Skip to main content
Log in

Synchronism in a metapopulation model

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

Abstract

We consider a spatially explicit metapopulation model with interaction among the two nearest neighbors to relate, with a simple mathematical expression, chaos in the local, uncoupled, populations, the degree of interaction among patches, size of the metapopulation, and the stability of the synchronized attractor. Since synchronism is strongly correlated with extinction, our results can provide useful information on factors leading to population extinction.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Allen, J. C., W. M. Schaffer and D. Rosko (1993). Chaos reduces species extinction by amplifying local population noise. Nature 364, 229–232.

    Article  Google Scholar 

  • Commins, H. N., M. P. Hassel and R. M. May (1992). The spatial dynamics of host parasitoid systems. J. Anim. Ecol. 61, 735–748.

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Gilpin, M. E. and I. Hanski (1991). Metapopulation Dynamics: Empirical and Theoretical Investigations, London: Academic Press.

    Google Scholar 

  • Hanski, I. (1997). Metapopulation Dynamics: from Concepts and Observations to Predictive Models, London: Academic Press.

    Google Scholar 

  • Hanski, I. and M. E. Gilpin (1997). Metapopulation Biology: Ecology Genetics and Evolution, London: Academic Press.

    Google Scholar 

  • Hassel, M. P. (1975). Density dependence in single species populations. J. Anim. Ecol. 44, 283–295.

    Google Scholar 

  • Hassel, M. P., H. N. Commins and R. M. May (1991). Spacial structure and chaos in insect population dynamics. Nature 353, 255–258.

    Article  Google Scholar 

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

    Google Scholar 

  • Hassel, M. P., J. N. Lawton and R. M. May (1976). Patterns of dynamical behavior in single-species populations. J. Anim. Ecol. 45, 471–486.

    Google Scholar 

  • Hastings, A. (1992). Age dependent dispersal is not a simple process: density dependence, stability, and chaos. Theor. Pop. Biol. 41, 388–400.

    Article  MATH  Google Scholar 

  • Hastings, A. (1993). Complex interactions between dispersal and dynamics: lessons from coupled logistic equations. Ecology 74, 1262–1272.

    Article  Google Scholar 

  • Kaneko, K. (1989a). Pattern dynamics in spatiotemporal chaos. Physica D 34, 1–41.

    Article  MATH  MathSciNet  Google Scholar 

  • Kaneko, K. (1989b). Spatiotemporal chaos in one-and two-dimensional coupled map lattices. Physica D 37, 60–82.

    Article  MathSciNet  Google Scholar 

  • Kaneko, K. (1993). Theory and Applications of Coupled Map Lattices, New York: Wiley & Sons.

    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. (1974). Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science 186, 645–647.

    Google Scholar 

  • May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459–469.

    Article  Google Scholar 

  • May, R. M. and G. F. Oster (1976). Bifurcations and dynamic complexity in simple ecological models. Am. Naturalist 110, 573–799.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Ruxton, G. M. (1996b). Synchronization between individuals and the dynamics of linked populations. J. Theor. Biol. 183, 47–54.

    Article  Google Scholar 

  • Solé, R. V. and J. P. G. Gamarra (1998). Chaos, dispersal and extinction in coupled ecosystems. J. Theor. Biol. 193, 539–541.

    Article  Google Scholar 

  • Solé, R. V. and J. Valls (1992a). Spiral waves, chaos and multiple attractors in lattice models of interaction populations. Phys. Lett. A 166, 123–128.

    Article  Google Scholar 

  • Solé, R. V. and J. Valls (1992b). On structural stability and chaos in biological systems. J. Theor. Biol. 155, 87–102.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Silva, J.A.L., De Castro, M.L. & Justo, D.A.R. Synchronism in a metapopulation model. Bull. Math. Biol. 62, 337–349 (2000). https://doi.org/10.1006/bulm.1999.0157

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1006/bulm.1999.0157

Keywords

Navigation