Prey System Research Articles

High order accuracy scheme for modeling the dynamics of predator and prey in heterogeneous environment

The aim of this work is to develop a compact finite-difference approach for modeling the dynamics of predator and prey based on reaction-diffusion-advection equations with variable coefficients. Methods. To discretize a spatially inhomogeneous problem with nonlinear terms of taxis and local interaction, the balance method is used. Species densities are determined on the main grid whereas fluxes are computed at the nodes of the staggered grid. Integration over time is carried out using the high-order Runge-Kutta method. Results. For the case of one-dimensional annular interval, the finite-difference scheme on the three-point stencil has been constructed that makes it possible to increase the order of accuracy compared to the standard second-order approximation scheme. The results of computational experiment are presented and comparison of schemes for stationary and non-stationary solutions is carried out. We conduct the calculation of accuracy order basing on the Aitken process for sequences of spatial grids. The calculated values of the effective order accuracy for the proposed scheme were greater than the standard two: for the diffusion problem, values of at least four were obtained. Decrease was obtained when directional migration was taken into account. This conclusion was also confirmed for non-stationary oscillatory regimes. Conclusion. The results demonstrate the effectiveness of the derived scheme for dynamics of predator and prey system in a heterogeneous environment.

Dynamics of a diffusive two predators- one prey system

This paper analyses a diffusive predator-prey model consisting of a single prey species and two predator species with modified Leslie-Gower term Holling type II functional response subject to the homogeneous Neumann boundary condition. Local stability condition is derived by the application of Routh-Hurwitz criterion. Global asymptotic stability of the unique positive steady state is shown by constructing a suitable Lyapunov function when self diffusion is allowed where as non-constant positive steady states can exist due to the presence of cross-diffusion, that means, cross-diffusion can induce stationary pattern. Taking the cross diffusion as a bifurcation parameter, one can show the existence of positive non-constant solutions with the help of bifurcation theory. A brief conclusion completes the paper.

Global bifurcation in a general Leslie–Gower type predator[formula omitted]prey system with indirect prey-taxis

The influence of the indirect prey-taxis on the spatiotemporal dynamics of a class predator−prey system with predator functional response is studied. By analyzing the corresponding characteristic equation, the local stability of the positive equilibrium and the related bifurcations of the system are discussed. The critical values of the indirect prey-taxis coefficient leading to the Hopf bifurcation, steady state bifurcation, Turing-Turing bifurcation and double-Hopf bifurcation are derived. Taking the indirect prey-taxis coefficient as the bifurcation parameter, we obtain the global structure of nonconstant steady states bifurcating from the positive equilibrium by an abstract bifurcation theorem. Moreover, the stability condition of bifurcation solutions is carried out. Our results suggest that attractive indirect prey-taxis can destabilize the positive equilibrium and induced the emergence of spatially inhomogeneous periodic solution. And the higher the secretion level of chemoattractant by the prey, the more likely the system is to exhibit spatial patterns.

Timing and synchrony of migration in a freshwater fish: Consequences for survival.

Animal migration is one of the most spectacular and visible behavioural phenomena in nature with profound implications for a range of ecological and evolutionary processes. Successful migration hinges on the ability to exploit temporary resources (e.g. food) and evade threats (e.g. predators) as they arise, and thus the timing of migration is often regarded as a dominant predictor of individual migratory success. However, with the exception of intensively studied taxa (mainly birds), relatively few studies have investigated inter-individual annual and seasonal variation in migratory timing and performance, or tested predictions on how migration across high and low predation-risk habitats may exert selection on migratory timing. In particular, studies that assess the survival consequences of variation in migratory timing remain rare, which is most likely due to the logistical challenges associated with monitoring survival success and population-level characteristics simultaneously. Here, we address the above-mentioned questions using roach Rutilus rutilus, a fish that migrates from lakes characterised by high predation risk into low-risk streams during winter. Specifically, we used individual-based tracking of roach in two European lake systems over multiple migration periods (9 and 7 years respectively), to obtain highly detailed (year-round scheduling, repeat journeys and the fate of individuals) data on the variability/synchrony of migratory timing in spring and autumn respectively. We report seasonal differences in the variability of migratory timing, with lower variance and higher migration synchrony in spring lake arrival timing as compared to autumn lake departure timing. Furthermore, the timing of autumn migration is more variable across years than the timing of spring migration. Second, we find that later arrival to the lake habitat is positively associated with apparent survival from 1 year to the next, whereas we found no effect of lake departure timing on survival probability. These findings represent rare evidence showing how intraspecific variation in timing in migratory fish differs across years and seasons, and how variation in timing can translate into survival consequences for prey in systems characterised by high predation risk.

Effects of the Invasive Fish Species Ameiurus nebulosus on Microbial Communities in Peat Pools

Disturbances in the functioning of peatlands, due to growing human impact, climate change and the appearance of alien invasive species, are becoming increasingly common. Analysis of trophic relationships in the predator (invasive alien species)–prey system is extremely important for understanding the functioning of peat pools—small water bodies formed in peatlands by peat extraction. These issues are, as yet, very little understood. The aim of this study was to examine the impact of Ameiurus nebulosus, an alien and invasive fish species dominant in these pools, on the microbial communities and small metazoa (phycoflora, bacteria, heterotrophic flagellates, ciliates, and crustaceans) in peat pools. The laboratory experiment included two groups of treatments simulating natural conditions: treatments without fish and treatments with brown bullhead. The water temperature was manipulated as well. The presence of brown bullhead in combination with climate changes was shown to cause a change in the structure of microbial communities. This is reflected in a decrease in the abundance of planktonic crustaceans and an increase in ciliates. The overlapping effects of alien species and gradual climate warming may intensify the eutrophication of peatland ecosystems and the increase in the proportion of cyanobacteria, thereby affecting the carbon cycle in these ecosystems.

Dynamics of discrete predator- prey system with fear effect and density dependent birth rate of the prey species

This paper analyses a discrete predator-prey system with fear effect and density dependent birth rate of the prey species. The fixed points of the system are determined and their stability is examined. The criterion for Neimark-Sacker bifurcation and flip bifurcation is developed. The chaotic orbit at an unstable fixed point can be stabilized by applying the state feedback control method. Numerically, we illustrate our analytical findings and observe the complex behaviour of the system that leads to stable state to chaotic one.

Dynamics Twin Cannibalism of Two Predator and Two Prey System with Prey Defense

The study discusses the condition of the existence of all non-negative equilibrium points. There are 9 realistic equilibrium points from the constructed model. A local stable condition is obtained, a point of equilibrium that is completely biologically feasible. The analytical method on the mathematically formed model is limited, so numerical simulation is also given to explore the model. Numerical simulation is intervened in a model that will show growth in trajectories. The tendency of trajectories in prey one and predator one species is relatively the same because the interactions that occur are intensive. Likewise, prey two and predator two occur, and the interactions that occur cause population growth grow to fluctuate. Differences occur in both types of species, namely predator-prey one and predator-prey two. In the one interaction group, growth tends to be more volatile and moves slowly towards the point of stability in population growth. Incidence is inversely proportional to the interaction of species two which tend to be faster towards the stability point. In general, the results of numerical simulations show that there is a pattern formation in the predator-prey system that grows sustainabley.

Production of SARS-CoV-2 N Protein-Specific Monoclonal Antibody and Its Application in an ELISA-Based Detection System and Targeting the Interaction Between the Spike C-Terminal Domain and N Protein.

SARS-CoV-2 infections continue to spread quickly by human-to-human transmission around the world. Therefore, developing methods to rapidly detect SARS-CoV-2 with high sensitivity are still urgently needed. We produced a monoclonal antibody that specifically detects the N protein of SARS-CoV-2 and recognizes N protein in cell lysates of SARS-CoV-2–infected Vero cells but not in cell lysates of MERS-CoV- or HCoV-OC43-infected Vero cells. This antibody recognized N protein in SARS-CoV-2 clades S, GR, and GH and recognized N protein in all the SARS-CoV-2 clades to ∼300 pfu. Previously, we reported that the coronavirus N protein interacts with the C-terminal domain of the spike protein (Spike CD). In this study, we developed an ELISA-based “bait and prey” system to confirm the interaction between SARS-CoV-2 Spike CD and N protein using recombinant fusion proteins. Furthermore, this system can be modified to quantitatively detect SARS-CoV-2 in culture media of infected cells by monitoring the interaction between the recombinant Spike CD fusion protein and the viral N protein, which is captured by the N protein–specific antibody. Therefore, we conclude that our N protein–specific monoclonal antibody and our ELISA-based bait and prey system could be used to diagnose SARS-CoV-2 infections.

Nonlinear dynamics of the predator – prey system in a heterogeneous habitat and scenarios of local interaction of species

The purpose of this work is to study the influence of various local models in the equations of diffusion–advection– reaction on the spatial processes of coexistence of predators and prey under conditions of a nonuniform distribution of the carrying capacity. We consider a system of nonlinear parabolic equations to describe diffusion, taxis, and local interaction of a predator and prey in a one-dimensional habitat. Methods. We carried out the study of the system using the dynamical systems approach and a computational experiment based on the method of lines and a scheme of staggered grids. Results. The behavior of the predator – prey system has been studied for various scenarios of local interaction, taking into account the hyperbolic law of prey growth and the Holling effect with nonuniform carrying capacity. We have established paradoxical scenarios of interaction between prey and predator for several modifications of the trophic function. Stationary and nonstationary solutions are analyzed considering diffusion and directed migration of species. Conclusion. The trophic function that considers the heterogeneity of the resource is proposed, which does not lead to paradoxical dynamics.

Global Analysis of Stage Structure Two Predators Two Prey Systems Under Harvesting Effect for Mature Predators

This article examines set a prey-predator population model system with structural stages. Development of a mathematical model of a sustainable population of a population of living things. Structure stages are formed in predator populations, namely immature and mature. The predation function that corresponds to the characteristics in the ecosystem is the predation process of Holling I. The interaction in the population model that is carried out analysis is the equilibrium value formed from the population model. There are eight equilibrium values that arise from simple simulations. The equilibrium is E 1(0,0,0,0), E 2(0, k,0,0), E 3(k,0,0,0), E 4(k, k,0,0), E 5(0,0,0, A 1), E 6(A 2,0, A 3, A 4), E 7(0, A 5, A 6, A 7) and E 8(A 8, A 9, A 10, A 11). However, only one equilibrium value is analyzed to obtain stability. Stability is seen by requiring four eigenvalues with the Jacobian matrix. As well as the chosen value is used to find the amount of harvest carried out. The linearization of differential equations is an alternative way in this study to obtain equilibrium values. Each equilibrium value has the characteristics and terms of its stability. The Routh-Hurwitz criterion becomes a condition of its stability characteristics. Meanwhile, exploitation efforts in the population are carried out to see the changes that occur. Harvesting carried out obtained harvesting business W = 0.01313666667. For the maximum benefit obtained π = 4.997259008. This advantage is the stability and sustainability of the ecosystem.

Balanced harvesting in two predators one prey system

In this research, we discuss balancing two essential ecosystem services, known as resilience and yield, in a harvested two predators one prey system. We study how these two ecosystem services respond to different types of harvesting plans applied to the system. In individual harvesting, we observe that prey harvesting is suitable for generating more yield while either predator harvesting gives more resilience. Several patterns are possible based on the intensity of harvesting efforts applied to prey or the predator in simultaneous harvesting. This study shows that a balanced harvest between prey and predators may give more than the selective harvesting of any species yielding and stabilizing the ecosystem. Even if this fair strategy is not a cooperative situation for both resilience and yield, it may be the most favorable approach to scale those services. Finally, we may state that it would help us correlate the safest position (corresponds to the maximizing resilience yield) and the good views (which corresponds to the maximum sustainable return) to safeguard our ecosystems.

Emergent effects of two rocky intertidal predators on prey: Interaction of crabs and sea-stars may reduce mussel mortality

Two predator – one prey systems are widespread in nature, and have been important to both ecological theory and practice. A primary question for these systems is whether the two predators produce “emergent effects”: greater or less prey mortality than expected based on the two predators acting alone. We conducted an in-lab experiment on a two predator (the crab Cancer productus and the sea-star Evasterias troschelii), one prey (the bivalve Mytilus trossulus) system common to the marine rocky intertidal of the northeastern Pacific. In 156 mesocosm experimental trials, mortality rates of M. trossulus were compared between Crabs only, Sea-stars only, and a Mixed treatment with both predators present. The experiment used a substitutive design, i.e., predator density was held constant. Based on a Linear Mixed Effects Model, the interactive effects of the number of predator species and water temperature had the greatest effect on mussel mortality. For the observed temperature range, the two predators in the Mixed treatment killed fewer mussels than expected based on the average mussel mortality of the one-predator treatments. As the two predators were never observed to interfere with each other directly, the reduced prey mortality is possibly a trait-mediated indirect interaction, involving behavioral modification (mutual avoidance) on the part of the predators. Temperature may mediate these results; crabs consumed more mussels at higher temperatures while sea-stars did so at lower temperatures. As these experiments were conducted over a large part of the known temperature range for this region, these results suggest that mussels may experience seasonal shifts in both predation rates and the identity of the predator, which should be investigated in future field studies. Increasingly warmer temperatures anticipated in the coming century could increase mussel mortality due to predation by cancrid crabs, which appear to have temperature responsive feeding rates. Understanding this two-predator one-prey system better is particularly important given that mussels are important foundational species, and recent climate change has affected abundances of the taxa involved.

Harmless Delay in Mutualist, Prey and Several Predators Systems

Harmless Delay in Mutualist, Prey and Several Predators Systems

Hopf–Zero bifurcation in an age-dependent predator–prey system with Monod–Haldane functional response comprising strong Allee effect

The article is intended to study the Hopf−Zero bifurcation of a novel age-dependent predator−prey system with Monod−Haldane functional response comprising strong Allee effect. Here in this system the predators fertility function f(x) is regarded as a piecewise function with respect to their maturation period τ. The system is interpreted as a non-densely defined abstract Cauchy problem, and the condition of the existence and uniqueness of the non-negative steady state for a coupled dynamic system both a partial differential equation and an ordinary differential equation is yielded. Via employing the center manifold theorem and normal form theory for semilinear equations with non-dense domain, we discover much richer fresh dynamical behavior in an age-dependent predator−prey system than the existing ones.

Opportunistic random searcher versus intentional search image user

We consider two types of optimal foragers: a random searcher and a search image user. A search image user can find its desired prey with higher and undesired prey with lower probability than a random searcher. Our model considers the density-dependent travelling time and the time duration of reproduction (oviposition). In the framework of optimal foraging theory for one predator–two prey systems, we find that there are ranges of prey densities in which the search image user has a higher net energy intake, and there are other ranges of prey densities in which the random searcher has higher net energy intake. The damsel bug Nabis pseudoferus Remane (Hemiptera: Nabidae) is a generalist predator rather than an omnivore. This species has a wide range of arthropod prey (predominantly insects and mites). Several aspects of the biology of this species have been studied, especially its cannibalistic behaviour, which is a quite important feature because N. pseudoferus is often used as a biological control agent against lepidopteran pests in greenhouse crops. Experimentally, we found that Nabis is a search image user in the above sense.

Dynamical study of two predators and one prey system with fractional Fourier transform method

In this work, we investigate both the analytical and numerical studies of the dynamical model comprising of three species systems. We analyze the linear stability of stationary solutions in the one‐dimensional multisystem modeling the interactions of two predators and one prey species. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. The analysis results presented have established the possibility of the three‐interacting species to coexist harmoniously, this feat is achieved by combining the local and global analyses to determine the global dynamics of the system. In the presence of a fractional diffusion term, we introduced a fractional Fourier transform for solving the system modeled by fractional partial differential equations. The main advantages of this method are that it yields a fully diagonal representation of the fractional operator with exponential accuracy and a completely straightforward extension to high spatial dimensions. The scheme is described in detail and justified by a number of computational experiments.

О динамике косимметричных систем хищников и жертв

О динамике косимметричных систем хищников и жертв

Spatiotemporal complexity of a discrete space-time predator−prey system with self- and cross-diffusion

In this research, we investigate the spatiotemporal dynamics of a discrete space-time predator−prey system with self- and cross-diffusion. Through stability analysis and bifurcation analysis, Turing pattern formation conditions are derived and two nonlinear mechanisms of pattern formation are found, i.e., pure Turing instability and Hopf-Turing instability. Numerical simulations reveal rich dynamics of the discrete predator−prey system. In spatially homogeneous case, stable homogeneous stationary states, homogeneous periodic, quasiperiodic and chaotic oscillating states are exhibited; in spatially heterogeneous case, a surprising variety of prey and predator patterns are described, including spotted, striped, labyrinth, gapped, spiral, circled patterns and many intermediate patterns. Moreover, sensitivity of spatiotemporal pattern formation to initial conditions is predicted along with Hopf-Turing instability, suggesting the self-organization of diverse patterns under identical parametric conditions. In comparison with former results in literature, the discrete version of reaction-diffusion model developed in this research capture more complicated and richer nonlinear dynamical behaviors, contributing to a new comprehending on the complex pattern formation of spatially extended discrete predator−prey systems.

Dynamics of a predator-prey system with a mate-finding Allee effect on prey

We consider a predator--prey system with nonmonotonic functional response and a hyperbolic type of mate-finding Allee effect on prey. A detailed mathematical analysis of the system, including the stability and a series of bifurcations (a saddle-node, a Hopf, and a Bogdanov--Takens bifurcation), has been given. The mathematical results show that the system is highly sensitive to the parameters and initial status. It exhibits a stable limit cycle, or different types of heteroclinic curves, or a homoclinic loop when parameters take suitable values.

Periodic Traveling Waves Generated by Invasion in Cyclic Predator--Prey Systems: The Effect of Unequal Dispersal

Periodic traveling waves (wavetrains) have been an invaluable tool in the understanding of spatiotemporal oscillations observed in ecological data sets. Various mechanisms are known to trigger this...