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 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.

Prey consumption in acarine predator-prey populations reared in the greenhouse

1971 ◽  
Vol 49 (6) ◽  
pp. 903-913 ◽  
Author(s):  
T. Burnett
Keyword(s):  
Tetranychus Urticae ◽  
Natural Enemy ◽  
Prey Density ◽  
Prey Consumption ◽  
Predator Prey ◽  
Amblyseius Fallacis ◽  
Two Factors ◽  
Prey Populations

Two factors, in addition to temperature, could affect the assessment of Amblyseius fallacis as a natural enemy of Tetranychus urticae infesting alfalfa. These are initial prey density and sampling of the predator–prey populations during daylight hours. The influence of these factors was determined by propagating predator–prey populations having different initial prey densities on alfalfa in the greenhouse, recording the subsequent variation in the numbers of the two species during daylight hours, and comparing estimates of the rates at which prey entered and were removed from the populations. A. fallacis was able to reduce prey density before webbing of the alfalfa plants occurred. Prey consumption by the predator populations was judged capable of inducing the observed decline in prey numbers.

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.

scholarly journals The stabilizing effects of genetic diversity on predator-prey dynamics

F1000Research ◽  
2013 ◽  
Vol 2 ◽  
pp. 43 ◽  
Author(s):  
Christopher F Steiner ◽  
Jordan Masse
Keyword(s):  
Genetic Diversity ◽  
Adaptive Capacity ◽  
Colony Size ◽  
Prey Abundance ◽  
Prey Population ◽  
General View ◽  
Population Abundance ◽  
Single Strain ◽  
Predator Prey ◽  
Prey Populations

Heterogeneity among prey in their susceptibility to predation is a potentially important stabilizer of predator-prey interactions, reducing the magnitude of population oscillations and enhancing total prey population abundance. When microevolutionary responses of prey populations occur at time scales comparable to population dynamics, adaptive responses in prey defense can, in theory, stabilize predator-prey dynamics and reduce top-down effects on prey abundance. While experiments have tested these predictions, less explored are the consequences of the evolution of prey phenotypes that can persist in both vulnerable and invulnerable classes. We tested this experimentally using a laboratory aquatic system composed of the rotifer Brachionus calyciflorus as a predator and the prey Synura petersenii, a colony-forming alga that exhibits genetic variation in its propensity to form colonies and colony size (larger colonies are a defense against predators). Prey populations of either low initial genetic diversity and low adaptive capacity or high initial genetic diversity and high adaptive capacity were crossed with predator presence and absence. Dynamics measured over the last 127 days of the 167-day experiment revealed no effects of initial prey genetic diversity on the average abundance or temporal variability of predator populations. However, genetic diversity and predator presence/absence interactively affected prey population abundance and stability; diversity of prey had no effects in the absence of predators but stabilized dynamics and increased total prey abundance in the presence of predators. The size structure of the genetically diverse prey populations diverged from single strain populations in the presence of predators, showing increases in colony size and in the relative abundance of cells found in colonies. Our work sheds light on the adaptive value of colony formation and supports the general view that genetic diversity and intraspecific trait variation of prey can play a vital role in the short-term dynamics and stability of planktonic predator-prey systems.

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.

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