Predator–prey interactions

2007 ◽  
Author(s):  
Michael B. Bonsall ◽  
Michael P. Hassell
Keyword(s):  
Population Size ◽  
Positive Impact ◽  
Parasitic Wasp ◽  
Prey Population ◽  
Volterra Model ◽  
Predator Population ◽  
Continuous Time Model ◽  
Predator Prey ◽  
Population Process ◽  
Prey Interaction

Predation is a widespread population process that has evolved many times within the metazoa. It can affect the distribution, abundance, and dynamics of species in ecosystems. For instance, the distribution of western tussock moth is known to be affected by a parasitic wasp (Maron and Harrison, 1997; Hastings et al., 1998), the abundance of different competitors can be shaped by the presence or absence of predators (e.g. Paine, 1966), and natural enemies (such as many parasitoids) can shape the dynamics of a number of ecological interactions (Hassell, 1978, 2000). The broad aim of this chapter is to explore the dynamical effects of predators (including the large groupings of insect parasitoids) and show how our understanding of predator–prey interactions scales from knowledge of the behaviour and local patch dynamics to the population and regional (metapopulation) levels. We draw on a number of approaches including behavioural studies, population dynamics, and time-series analysis, and use models to describe the data and dynamics of the interaction between predators and prey. Predator–prey interactions have an inherent tendency to fluctuate and show oscillatory behaviour. If predators are initially rare, then the size of the prey population can increase. As prey population size increases, the predator populations also begins to increase, which in turn has a detrimental effect on the prey population leading to a decline in prey numbers. As prey become scarce then the predator population size declines and the cycle starts again. These intuitive dynamics can be captured by one of the simplest mathematical descriptions of a predator–prey interaction: the Lotka–Volterra model (Lotka, 1925; Volterra, 1926). Specifically, the Lotka–Volterra model for an interaction between a predator (P) and its prey (N) is a continuous-time model and has the form : where r is the prey-population growth rate in the absence of predators, α is the predator attack rate, c is the (positive) impact of prey on predators, and d is the death rate of predators in the absence of their prey resource.

scholarly journals Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hui Zhang ◽  
Zhihui Ma ◽  
Gongnan Xie ◽  
Lukun Jia
Keyword(s):  
Time Scale ◽  
Stable State ◽  
Volterra Model ◽  
Fast Time ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction ◽  
Game Dynamic

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.

A linear birth-and-death predator–prey process

1995 ◽  
Vol 32 (01) ◽  
pp. 274-277
Author(s):  
John Coffey
Keyword(s):  
Death Rate ◽  
Birth Rate ◽  
Prey Population ◽  
Death Process ◽  
Predator Population ◽  
Birth And Death Process ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ 1 X and death rate μ 1 X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ 2 Y and the death rate is . It is proven that and iff

EFFECT OF VIRAL INFECTION ON THE GENERALIZED GAUSE MODEL OF PREDATOR-PREY SYSTEM

2003 ◽  
Vol 11 (01) ◽  
pp. 19-26 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A. MUKHOPADHYAY ◽  
P. K. ROY
Keyword(s):  
Viral Infection ◽  
Specific Growth ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Stability Behavior ◽  
Force Of Infection ◽  
Prey System ◽  
Infected Prey

The generalized Gause model of predator-prey system is revisited with an introduction of viral infection on prey population. Stability behavior of such modified system is carried out to observe the change of dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.

scholarly journals The Study of a Predator-Prey Model with Fear Effect Based on State-Dependent Harvesting Strategy

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Y. Tian ◽  
H. M. Li
Keyword(s):  
Numerical Simulation ◽  
Periodic Solution ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Positive Order ◽  
Predator Prey ◽  
Predator Prey Model ◽  
State Dependent ◽  
The Stability

In presence of predator population, the prey population may significantly change their behavior. Fear for predator population enhances the survival probability of prey population, and it can greatly reduce the reproduction of prey population. In this study, we propose a predator-prey fishery model introducing the cost of fear into prey reproduction with Holling type-II functional response and prey-dependent harvesting and investigate the global dynamics of the proposed model. For the system without harvest, it is shown that the level of fear may alter the stability of the positive equilibrium, and an expression of fear critical level is characterized. For the harvest system, the existence of the semitrivial order-1 periodic solution and positive order- q ( q ≥ 1 ) periodic solution is discussed by the construction of a Poincaré map on the phase set, and the threshold conditions are given, which can not only transform state-dependent harvesting into a cycle one but also provide a possibility to determine the harvest frequency. In addition, to ensure a certain robustness of the adopted harvest policy, the threshold condition for the stability of the order- q periodic solution is given. Meanwhile, to achieve a good economic profit, an optimization problem is formulated and the optimum harvest level is obtained. Mathematical findings have been validated in numerical simulation by MATLAB. Different effects of different harvest levels and different fear levels have been demonstrated by depicting figures in numerical simulation using MATLAB.

scholarly journals Dynamics of Predator-Prey Community with Age Structures and Its Changing Due To Harvesting

2020 ◽  
Vol 15 (1) ◽  
pp. 73-92
Author(s):  
G.P. Neverova ◽  
O.L. Zhdanova ◽  
E.Ya. Frisman
Keyword(s):  
Community Dynamics ◽  
Initial Conditions ◽  
Reproductive Potential ◽  
Stable State ◽  
Stability Domain ◽  
Prey Population ◽  
Dynamic Mode ◽  
Predator Population ◽  
Time Model ◽  
Predator Prey

The paper studies dynamic modes of discrete-time model of structured predator-prey community like “arctic fox – rodent” and changing its dynamic modes due to interspecific interaction. We paid special attention to the analysis of situations in which changes in the dynamic modes are possible. In particularly, 3-cycle emerging in prey population can result in predator extinction. Moreover, this solution corresponding to an incomplete community simultaneously coexists with the solution describing dynamics of complete community, which can be both stable and unstable. The anthropogenic impact on the community dynamics is studied, that is realized as harvest of some part of predator or prey population. It is shown that prey harvesting leads to expansion of parameter space domain with non-trivial stable numbers of community populations. In this case, the prey harvest has little effect on the predator dynamics; changes are mainly associated with multistability areas. In particular, the multistability domain narrows, in which changing initial conditions leads to different dynamic regimes, such as the transition to a stable state or periodic oscillations. As a result, community dynamics becomes more predictable. It is shown that the dynamics of prey population is sensitive to its harvesting. Even a small harvest rate results in disappearance of population size fluctuations: the stable state captures the entire phase space in multistability areas. In the case of the predator population harvest, stability domain of the nontrivial fixed point expands along the parameter of the predator birth rate. Accordingly, a case where predator determines the prey population dynamics is possible only at high values of predator reproductive potential. It is shown that in the case of predator harvest, a change in the community dynamic mode is possible because of a shifting dynamic regime in the prey population initiating the same nature fluctuations in the predator population. The dynamic regimes emerging in the community models with and without harvesting were compared.

scholarly journals Analisis Kestabilan Model Predator-Prey dengan Adanya Faktor Tempat Persembunyian Menggunakan Fungsi Respon Holling Tipe III

2021 ◽  
Vol 3 (2) ◽  
pp. 88
Author(s):  
Riris Nur Patria Putri ◽  
Windarto Windarto ◽  
Cicik Alfiniyah
Keyword(s):  
Numerical Simulation ◽  
Response Function ◽  
Equilibrium Points ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Asymptotic Stable ◽  
Simulation Results ◽  
Model Predator

Predation is interaction between predator and prey, where predator preys prey. So predators can grow, develop, and reproduce. In order for prey to avoid predators, then prey needs a refuge. In this thesis, a predator-prey model with refuge factor using Holling type III response function which has three populations, i.e. prey population in the refuge, prey population outside the refuge, and predator population. From the model, three equilibrium points were obtained, those are extinction of the three populations which is unstable, while extinction of predator population and coexistence are asymptotic stable under certain conditions. The numerical simulation results show that refuge have an impact the survival of the prey.

scholarly journals Dynamics of a Predator-Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-38
Author(s):  
Sudeshna Mondal ◽  
G. P. Samanta ◽  
Juan J. Nieto
Keyword(s):  
Equilibrium Points ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Food Sources ◽  
Prey Population ◽  
Predator Population ◽  
Input Rate ◽  
Prey Refuge ◽  
Predator Prey ◽  
The Impact

In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources.

Effect of temperature on a greenhouse acarine predator–prey population

1970 ◽  
Vol 48 (3) ◽  
pp. 555-562 ◽  
Author(s):  
T. Burnett
Keyword(s):  
Tetranychus Urticae ◽  
Age Structure ◽  
The Other ◽  
Prey Abundance ◽  
Prey Population ◽  
Effect Of Temperature ◽  
Initial Increase ◽  
Predator Population ◽  
Predator Prey ◽  
Amblyseius Fallacis

Populations of the two-spotted mite, Tetranychus urticae, and its acarine predator, Amblyseius fallacis, were propagated on alfalfa in the greenhouse at constant temperatures in the range 65 to 85 °F (18.3–29.4 °C). The predator limited the initial increase in prey abundance only at temperatures above about 70 °F (21.1 °C). At 80 and 85 °F (26.7 and 29.4 °C) fluctuations in prey and predator numbers increased in amplitude as propagation continued. The age structure of the predator population reared at 75 °F (23.9 °C) differed from that of populations propagated at the other temperatures.

A mathematical study of a predator–prey model with disease circulating in the both populations

2015 ◽  
Vol 08 (02) ◽  
pp. 1550015 ◽  
Author(s):  
Krishna Pada Das ◽  
J. Chattopadhyay
Keyword(s):  
Equilibrium Point ◽  
Prey Population ◽  
Global Dynamics ◽  
Predator Population ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Force Of Infection ◽  
Predator Prey Model ◽  
High Infection ◽  
Infected Prey

Disease in ecological systems plays an important role. In the present investigation we propose and analyze a predator–prey mathematical model in which both species are affected by infectious disease. The parasite is transmitted directly (by contact) within the prey population and indirectly (by consumption of infected prey) within the predator population. We derive biologically feasible and insightful quantities in terms of ecological as well as epidemiological reproduction numbers that allow us to describe the dynamics of the proposed system. Our observations indicate that predator–prey system is stable without disease but high infection rate drive the predator population toward extinction. We also observe that predation of vulnerable infected prey makes the disease to eradicate into the community composition of the model system. Local stability analysis of the interior equilibrium point near the disease-free equilibrium point is worked out. To study the global dynamics of the system, numerical simulations are performed. Our simulation results show that for higher values of the force of infection in the prey population the predator population goes to extinction. Our numerical analysis reveals that predation rates specially on susceptible prey population and recovery of infective predator play crucial role for preventing the extinction of the susceptible predator and disease propagation.

Time-delayed predator–prey interaction with the benefit of antipredation response in presence of refuge

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Sudeshna Mondal ◽  
Guruprasad Samanta
Keyword(s):  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Prey ◽  
Terrestrial Vertebrates ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Refuge Area ◽  
Prey Interaction ◽  
Transcritical Bifurcations

AbstractA field experiment on terrestrial vertebrates observes that direct predation on predator–prey interaction can not only affect the population dynamics but the indirect effect of predator’s fear (felt by prey) through chemical and/or vocal cues may also reduce the reproduction of prey and change their life history. In this work, we have described a predator–prey model with Holling type II functional response incorporating prey refuge. Irrespective of being considering either a constant number of prey being refuged or a proportion of the prey population being refuged, a different growth rate and different carrying capacity for the prey population in the refuge area are considered. The total prey population is divided into two subclasses: (i) prey x in the refuge area and (ii) prey y in the predatory area. We have taken the migration of the prey population from refuge area to predatory area. Also, we have considered a benefit from the antipredation response of the prey population y in presence of cost of fear. Feasible equilibrium points of the proposed system are derived, and the dynamical behavior of the system around equilibria is investigated. Birth rate of prey in predatory region has been regarded as bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the interior equilibrium point. Moreover, the conditions for occurrence of transcritical bifurcations have been determined. Further, we have incorporated discrete-type gestational delay on the system to make it more realistic. The dynamical behavior of the delayed system is analyzed. Finally, some numerical simulations are given to verify the analytical results.

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