Skip to main content
SpringerLink
Log in

Equilibrium stability of single-species metapopulations

  • Note
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We investigate the effect of migration between local populations of a single discrete-generation species living in a ring or an array of habitats. The commonly used symmetric dispersal assumption is relaxed to include the biologically more reasonable asymmetric dispersion. It is demonstrated analytically that density independent migration has no effect on the equilibrium stability of individual populations. However, the positive equilibrium may be destabilizing if the migration is density dependent in such a way that it increases with increasing population density at the source patch.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bascompte, J. and R. V. Solé (1994). Spatially induced bifurcations in single-species population dynamics. J. Anim. Ecol. 63, 256–264.

    Google Scholar 

  • Doebeli, M. (1995). Dispersal and dynamics. Theor. Pop. Biol. 47, 82–106.

    Article  MATH  Google Scholar 

  • Doebeli, M. and G. D. Ruxton (1997). Controlling spatial chaos in metapopulations with long-range dispersal. Bull. Math. Biol. 59, 497–515.

    Article  Google Scholar 

  • Hassell, M. P., O. Miramontes, P. Rohani and R. M. May (1995). Appropriate formations for dispersal in spatially structured models: comments on Bascompte and Solé. J. Anim. Ecol. 64, 662–664.

    Google Scholar 

  • Lloyd, A. L. (1995). The coupled logistic map: a simple model for the effects of spatial heterogeneity on population dynamics. J. Theor. Biol. 173, 217–230.

    Article  Google Scholar 

  • May, R. M. (1973). Stability and Complexity in Model Ecosystems, Princeton, NJ: Princeton University Press.

    Google Scholar 

  • Maynard Smith, J. and M. Slatkin (1973). The stability of predator-prey systems. Ecology 54, 384–391.

    Article  Google Scholar 

  • Reeve, J. D. (1988). Environmental variability, migration, and persistence in host-parasitoid models. Am. Nat. 132, 810–836.

    Article  Google Scholar 

  • Rohani, P., R. M. May and M. P. Hassell (1996). Metapopulations and equilibrium stability: the effects of spatial structure. J. Theor. Biol. 181, 97–109.

    Article  Google Scholar 

  • Ruxton, G. D. (1996). Density-dependent migration and stability in a system of linked populations. Bull. Math. Biol. 58, 643–660.

    Article  MATH  Google Scholar 

  • Varga, R. S. (1962). Matrix Iterative Analysis, Englewood Cliffs, NJ: Prentice-Hall.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Texas Tech. University, Lubbock, TX, 79409-1042, USA

    S. R. -J. Jang & Arun K. Mitra

Authors
  1. S. R. -J. Jang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Arun K. Mitra
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jang, S.R.J., Mitra, A.K. Equilibrium stability of single-species metapopulations. Bull. Math. Biol. 62, 155–161 (2000). https://doi.org/10.1006/bulm.1999.0145

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1006/bulm.1999.0145

Keywords

Search

Navigation