American Institute of Mathematical Sciences

Advanced
2005, 2(2): 279-288. doi: 10.3934/mbe.2005.2.279

The Dynamics of the Schoener-Polis-Holt model of Intra-Guild Predation

Eric Ruggieri 1, and  Sebastian J. Schreiber 2,

1. 

Department of Mathematics, Providence College, Providence, Rhode Island 02918, United States
2. 

Department of Mathematics, College of William and Mary, P.O. Box 8795, Williamsburg, VA 23187-8795, United States

Received  October 2004 Revised  March 2005 Published  March 2005

Intraguild predation occurs when one species (the intraguild predator) predates on and competes with another species (the intraguild prey). A classic model of this interaction was introduced by Gary Polis and Robert Holt building on a model of competing species by Thomas Schoener. A global analysis reveals that this model exhibits generically six dynamics: extinction of one or both species; coexistence about a globally stable equilibrium; contingent exclusion in which the first established species prevents the establishment of the other species; contingent coexistence in which coexistence or displacement of the intraguild prey depend on initial conditions; exclusion of the intraguild prey; and exclusion of the intraguild predator. Implications for biological control and community ecology are discussed.
Keywords: ecology, nonlinear dynamics, intraguild predation..
Mathematics Subject Classification: 92D4.
Citation: Eric Ruggieri, Sebastian J. Schreiber. The Dynamics of the Schoener-Polis-Holt model of Intra-Guild Predation. Mathematical Biosciences & Engineering, 2005, 2 (2) : 279-288. doi: 10.3934/mbe.2005.2.279
[1]

Hua Nie, Sze-Bi Hsu, Feng-Bin Wang. Global dynamics of a reaction-diffusion system with intraguild predation and internal storage. Discrete and Continuous Dynamical Systems - B, 2020, 25 (3) : 877-901. doi: 10.3934/dcdsb.2019194
[2]

Robert Stephen Cantrell, Xinru Cao, King-Yeung Lam, Tian Xiang. A PDE model of intraguild predation with cross-diffusion. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3653-3661. doi: 10.3934/dcdsb.2017145
[3]

Daniel Ryan, Robert Stephen Cantrell. Avoidance behavior in intraguild predation communities: A cross-diffusion model. Discrete and Continuous Dynamical Systems, 2015, 35 (4) : 1641-1663. doi: 10.3934/dcds.2015.35.1641
[4]

Luca Gerardo-Giorda, Pierre Magal, Shigui Ruan, Ousmane Seydi, Glenn Webb. Preface: Population dynamics in epidemiology and ecology. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : i-ii. doi: 10.3934/dcdsb.2020125
[5]

Renji Han, Binxiang Dai, Lin Wang. Delay induced spatiotemporal patterns in a diffusive intraguild predation model with Beddington-DeAngelis functional response. Mathematical Biosciences & Engineering, 2018, 15 (3) : 595-627. doi: 10.3934/mbe.2018027
[6]

Guohong Zhang, Xiaoli Wang. Extinction and coexistence of species for a diffusive intraguild predation model with B-D functional response. Discrete and Continuous Dynamical Systems - B, 2018, 23 (9) : 3755-3786. doi: 10.3934/dcdsb.2018076
[7]

Maria Paola Cassinari, Maria Groppi, Claudio Tebaldi. Effects of predation efficiencies on the dynamics of a tritrophic food chain. Mathematical Biosciences & Engineering, 2007, 4 (3) : 431-456. doi: 10.3934/mbe.2007.4.431
[8]

Jean-Jacques Kengwoung-Keumo. Dynamics of two phytoplankton populations under predation. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1319-1336. doi: 10.3934/mbe.2014.11.1319
[9]

Evariste Sanchez-Palencia, Philippe Lherminier. Paradoxes of vulnerability to predation in biological dynamics and mediate versus immediate causality. Discrete and Continuous Dynamical Systems - S, 2020, 13 (8) : 2195-2209. doi: 10.3934/dcdss.2020185
[10]

Alex John Quijano, Michele L. Joyner, Edith Seier, Nathaniel Hancock, Michael Largent, Thomas C. Jones. An aggregate stochastic model incorporating individual dynamics for predation movements of anelosimus studiosus. Mathematical Biosciences & Engineering, 2015, 12 (3) : 585-607. doi: 10.3934/mbe.2015.12.585
[11]

Mohan Mallick, Sarath Sasi, R. Shivaji, S. Sundar. Bifurcation, uniqueness and multiplicity results for classes of reaction diffusion equations arising in ecology with nonlinear boundary conditions. Communications on Pure and Applied Analysis, 2022, 21 (2) : 705-726. doi: 10.3934/cpaa.2021195
[12]

Feng Rao, Carlos Castillo-Chavez, Yun Kang. Dynamics of a stochastic delayed Harrison-type predation model: Effects of delay and stochastic components. Mathematical Biosciences & Engineering, 2018, 15 (6) : 1401-1423. doi: 10.3934/mbe.2018064
[13]

Andrey V. Kremnev, Alexander S. Kuleshov. Nonlinear dynamics and stability of the skateboard. Discrete and Continuous Dynamical Systems - S, 2010, 3 (1) : 85-103. doi: 10.3934/dcdss.2010.3.85
[14]

Christopher M. Kribs-Zaleta. Sharpness of saturation in harvesting and predation. Mathematical Biosciences & Engineering, 2009, 6 (4) : 719-742. doi: 10.3934/mbe.2009.6.719
[15]

Behrooz Yousefzadeh. Computation of nonreciprocal dynamics in nonlinear materials. Journal of Computational Dynamics, 2022  doi: 10.3934/jcd.2022010
[16]

Torsten Lindström. Discrete models and Fisher's maximum principle in ecology. Conference Publications, 2003, 2003 (Special) : 571-579. doi: 10.3934/proc.2003.2003.571
[17]

Zaizheng Li, Zhitao Zhang. Uniqueness and nondegeneracy of positive solutions to an elliptic system in ecology. Electronic Research Archive, 2021, 29 (6) : 3761-3774. doi: 10.3934/era.2021060
[18]

Tomás Caraballo, Juan L. G. Guirao. New trends on nonlinear dynamics and its applications. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : i-ii. doi: 10.3934/dcdss.2015.8.6i
[19]

Mark J. Ablowitz, Terry S. Haut, Theodoros P. Horikis, Sean D. Nixon, Yi Zhu. Nonlinear wave dynamics: From lasers to fluids. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 923-955. doi: 10.3934/dcdss.2011.4.923
[20]

Jianquan Li, Yicang Zhou, Jianhong Wu, Zhien Ma. Complex dynamics of a simple epidemic model with a nonlinear incidence. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 161-173. doi: 10.3934/dcdsb.2007.8.161

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (43)
  • HTML views (0)
  • Cited by (15)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy