scholarly journals Scrounging by foragers can resolve the paradox of enrichment

2016 ◽  
Author(s):  
Wataru Toyokawa
Keyword(s):  
Group Living ◽  
Theoretical Models ◽  
Social Foraging ◽  
Predator Population ◽  
Ecological Communities ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Prey System ◽  
The Stability ◽  
Predator System

AbstractTheoretical models of predator-prey system predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). While real ecological communities contain many gregarious species whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might be a resolution of the paradox. I considered a predator population in which individuals play the producer-scrounger foraging game both in a one-prey-one-predator system and a two-prey-one-predator system. I analysed the stability of a coexisting equilibrium point in the former one-prey system and that of non-equilibrium dynamics of the latter two-prey system. The result showed that social foraging can stabilise both systems and thereby resolves the paradox of enrichment when scrounging behaviour is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on sustainability of ecological communities.

scholarly journals Scrounging by foragers can resolve the paradox of enrichment

2017 ◽  
Vol 4 (3) ◽  
pp. 160830 ◽  
Author(s):  
Wataru Toyokawa
Keyword(s):  
Group Living ◽  
Theoretical Models ◽  
Social Foraging ◽  
Predator Population ◽  
Ecological Communities ◽  
Predator Prey ◽  
Paradox Of Enrichment ◽  
Prey System ◽  
The Stability ◽  
The One

Theoretical models of predator–prey systems predict that sufficient enrichment of prey can generate large amplitude limit cycles, paradoxically causing a high risk of extinction (the paradox of enrichment). Although real ecological communities contain many gregarious species, whose foraging behaviour should be influenced by socially transmitted information, few theoretical studies have examined the possibility that social foraging might resolve this paradox. I considered a predator population in which individuals play the producer–scrounger foraging game in one-prey-one-predator and two-prey-one-predator systems. I analysed the stability of a coexisting equilibrium point in the one-prey system and that of non-equilibrium dynamics in the two-prey system. The results revealed that social foraging could stabilize both systems, and thereby resolve the paradox of enrichment when scrounging behaviour (i.e. kleptoparasitism) is prevalent in predators. This suggests a previously neglected mechanism underlying a powerful effect of group-living animals on the sustainability of ecological communities.

NONCONSTANT PREY HARVESTING IN RATIO-DEPENDENT PREDATOR–PREY SYSTEM INCORPORATING A CONSTANT PREY REFUGE

2012 ◽  
Vol 05 (02) ◽  
pp. 1250021 ◽  
Author(s):  
SAPNA DEVI
Keyword(s):  
Rate Function ◽  
Predator Population ◽  
Catch Per Unit Effort ◽  
Prey Refuge ◽  
Predator Prey ◽  
Prey System ◽  
Optimal Harvest ◽  
Ratio Dependent ◽  
The Stability ◽  
Optimal Harvest Policy

This paper deals with the problem of nonconstant harvesting of prey in a ratio-dependent predator–prey system incorporating a constant prey refuge. Here we use the reasonable catch-rate function instead of usual catch-per-unit-effort hypothesis. The existence, as well as the stability of possible equilibria, is carried out. Bionomic equilibrium of the system is determined and optimal harvest policy is studied with the help of Pontryagin's maximum principle. The key results developed in this paper are illustrated using numerical simulations. Our results indicate that dynamic behavior of the system very much depends on the prey refuge parameter and increasing amount of refuge could increase prey density and may lead to the extinction of predator population density.

scholarly journals Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Heping Jiang ◽  
Huiping Fang ◽  
Yongfeng Wu
Keyword(s):  
Hopf Bifurcation ◽  
Neumann Boundary ◽  
Herd Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Prey Model ◽  
Homogeneous Neumann Boundary Condition ◽  
The Stability

Abstract This paper mainly aims to consider the dynamical behaviors of a diffusive delayed predator–prey system with Smith growth and herd behavior subject to the homogeneous Neumann boundary condition. For the analysis of the predator–prey model, we have studied the existence of Hopf bifurcation by analyzing the distribution of the roots of associated characteristic equation. Then we have proved the stability of the periodic solution by calculating the normal form on the center of manifold which is associated to the Hopf bifurcation points. Some numerical simulations are also carried out in order to validate our analysis findings. The implications of our analytical and numerical findings are discussed critically.

Impact of Predator Signals on the Stability of a Predator–Prey System: A Z-Control Approach

2018 ◽  
Author(s):  
Sk Shahid Nadim ◽  
Sudip Samanta ◽  
Nikhil Pal ◽  
Ibrahim M. ELmojtaba ◽  
Indranil Mukhopadhyay ◽  
...  
Keyword(s):  
Predator Prey ◽  
Control Approach ◽  
System A ◽  
Prey System ◽  
The Stability ◽  
Predator Signals

scholarly journals The Hopf Bifurcation for a Predator-Prey System with -Logistic Growth and Prey Refuge

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shaoli Wang ◽  
Zhihao Ge
Keyword(s):  
Hopf Bifurcation ◽  
Logistic Growth ◽  
Positive Equilibrium ◽  
Prey Refuge ◽  
Normal Form Theory ◽  
Center Manifold Reduction ◽  
Predator Prey ◽  
Prey System ◽  
Form Theory ◽  
The Stability

The Hopf bifurcation for a predator-prey system with -logistic growth and prey refuge is studied. It is shown that the ODEs undergo a Hopf bifurcation at the positive equilibrium when the prey refuge rate or the index- passed through some critical values. Time delay could be considered as a bifurcation parameter for DDEs, and using the normal form theory and the center manifold reduction, explicit formulae are derived to determine the direction of bifurcations and the stability and other properties of bifurcating periodic solutions. Numerical simulations are carried out to illustrate the main results.

Harvesting Analysis of a Predator-Prey System with Functional Response

2013 ◽  
Vol 805-806 ◽  
pp. 1957-1961
Author(s):  
Ting Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Optimal Harvesting Policy ◽  
Prey System ◽  
The Stability ◽  
Maximal Principle

In this paper, a predator-prey system with functional response is studied,and a set of sufficient conditions are obtained for the stability of equilibrium point of the system. Moreover, optimal harvesting policy is obtained by using the maximal principle,and numerical simulation is applied to illustrate the correctness.

scholarly journals Stability and Hopf Bifurcation of Delayed Predator-Prey System Incorporating Harvesting

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Fengying Wei ◽  
Lanqi Wu ◽  
Yuzhi Fang
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Hopf Bifurcations ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Prey System ◽  
Theoretical Predictions ◽  
Form Theory ◽  
The Stability

A kind of delayed predator-prey system with harvesting is considered in this paper. The influence of harvesting and delay is investigated. Our results show that Hopf bifurcations occur as the delayτpasses through critical values. By using of normal form theory and center manifold theorem, the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are obtained. Finally, numerical simulations are given to support our theoretical predictions.

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

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.

EFFECT OF KAIROMONE ON PREDATOR–PREY DYNAMICS — A DELAY MODEL

2013 ◽  
Vol 06 (05) ◽  
pp. 1350035 ◽  
Author(s):  
SUDIP SAMANTA ◽  
JOYDEV CHATTOPADHYAY
Keyword(s):  
Vertical Migration ◽  
Defense Mechanisms ◽  
Multiple Delays ◽  
Predator Population ◽  
Delay Model ◽  
Refuge Use ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fish Kairomone ◽  
The Stability

In most of the predator–prey systems, prey individuals make transitions between vulnerable and invulnerable states or locations. This transition is regulated by various inducible defense mechanisms. Diel vertical migration (DVM) in zooplankton is the most effective and instantaneous defense observed in zooplankton population. Zooplankton shows downward vertical migration in the daytime in the presence of predators (or predator kairomones) to avoid predation (i.e. refuge use), and it enters into the surface water again at night to graze phytoplankton. The dynamics of the planktonic ecosystem under DVM of zooplankton along with fish kairomone and the multiple delays due to migration for vulnerable and invulnerable prey and reproduction in the predator population is of considerable interest both in theoretical and experimental ecologists. By developing mathematical model, we analyze such a system. The conditions for which the system enters into Hopf-bifurcation are obtained. Moreover, the conditions for which the bifurcating branches are supercritical are also derived. Our results indicate that DVM along with the effect of kairomone and multiple delays with a certain range are responsible to enhance the stability of the system around the positive interior equilibrium point.

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