2004, 1(1): 131-145. doi: 10.3934/mbe.2004.1.131

Coexistence in a metapopulation model with explicit local dynamics

1. 

Department of Mathematics, Purdue University, West Lafayette, IN 47907, United States

2. 

Department of Forestry and Natural Resources, Purdue University, West Lafayette, IN 47907, United States

3. 

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States

4. 

Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3

Received  February 2004 Revised  March 2004 Published  March 2004

Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We studied a metapopulation model that explicitly incorporates the local population dynamics of two competing species. The singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to more complex outcomes than simple patch models which do not include explicit local dynamics. We also discuss implications of the model for ecological systems in fragmented landscapes.
Citation: Zhilan Feng, Robert Swihart, Yingfei Yi, Huaiping Zhu. Coexistence in a metapopulation model with explicit local dynamics. Mathematical Biosciences & Engineering, 2004, 1 (1) : 131-145. doi: 10.3934/mbe.2004.1.131
[1]

David M. Chan, Matt McCombs, Sarah Boegner, Hye Jin Ban, Suzanne L. Robertson. Extinction in discrete, competitive, multi-species patch models. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1583-1590. doi: 10.3934/dcdsb.2015.20.1583

[2]

Roberto A. Saenz, Herbert W. Hethcote. Competing species models with an infectious disease. Mathematical Biosciences & Engineering, 2006, 3 (1) : 219-235. doi: 10.3934/mbe.2006.3.219

[3]

Linda J. S. Allen, Vrushali A. Bokil. Stochastic models for competing species with a shared pathogen. Mathematical Biosciences & Engineering, 2012, 9 (3) : 461-485. doi: 10.3934/mbe.2012.9.461

[4]

Henri Berestycki, Jean-Michel Roquejoffre, Luca Rossi. The periodic patch model for population dynamics with fractional diffusion. Discrete & Continuous Dynamical Systems - S, 2011, 4 (1) : 1-13. doi: 10.3934/dcdss.2011.4.1

[5]

Julián López-Gómez. On the structure of the permanence region for competing species models with general diffusivities and transport effects. Discrete & Continuous Dynamical Systems - A, 1996, 2 (4) : 525-542. doi: 10.3934/dcds.1996.2.525

[6]

Dashun Xu, Z. Feng. A metapopulation model with local competitions. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 495-510. doi: 10.3934/dcdsb.2009.12.495

[7]

Wei Feng, Jody Hinson. Stability and pattern in two-patch predator-prey population dynamics. Conference Publications, 2005, 2005 (Special) : 268-279. doi: 10.3934/proc.2005.2005.268

[8]

Sze-Bi Hsu, Chiu-Ju Lin. Dynamics of two phytoplankton species competing for light and nutrient with internal storage. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1259-1285. doi: 10.3934/dcdss.2014.7.1259

[9]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Corrigendum: Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4989-4995. doi: 10.3934/dcds.2014.34.4989

[10]

Xinfu Chen, King-Yeung Lam, Yuan Lou. Dynamics of a reaction-diffusion-advection model for two competing species. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3841-3859. doi: 10.3934/dcds.2012.32.3841

[11]

Kaifa Wang, Yang Kuang. Fluctuation and extinction dynamics in host-microparasite systems. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1537-1548. doi: 10.3934/cpaa.2011.10.1537

[12]

Qingshan Yang, Xuerong Mao. Stochastic dynamics of SIRS epidemic models with random perturbation. Mathematical Biosciences & Engineering, 2014, 11 (4) : 1003-1025. doi: 10.3934/mbe.2014.11.1003

[13]

Chiun-Chuan Chen, Li-Chang Hung, Chen-Chih Lai. An N-barrier maximum principle for autonomous systems of $n$ species and its application to problems arising from population dynamics. Communications on Pure & Applied Analysis, 2019, 18 (1) : 33-50. doi: 10.3934/cpaa.2019003

[14]

Donald L. DeAngelis, Bo Zhang. Effects of dispersal in a non-uniform environment on population dynamics and competition: A patch model approach. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3087-3104. doi: 10.3934/dcdsb.2014.19.3087

[15]

Gang Huang, Yasuhiro Takeuchi, Rinko Miyazaki. Stability conditions for a class of delay differential equations in single species population dynamics. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2451-2464. doi: 10.3934/dcdsb.2012.17.2451

[16]

Dianmo Li, Zengxiang Gao, Zufei Ma, Baoyu Xie, Zhengjun Wang. Two general models for the simulation of insect population dynamics. Discrete & Continuous Dynamical Systems - B, 2004, 4 (3) : 623-628. doi: 10.3934/dcdsb.2004.4.623

[17]

B. E. Ainseba, W. E. Fitzgibbon, M. Langlais, J. J. Morgan. An application of homogenization techniques to population dynamics models. Communications on Pure & Applied Analysis, 2002, 1 (1) : 19-33. doi: 10.3934/cpaa.2002.1.19

[18]

Robert Carlson. Myopic models of population dynamics on infinite networks. Networks & Heterogeneous Media, 2014, 9 (3) : 477-499. doi: 10.3934/nhm.2014.9.477

[19]

Chiun-Chuan Chen, Yin-Liang Huang, Li-Chang Hung, Chang-Hong Wu. Semi-exact solutions and pulsating fronts for Lotka-Volterra systems of two competing species in spatially periodic habitats. Communications on Pure & Applied Analysis, 2020, 19 (1) : 1-18. doi: 10.3934/cpaa.2020001

[20]

Nathan Glatt-Holtz, Mohammed Ziane. Singular perturbation systems with stochastic forcing and the renormalization group method. Discrete & Continuous Dynamical Systems - A, 2010, 26 (4) : 1241-1268. doi: 10.3934/dcds.2010.26.1241

2018 Impact Factor: 1.313

Metrics

  • PDF downloads (7)
  • HTML views (0)
  • Cited by (2)

[Back to Top]