have analyzed, considering the prey refuge is proportional to both the prey and predator species with Beddington–DeAngelis functional response. None, single, or two coexistence equilibria can exist at the first quadrant of the phase space considering strong additive Allee effect in the system. The permanence, local stability, saddle-node bifurcation, existence of a stable limit cycle and Hopf bifurcation are examined under some parametric conditions. We have also calculated the first Lyapunov number to define the nature of Hopf bifurcating periodic solution. Moreover, it has established a parameter subset at which the dynamical system may have a cusp point of co dimension 2 (Bogdanov–Takens bifurcation). Finally, we have executed an adequate numerical simulation to authenticate our analytical findings.

Prey-taxis is the process that predators move preferentially toward patches with highest density of prey. It is well known to have an important role in biological control and the maintenance of biodiversity. To model the coexistence and spatial distributions of predator and prey species, this paper concerns nonconstant positive steady states of a wide class of prey-taxis systems with general functional responses over 1D domain. Linearized stability of the positive equilibrium is analyzed to show that prey-taxis destabilizes prey–predator homogeneity when prey repulsion (e.g., due to volume-filling effect in predator species or group defense in prey species) is present, and prey-taxis stabilizes the homogeneity otherwise. Then, we investigate the existence and stability of nonconstant positive steady states to the system through rigorous bifurcation analysis. Moreover, we provide detailed and thorough calculations to determine properties such as pitchfork and turning direction of the local branches. Our stability results also provide a stable wave mode selection mechanism for thee reaction–advection–diffusion systems including prey-taxis models considered in this paper. Finally, we provide numerical studies of prey-taxis systems with Holling–Tanner kinetics to illustrate and support our theoretical findings. Our numerical simulations demonstrate that the $$2\times 2$$ prey-taxis system is able to model the formation and evolution of various striking patterns, such as spikes, periodic oscillations, and coarsening even when the domain is one-dimensional. These dynamics can model the coexistence and spatial distributions of interacting prey and predator species. We also give some insights on how system parameters influence pattern formation in these models.

Dynamics of a stochastic prey–predator system with prey refuge, predation fear and its carry-over effects

In predator-prey interactions, the efficiency of the predator is dependent on characteristics of both the predator and the prey, as well as the structure of the environment. In a field enclosure experiment, we tested the effects of a prey refuge on predator search mode, predator efficiency and prey behaviour. Replicated enclosures containing young of the year (0+) and 1-year-old (1+) perch were stocked with 3 differentially sized individuals of either of 2 piscivorous species, perch (Perca fluviatilis), pike (Esox lucius) or no piscivorous predators. Each enclosure contained an open predator area with three small vegetation patches, and a vegetated absolute refuge for the prey. We quantified the behaviour of the predators and the prey simultaneously, and at the end of the experiment the growth of the predators and the mortality and habitat use of the prey were estimated. The activity mode of both predator species was stationary. Perch stayed in pairs in the vegetation patches whereas pike remained solitary and occupied the corners of the enclosure. The largest pike individuals stayed closest to the prey refuge whereas the smallest individuals stayed farthest away from the prey refuge, indicating size-dependent interference among pike. Both size classes of prey showed stronger behavioural responses to pike than to perch with respect to refuge use, distance from refuge and distance to the nearest predator. Prey mortality was higher in the presence of pike than in the presence of perch. Predators decreased in body mass in all treatments, and perch showed a relatively stronger decrease in body mass than pike during the experiment. Growth differences of perch and pike, and mortality differences of prey caused by predation, can be explained by predator morphology, predator attack efficiency and social versus interference behaviour of the predators. These considerations suggest that pike are more efficient piscivores around prey refuges such as the littoral zones of lakes, whereas perch have previously been observed to be more efficient in open areas, such as in the pelagic zones of lakes.

A predator–prey model with Holling type II functional response incorporating a constant prey refuge and independent harvesting in either species is investigated. Some sufficient conditions of the instability and stability properties to the equilibria and the existence and uniqueness to limit cycles for the model are obtained. We also show that influence of prey refuge and harvesting efforts on equilibrium density values. One of the surprising finding is that for fixed prey refuge, harvesting has no influence on the final density of the prey species, while the density of predator species is decreasing with the increasing of harvesting effort on prey species and the fixation of harvesting effort on predator species. Numerical simulations are carried out to illustrate the obtained results and the dependence of the dynamic behavior on the harvesting efforts or prey refuge.

Interactive effects of prey refuge and additional food for predator in a diffusive predator-prey system

Influence of predator mutual interference and prey refuge on Lotka–Volterra predator–prey dynamics

On a Leslie–Gower predator–prey model incorporating a prey refuge

Local dispersal, trophic interactions and handling times mediate contrasting effects in prey-predator dynamics

In an environment, the food chains are balanced by the prey–predator interactions. When a predator species is provided with more than one prey population, it avails the option of prey switching between prey species according to their availability. So, prey switching of predators mainly helps to increase the overall growth rate of a predator species. In this work, we have proposed a two prey–one predator system where the predator population adopts switching behavior between two prey species at the time of consumption. Both the prey population exhibit a strong Allee effect and the predator population is considered to be a generalist one. The proposed system is biologically well-defined as the system variables are positive and do not increase abruptly with time. The local stability analysis reveals that all the predator-free equilibria are saddle points whereas the prey-free equilibrium is always stable. The intrinsic growth rates of prey, the strong Allee parameters, and the prey refuge parameters are chosen to be the controlling parameters here. The numerical simulation reveals that in absence of one prey, the other prey refuge parameter can change the system dynamics by forming a stable or unstable limit cycle. Moreover, a situation of bi-stability, tri-stability, or even multi-stability of equilibrium points occurs in this system. As in presence of the switching effect, the predator chooses prey according to their abundance, so, increasing refuge in one prey population decreases the count of the second prey population. It is also observed that the count of predator population reaches a comparatively higher value even if they get one prey population at its fullest quantity and only a portion of other prey species. So, in the scarcity of one prey species, switching to the other prey is beneficial for the growth of the predator population.

In this paper, the dynamical behaviors of a modified Leslie-Gower predator-prey model incorporating fear effect and prey refuge are investigated. We delve into the construction of the model and its biological significance, with preliminary results encompassing positivity, boundedness, and persistence. The stability of the system’s boundary and positive equilibrium points is proven by calculating the real part of the eigenvalues of the Jacobian matrix. At the positive equilibrium point, we demonstrate that the system’s unique positive equilibrium is globally asymptotically stable by using the Dulac criterion. Furthermore, at this equilibrium point, we employ the Implicit Function Theorem to discuss how fear effects and prey refuges influence the population densities of both prey and predators. Finally, numerical simulations are conducted to validate the above-mentioned conclusions and explored the impact of Predator-taxis sensitivity α on dynamics of the system.

Can adaptive prey refuge facilitate species coexistence in Bazykin’s prey–predator model?