Models Of Predator-prey Interactions Research Articles

The umbrella value of caribou management strategies for biodiversity conservation in boreal forests under global change

Single-species conservation management is often proposed to preserve biodiversity in human-disturbed landscapes. How global change will impact the umbrella value of single-species management strategies remains an open question of critical conservation importance. We assessed the effectiveness of threatened boreal caribou as an umbrella for bird and beetle conservation under global change. We combined mechanistic, spatially explicit models of forest dynamics and predator-prey interactions to forecast the impact of management strategies on the survival of boreal caribou in boreal forest. We then used predictive models of species occupancy to characterize concurrent impacts on bird and beetle diversity. Landscapes were simulated based on three scenarios of climate change and four of forest management. We found that strategies that best mitigate human impact on boreal caribou were an effective umbrella for maintaining bird and beetle assemblages. While we detected a stronger effect of land-use change compared to climate change, the umbrella value of management strategies for caribou habitat conservation were still impacted by the severity of climate change. Our results showed an interplay among changes in forest attributes, boreal caribou mortality, as well as bird and beetle species assemblages. The conservation status of some species mandates the development of recovery strategies, highlighting the importance of our study which shows that single-species conservation can have important umbrella benefits despite global change.

Ransomware as a Predator: Modelling the Systemic Risk to Prey

The accelerated pace with which companies, governments, and institutions embrace digital transformation is creating opportunities for economic prosperity, but also increases the threat landscape. Recent orchestrated cyber-attacks have revealed the unpredictability of the harm they can cause in our society, rendering the creation of new models that capture systemic risk more critical than ever. In this article, we model the behaviour of one of the most prominent cyber-attacks: ransomware; in particular, ransomware that propagates between organisations via the Internet. We draw concepts from epidemiological models of viral propagation to reason about policies that can reduce the systemic cyber-risk to the community. To achieve this, we present a compartment-based epidemiological model of predator-prey interactions and run simulations to validate the importance of defensive controls that reduce the propagation of ransomware. Our model suggests that with specific defensive controls in place, other response policies may also become more effective. A prey policy to not pay the ransom may improve the ability of the victim population to recover; while information-sharing may reduce the number of organisations compromised if certain conditions on the speed of threat-intelligence sharing practices are met. These results indicate the validity of the approach, which we believe could be extended to explore the impacts of a broad range of attacker and defender behaviours and characteristics of the digital environment on systemic risk.

CAN GLOBAL WARMING CHANGE PREDATOR–PREY DYNAMICS: A MODELLING STUDY

In this paper, a two-species predator–prey interaction model has been developed. It is assumed that prey grows logistically in the absence of global warming and predator species. The harvesting of predator has been considered to study the model. It is considered that global warming in the environment increased gradually due to different natural processes and human activities. Also, it is considered that global warming may decrease due to increase of prey. Again, it is assumed that global warming may decrease due to natural decay rate. Different equilibrium points are determined and the stability of the model has been investigated around these equilibrium points. Existence condition of Hopf bifurcation has been studied with respect to the growth rate of prey [Formula: see text]. It is observed that the increase of intrinsic growth rate prey may stabilize the model. It is also observed that the increase of consumption rate of prey in the presence of global warming may show some interesting dynamics. It is found that the harvesting rate decreases due to the increase of global warming.

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.

Stability and Hopf bifurcation in an eco-epidemiological system with the cost of anti-predator behaviors.

The fear effect is a powerful force in prey-predator interaction, eliciting a variety of anti-predator responses which lead to a reduction of prey growth rate. To study the impact of the fear effect on population dynamics of the eco-epidemiological system, we develop a predator-prey interaction model that incorporates infectious disease in predator population as well as the cost of anti-predator behaviors. Detailed mathematical results, including well-posedness of solutions, stability of equilibria and the occurrence of Hopf bifurcation are provided. It turns out that population density diminishes with increasing fear, and the fear effect can either destabilize the stability or induce the occurrence of periodic behavior. The theoretical results here provide a sound foundation for understanding the effect of the anti-predator behaviors on the eco-epidemiological interaction.

Larval fish counteract ram and suction to capture evasive prey.

A simple hydrodynamic model of predator-prey interactions between larval clownfish and copepod prey is used to elucidate how larval fish capture highly evasive copepods. Fish larvae are considered to be suction feeders; however, video observations revealed that successful captures by clownfish larvae were preceded by rapidly accelerating lunges (ram), while the role of suction to draw prey into the fish's mouth was less clear. Simulations were made of the fish's strike, varying strengths of ram and suction to characterize optimal strategies for copepod capture given known evasive capabilities. Our results suggest that, contrary to expectations, suction feeding is dominant only in older larvae, whereas ram feeding is the dominant mode for early larvae. Despite the relatively weak suction produced by smaller larvae, it still plays a crucial role in prey capture through hydrodynamic stealth. Escape-triggering water deformations from the strike can be cancelled through controlled suction. Experimental data obtained from larval clownfish agree with model results, suggesting that the primary role of suction in early larvae is providing hydrodynamic stealth rather than capture.

The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

Misic, a general deep learning-based method for the high-throughput cell segmentation of complex bacterial communities.

Studies of bacterial communities, biofilms and microbiomes, are multiplying due to their impact on health and ecology. Live imaging of microbial communities requires new tools for the robust identification of bacterial cells in dense and often inter-species populations, sometimes over very large scales. Here, we developed MiSiC, a general deep-learning-based 2D segmentation method that automatically segments single bacteria in complex images of interacting bacterial communities with very little parameter adjustment, independent of the microscopy settings and imaging modality. Using a bacterial predator-prey interaction model, we demonstrate that MiSiC enables the analysis of interspecies interactions, resolving processes at subcellular scales and discriminating between species in millimeter size datasets. The simple implementation of MiSiC and the relatively low need in computing power make its use broadly accessible to fields interested in bacterial interactions and cell biology.

A chemotaxis predator-prey model with indirect pursuit-evasion dynamics and parabolic signal

We analyse a reaction-diffusion model for predator-prey interaction featuring both prey and predator taxis mediated by two signals. Both predator and prey densities are governed by parabolic equations, and the prey and predator detect each other indirectly by means of odor or visibility fields modelled by parabolic or elliptic equations – instead of only elliptic equations, as in earlier work. We prove the global well-posedness of the systems, as well as boundedness properties using the de Giorgi method and estimates in Lebesgue spaces. We also present some numerical simulations to illustrate the dynamical behaviour.

Mathematical analysis of the influence of prey escaping from prey herd on three species fractional predator-prey interaction model

This research investigates the impact of prey herd dread from the two types of predators using a fractional-order-derivative model. The investigated model considers one type of prey next to predator and super predator. Note that the pray that exhibits herd behavior with the possibility of quitting the group due to the fear generated by the pursuit of predators, it is also considered that there is a predator consumes this prey and a super-predator consumes them both (prey and predator). This dread can be elaborated by the number of the escaped prey from the herd, which influences the evolution of the whole food chain. Our purpose is to study how this fear can affect the existence of the species, where we will discuss it in details through this paper. Indeed, it is obtained that the considered system undergoes an interesting behavior, which is elaborated by the presence of Hopf bifurcation. The obtained mathematical and ecological results are discussed numerically using a numerical scheme used for obtaining the graphical representations.

Dynamical analysis and effects of law enforcement in a social interaction model

Crime is a rising problem all over the world. Over the years, several researches have been conducted to coin suitable model systems and intervention strategies that would decrease delinquent behavior and promote prosocial development. Being dynamic and complex process, the spread of crime requires a system level approach. In this paper, we formulate and analyze a series of dynamical model systems of the dilation of crime incorporating law enforcement. The population models of social interactions have been constructed based on predator–prey interaction models with Holling type II response function. Two different types of populations (criminal minded and non-criminal minded) have been assumed in the given community/society. According to law policy for crime control, we scrutinize the dynamic behavior of the model system concerning law enforcement on the criminal minded population. Along with analytical expressions for the existence of different equilibrium points and their stability, we have also provided their geometrical interpretations using isocline analysis. The expressions obtained for the existence and stability of equilibrium points have been used to investigate the effects of coefficient of law enforcement and the logistic growth term on the prevalence of crime. It is observed that for a threshold value of law enforcement, a stable limit cycle exists. In particular, a threshold of law enforcement is determined beyond which the associated place/community could be made crime free. A threshold value R0 (similar to basic reproduction number in epidemiology) has also been introduced. It is shown that when R0<1, crime free equilibrium is stable. The elimination and persistence of crime have been discussed via two parameters (law enforcement and half saturation constant) bifurcation diagram. Theoretical results have been supported via numerical simulations followed by discussion and societal impacts of the present study.

Bifurcation and stability of a dynamical system with threshold prey harvesting

In this study, a predator-prey interaction model with Holling type II functional response is studied. As the continuous threshold prey harvesting is introduced, the proposed model displays a dynami...

Dynamics in a ratio-dependent eco-epidemiological predator-prey model having cross species disease transmission

We have proposed and analyzed an eco-epidemiological predator-prey interaction model having disease in both the population with ratio-dependent functional response. The total population has been classified into susceptible prey, infected prey, susceptible predator, and infected predator. The infection propagation is considered directly proportional to the number of individuals come in to contact with one infected individual. The predation ability of infected predator is neglected during the disease. The infection is considered to be weak infection in case of predator. Predator can recover themselves due to their natural immune system or application of external curative stimulants. Though such weak infections are not generally considered for study but these cannot be completely ignored. The positivity of the solutions, the existence of various biologically feasible equilibrium points, their stability are investigated. The numerical analysis is carried out with hypothetical set of parameters to substantiate the analytical findings that our model exhibits. The oscillatory coexistence of the species which is very common in nature is observed for disease free as well as coexisting system. The stability nature of the Hopf-bifurcating periodic solutions of the disease free as well as coexisting equilibrium are determined by computing the Lyapunov coefficients. Further, the system undergoes the Bogdanov-Takens bifurcation in two-parameter space around the disease free as well as coexisting equilibrium. It is also observed that the system will be disease free through proper predational strategies.

A Predator-Prey model in the chemostat with Holling Type II response function

A model of predator-prey interaction in a chemostat with Holling Type II functional and numerical response functions of the Monod or Michaelis-Menten form is considered. It is proved that local asymptotic stability of the coexistence equilibrium implies that it is globally asymptotically stable. It is also shown that when the coexistence equilibrium exists but is unstable, solutions converge to a unique, orbitally asymptotically stable periodic orbit. Thus the range of the dynamics of the chemostat predator-prey model is the same as for the analogous classical Rosenzweig-MacArthur predator-prey model with Holling Type II functional response. An extension that applies to other functional rsponses is also given.

Mathematical Modeling of Echinococcosis in Humans, Dogs, and Sheep

In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number R 0 and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if R 0 &gt; 1 . We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if R 0 &lt; 1 . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep ( β es ). Thus, the effective controlling strategies are associated with this parameter.

A Novel Prey-Predator Quadratic Harvesting Model via Optimal Control Theory and Hopf Bifurcation

In this investigation, a predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed. In the absence of Zooplankton and Fish, it is assumed that Phytoplankton grows logistically. It is assumed that Zooplankton consumes Phytoplankton and Fish consumes Phytoplankton as well as Zooplankton. Holling type I &amp; II functional responses have been considered to formulate the our proposed model. It is considered that Phytoplankton releases some toxin in the aquatic environment which makes some death in Zooplankton population. Quadratic harvesting is considered on Fish species. Boundedness of the solution of our proposed model has also been studied. Local stability of the system around each equilibrium point has been investigated. Also, the global stability of the interior equilibrium point has been studied. Existence condition of Hopf bifurcation of our proposed system has been studied. It is found that half saturation constant (α) can change the system dynamics. It is also found that the harvesting rate of Fish (E) and consumption rate of Zooplankton (γ1) has a significant role in the stability of the system. Again, it is found that the harvesting of Fish species will be increased if the selling price of Fish (p) and the annual discount (δ1) of Fish production cost increases. It is also found that the optimal harvesting rate of Fish decreases due to the increase of cost (c) of harvesting of Fish. Finally, some numerical simulation results have been presented to verify our analytical findings.

Dynamics of a stage structure prey-predator model with ratio-dependent functional response and anti-predator behavior of adult prey

In this paper, a predator-prey interaction model among juvenile prey, adult prey and predator has been developed where stage structure is considered on prey species. The functional responses has been considered as ratio dependent. It is assumed that that the adult prey is strong enough such that it has an anti-predator characteristic. Global dynamics of the co-existing equilibrium point has been discussed with the help of the geometric approach. Furthermore, it is established that the proposed system undergoes through a Hopf bifurcation with respect to some important parameters. Finally, some numerical simulations have been done to test our theoretical results.

An Innate Color Preference Displayed by Xenopus Tadpoles Is Persistent and Requires the Tegmentum.

Many animals, especially those that develop externally, are equipped with innate color preferences that promote survival. For example, Xenopus tadpoles are known to phototax most robustly towards mid-spectrum (“green”) wavelengths of light while avoiding shorter (“blue”) wavelengths. The innate preference to phototax towards green likely promotes survival by guiding the tadpoles to green aquatic plants—their source of both food and safety. Here, we characterize the dynamics and circuitry that give rise to this intriguing hard-wired behavior. Using a novel open-field experimental paradigm we found that free-swimming tadpoles indeed spend most of their time in the green portion of the test dish, whether green is pitted against white (brighter than green) or black (darker than green). This preference was modest yet incredibly persistent over time, which, according to the shell game model of predator-prey interactions, minimizes being found by the predator. Furthermore, we found that this innate preference for the color green was experience-independent, and manifested mainly via profoundly slower swimming speeds while in the green region of the test dish. Ablation experiments showed that, at the circuit level, the color-guided swimming behavior requires the tegmentum, but not the optic tectum (OT). Lastly, we determined that exposing tadpoles to the selective serotonin reuptake inhibitor (SSRI) trazodone switched the tadpoles’ preference from color-based to luminance-based, implicating two distinct visual circuits in the tadpole, one that is associated with color-driven behaviors, another associated with luminance-driven behaviors.

Singular perturbations of the Holling I predator-prey system with a focus

We study the occurrence of limit cyles in a model for two-species predator-prey interaction (referred to as Holling I). This model is based on the phenomenological fitting of the so-called functional response function to observed data in nature by a continuous, piecewise differentiable function. Of the original models presented by Holling it is the only model for which the possible asymptotic behaviour of the prey and predator densities has not been determined yet.We extend the work of Liu who showed that for certain values of parameters of the Holling I system at least two nested limit cycles will occur surrounding a focus. His case corresponds to a bifurcation problem where limit cycles are created from a system with a continuum of singularities, i.e. a singular perturbation problem with slow-fast solutions.We prove that exactly two hyperbolic limit cycles occur after perturbation.

Impact of fear effect on the growth of prey in a predator-prey interaction model

Several field data and experiments on a terrestrial vertebrates exhibited that the fear of predators would cause a substantial variability of prey demography. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. Based on the experimental evidence, we proposed and analyzed a prey-predator system introducing the cost of fear into prey reproduction with Holling type-II functional response. We investigate all the biologically feasible equilibrium points, and their stability is analyzed in terms of the model parameters. Our mathematical analysis exhibits that for strong anti-predator responses can stabilize the prey-predator interactions by ignoring the existence of periodic behaviors. Our model system undergoes Hopf bifurcation by considering the birth rate r0 as a bifurcation parameter. For larger prey birth rate, we investigate the transition to a stable coexisting equilibrium state, with oscillatory approach to this equilibrium state, indicating that the greatest characteristic eigenvalues are actually a pair of imaginary eigenvalues with real part negative, which is increasing for r0. We obtained the conditions for the occurrence of Hopf bifurcation and conditions governing the direction of Hopf bifurcation, which imply that the prey birth rate will not only influence the occurrence of Hopf bifurcation but also alter the direction of Hopf bifurcation. We identify the parameter regions associated with the extinct equilibria, predator-free equilibria and coexisting equilibria with respect to prey birth rate, predator mortality rates. Fear can stabilize the predator-prey system at an interior steady state, where all the species can exists together, or it can create the oscillatory coexistence of all the populations. We performed some numerical simulations to investigate the relationship between the effects of fear and other biologically related parameters (including growth/decay rate of prey/predator), which exhibit the impact that fear can have in prey-predator system. Our numerical illustrations also demonstrate that the prey become less sensitive to perceive the risk of predation with increasing prey growth rate or increasing predators decay rate.