Journal of Mathematical Biology

, Volume 47, Issue 6, pp 483–517 | Cite as

The evolution of dispersal

  • V. Hutson
  • S. Martinez
  • K. Mischaikow
  • G.T. VickersEmail author


A non-local model for dispersal with continuous time and space is carefully justified and discussed. The necessary mathematical background is developed and we point out some interesting and challenging problems. While the basic model is not new, a ‘spread’ parameter (effectively the width of the dispersal kernel) has been introduced along with a conventional rate paramter, and we compare their competitive advantages and disadvantages in a spatially heterogeneous environment. We show that, as in the case of reaction-diffusion models, for fixed spread slower rates of diffusion are always optimal. However, fixing the dispersal rate and varying the spread while assuming a constant cost of dispersal leads to more complicated results. For example, in a fairly general setting given two phenotypes with different, but small spread, the smaller spread is selected while in the case of large spread the larger spread is selected.


General Setting Competitive Advantage Slow Rate Dispersal Rate Continuous Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • V. Hutson
    • 1
  • S. Martinez
    • 2
  • K. Mischaikow
    • 3
  • G.T. Vickers
    • 4
    Email author
  1. 1.Department of Applied MathematicsThe University of SheffieldSheffieldU.K
  2. 2.Departamento de Ingeniería MatemáticaUniversidad de ChileSantiagoChile
  3. 3.Department of MathematicsGeorgia Institute of TechnologyAtlantaU.S.A
  4. 4.Department of Applied MathematicsThe University of SheffieldSheffieldU.K

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