Journal Article

Dispersal and stability in metapopulations


in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 16, issue 3, pages 297-306
Published in print September 1999 | ISSN: 1477-8599
Published online September 1999 | e-ISSN: 1477-8602 | DOI:
Dispersal and stability in metapopulations

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  • Applied Mathematics
  • Biomathematics and Statistics


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What are the stability consequences of density-independent dispersal between locally distinct populations? Can such dispersal stabilize population dynamics or is it more likely to be a destabilizing influence? If so, what are the conditions required for dispersalinduced instability? We address these questions firstly by briefly reviewing the current literature, where it has been established that equilibrium stability in single-species models is not affected by dispersal. We then present a general model for two-species interaction, and establish, using analytic techniques, that density-independent movement between populations is never stabilizing; it may, however, destabilize. We conclude that in discrete time models, dispersal may be destabilizing if the following three criteria are satisfied: (1) there is more than one variable (species or age class) in the system, (2) the movement fractions of the two variables (species or age classes) are very different, and (3) the interaction between the variables (species or age classes) is semi-antagonistic (e.g. a predator-prey system).

Keywords: population dynamics; stability; dispersal; metapopulation; predator-prey model

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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