scholarly journals The uneasy coexistence of predators and pathogens

2019 ◽  
Author(s):  
Andreas Eilersen ◽  
Kim Sneppen
Keyword(s):  
Host Species ◽  
Prey Species ◽  
Scaling Relations ◽  
Predator Species ◽  
Predator Prey ◽  
Mass Scaling ◽  
Prey System ◽  
Model Equations ◽  
Extinction Events ◽  
Parameter Values

Disease and predation are both highly important in ecology, and pathogens with multiple host species have turned out to be common. Nonetheless, the interplay between multi-host epidemics and predation has received relatively little attention. Here, we analyse a model of a predator-prey system with disease in both prey and predator populations and determine reasonable parameter values using allometric mass scaling relations. Our analysis focuses on the possibility of extinction events rather than the linear stability of the model equations. We find that if the predator is a specialist, epidemics frequently drive the predator species to extinction. If the predator has an additional, immune prey species, predators will usually survive. Coexistence of predator and disease is impossible in the single-prey model. We conclude that for the prey species, carrying a pathogen can be an effective weapon against predators, and that being a generalist is a major advantage for a predator.

scholarly journals The uneasy coexistence of predators and pathogens

2020 ◽  
Vol 43 (7) ◽  
Author(s):  
Andreas Eilersen ◽  
Kim Sneppen
Keyword(s):  
Host Species ◽  
Prey Species ◽  
Scaling Relations ◽  
Predator Species ◽  
Predator Prey ◽  
Mass Scaling ◽  
Prey System ◽  
Model Equations ◽  
Extinction Events ◽  
Parameter Values

Abstract. Disease and predation are both highly important in ecology, and pathogens with multiple host species have turned out to be common. Nonetheless, the interplay between multi-host epidemics and predation has received relatively little attention. Here, we analyse a model of a predator-prey system with disease in both prey and predator populations and determine reasonable parameter values using allometric mass scaling relations. Our analysis focuses on the possibility of extinction events rather than the linear stability of the model equations, and we derive approximate relations for the parameter values at which we expect these events to occur. We find that if the predator is a specialist, epidemics frequently drive the predator species to extinction. If the predator has an additional, immune prey species, predators will usually survive. Coexistence of predator and disease is impossible in the single-prey model. We conclude that for the prey species, carrying a pathogen can be an effective weapon against predators, and that being a generalist is a major advantage for a predator in the event of an epidemic affecting the prey or both species. Graphical abstract

scholarly journals Comparison and analysis of two forms of harvesting functions in the two-prey and one-predator model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xinxin Liu ◽  
Qingdao Huang
Keyword(s):  
Prey Species ◽  
Equilibrium Points ◽  
Maximum Sustainable Yield ◽  
Predator Prey ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Model ◽  
Model Equations ◽  
The Given

AbstractA new way to study the harvested predator–prey system is presented by analyzing the dynamics of two-prey and one-predator model, in which two teams of prey are interacting with one team of predators and the harvesting functions for two prey species takes different forms. Firstly, we make a brief analysis of the dynamics of the two subsystems which include one predator and one prey, respectively. The positivity and boundedness of the solutions are verified. The existence and stability of seven equilibrium points of the three-species model are further studied. Specifically, the global stability analysis of the coexistence equilibrium point is investigated. The problem of maximum sustainable yield and dynamic optimal yield in finite time is studied. Numerical simulations are performed using MATLAB from four aspects: the role of the carrying capacity of prey, the simulation about the model equations around three biologically significant steady states, simulation for the yield problem of model system, and the comparison between the two forms of harvesting functions. We obtain that the new form of harvesting function is more realistic than the traditional form in the given model, which may be a better reflection of the role of human-made disturbance in the development of the biological system.

PERMANENCE IN A PERIODIC PREDATOR–PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENT

2006 ◽  
Vol 14 (04) ◽  
pp. 491-507 ◽  
Author(s):  
LONG ZHANG ◽  
ZHIDONG TENG
Keyword(s):  
Periodic Solution ◽  
Prey Species ◽  
Positive Periodic Solution ◽  
Analytic Method ◽  
Predator Density ◽  
Volterra Type ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Theoretical Results

In this paper, we study two-species predator–prey Lotka–Volterra-type dispersal system with periodic coefficients, in which the prey species can disperse among n-patches, but the predator species which is density-independent is confined to some patches and cannot disperse. By utilizing the analytic method, sufficient and realistic conditions on the boundedness, permanence, extinction, and the existence of positive periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.

scholarly journals Dynamic behaviors of a Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species

2019 ◽  
Vol 17 (1) ◽  
pp. 1186-1202 ◽  
Author(s):  
Fengde Chen ◽  
Xinyu Guan ◽  
Xiaoyan Huang ◽  
Hang Deng
Keyword(s):  
Birth Rate ◽  
Allee Effect ◽  
Prey Species ◽  
Positive Equilibrium ◽  
Volterra Type ◽  
Predator Species ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Density Dependent ◽  
Prey System

Abstract A Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species is proposed and studied. For non-delay case, such topics as the persistent of the system, the local stability property of the equilibria, the global stability of the positive equilibrium are investigated. For the system with infinite delay, by using the iterative method, a set of sufficient conditions which ensure the global attractivity of the positive equilibrium is obtained. By introducing the density dependent birth rate, the dynamic behaviors of the system becomes complicated. The system maybe collapse in the sense that both the species will be driven to extinction, or the two species could be coexist in a stable state. Numeric simulations are carried out to show the feasibility of the main results.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

scholarly journals Permanence of Periodic Predator-Prey System with Functional Responses and Stage Structure for Prey

2008 ◽  
Vol 2008 ◽  
pp. 1-15 ◽  
Author(s):  
Can-Yun Huang ◽  
Min Zhao ◽  
Hai-Feng Huo
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Functional Responses ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Ii Functional Response

A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

scholarly journals Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Wanlin Chen ◽  
Yuhua Lin
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.

scholarly journals CODIMENSION TWO BIFURCATIONS IN A PREDATOR–PREY SYSTEM WITH GROUP DEFENSE

2001 ◽  
Vol 11 (08) ◽  
pp. 2123-2131 ◽  
Author(s):  
DONGMEI XIAO ◽  
SHIGUI RUAN
Keyword(s):  
Homoclinic Bifurcation ◽  
Qualitative Behavior ◽  
Homoclinic Loop ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Group Defense ◽  
Nonmonotonic Functional Response ◽  
Parameter Values

In this paper we study the qualitative behavior of a predator–prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov–Takens bifurcation) but no bifurcations of codimension three.

Sign in / Sign up

Export Citation Format

Share Document