2010, 7(3): 603-622. doi: 10.3934/mbe.2010.7.603

Mechanisms for stable coexistence in an insect community

1. 

School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China

2. 

School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, China

3. 

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received  May 2009 Revised  March 2010 Published  June 2010

In this paper, we formulate a three-species ecological community model consisting of two aphid species ( Acyrthosiphon pisum and Megoura viciae) and a specialist parasitoid ( Aphidius ervi) that attacks only one of the aphids ( A pisum). The model incorporates both density-mediated and trait-mediated host-parasitoid interactions. Our analysis shows that the model possesses much richer and more realistic dynamics than earlier models. Our theoretical results reveal a new mechanism for stable coexistence in a three-species community in which any two species alone do not co-exist. More specifically, it is known that, when a predator is introduced into a community of two competing species, if the predator only predates on the strong competitor, it can allow the weak competitor to survive, but may drive the strong competitor to extinction through over-exploitation. We show that if the weak competitor interferes the predation on the strong competitor through trait-mediated indirect effects, then all three species can stably co-exist.
Citation: Meng Fan, Bingbing Zhang, Michael Yi Li. Mechanisms for stable coexistence in an insect community. Mathematical Biosciences & Engineering, 2010, 7 (3) : 603-622. doi: 10.3934/mbe.2010.7.603
[1]

Willard S. Keeran, Patrick D. Leenheer, Sergei S. Pilyugin. Feedback-mediated coexistence and oscillations in the chemostat. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 321-351. doi: 10.3934/dcdsb.2008.9.321

[2]

Zhilan Feng, Wenzhang Huang, Donald L. DeAngelis. Spatially heterogeneous invasion of toxic plant mediated by herbivory. Mathematical Biosciences & Engineering, 2013, 10 (5&6) : 1519-1538. doi: 10.3934/mbe.2013.10.1519

[3]

Azmy S. Ackleh, Youssef M. Dib, S. R.-J. Jang. Competitive exclusion and coexistence in a nonlinear refuge-mediated selection model. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 683-698. doi: 10.3934/dcdsb.2007.7.683

[4]

Youshan Tao, J. Ignacio Tello. Nonlinear stability of a heterogeneous state in a PDE-ODE model for acid-mediated tumor invasion. Mathematical Biosciences & Engineering, 2016, 13 (1) : 193-207. doi: 10.3934/mbe.2016.13.193

[5]

Sandesh Athni Hiremath, Christina Surulescu, Anna Zhigun, Stefanie Sonner. On a coupled SDE-PDE system modeling acid-mediated tumor invasion. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2339-2369. doi: 10.3934/dcdsb.2018071

[6]

Rafael Diaz, Laura Gomez. Indirect influences in international trade. Networks & Heterogeneous Media, 2015, 10 (1) : 149-165. doi: 10.3934/nhm.2015.10.149

[7]

Kazuhisa Ichikawa. Synergistic effect of blocking cancer cell invasion revealed by computer simulations. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1189-1202. doi: 10.3934/mbe.2015.12.1189

[8]

Roberto Guglielmi. Indirect stabilization of hyperbolic systems through resolvent estimates. Evolution Equations & Control Theory, 2017, 6 (1) : 59-75. doi: 10.3934/eect.2017004

[9]

Francesco Piazza, Yves-Henri Sanejouand. Breather-mediated energy transfer in proteins. Discrete & Continuous Dynamical Systems - S, 2011, 4 (5) : 1247-1266. doi: 10.3934/dcdss.2011.4.1247

[10]

Willard S. Keeran, Patrick D. Leenheer, Sergei S. Pilyugin. Circular and elliptic orbits in a feedback-mediated chemostat. Discrete & Continuous Dynamical Systems - B, 2007, 7 (4) : 779-792. doi: 10.3934/dcdsb.2007.7.779

[11]

Sarthok Sircar, Anthony Roberts. Ion mediated crosslink driven mucous swelling kinetics. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1937-1951. doi: 10.3934/dcdsb.2016030

[12]

W. E. Fitzgibbon, M. Langlais, J.J. Morgan. A reaction-diffusion system modeling direct and indirect transmission of diseases. Discrete & Continuous Dynamical Systems - B, 2004, 4 (4) : 893-910. doi: 10.3934/dcdsb.2004.4.893

[13]

Tomás Caraballo, Renato Colucci, Xiaoying Han. Semi-Kolmogorov models for predation with indirect effects in random environments. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2129-2143. doi: 10.3934/dcdsb.2016040

[14]

Liming Cai, Maia Martcheva, Xue-Zhi Li. Epidemic models with age of infection, indirect transmission and incomplete treatment. Discrete & Continuous Dynamical Systems - B, 2013, 18 (9) : 2239-2265. doi: 10.3934/dcdsb.2013.18.2239

[15]

Fatiha Alabau-Boussouira, Piermarco Cannarsa, Roberto Guglielmi. Indirect stabilization of weakly coupled systems with hybrid boundary conditions. Mathematical Control & Related Fields, 2011, 1 (4) : 413-436. doi: 10.3934/mcrf.2011.1.413

[16]

Bopeng Rao, Zhuangyi Liu. A spectral approach to the indirect boundary control of a system of weakly coupled wave equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 399-414. doi: 10.3934/dcds.2009.23.399

[17]

Curtis L. Wesley, Linda J. S. Allen, Michel Langlais. Models for the spread and persistence of hantavirus infection in rodents with direct and indirect transmission. Mathematical Biosciences & Engineering, 2010, 7 (1) : 195-211. doi: 10.3934/mbe.2010.7.195

[18]

Fabien Marpeau. Modeling the indirect contamination of a structured population with continuous levels of exposure. Discrete & Continuous Dynamical Systems - B, 2007, 8 (4) : 879-900. doi: 10.3934/dcdsb.2007.8.879

[19]

Mengyao Ding, Wei Wang. Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production. Discrete & Continuous Dynamical Systems - B, 2017, 22 (11) : 1-20. doi: 10.3934/dcdsb.2018328

[20]

Mohammad El Smaily, François Hamel, Lionel Roques. Homogenization and influence of fragmentation in a biological invasion model. Discrete & Continuous Dynamical Systems - A, 2009, 25 (1) : 321-342. doi: 10.3934/dcds.2009.25.321

2017 Impact Factor: 1.23

Metrics

  • PDF downloads (5)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]