Journal of Mathematical Biology

, Volume 67, Issue 2, pp 329–358 | Cite as

Two-patch population models with adaptive dispersal: the effects of varying dispersal speeds

  • Ross Cressman
  • Vlastimil KřivanEmail author


The population-dispersal dynamics for predator–prey interactions and two competing species in a two patch environment are studied. It is assumed that both species (i.e., either predators and their prey, or the two competing species) are mobile and their dispersal between patches is directed to the higher fitness patch. It is proved that such dispersal, irrespectively of its speed, cannot destabilize a locally stable predator–prey population equilibrium that corresponds to no movement at all. In the case of two competing species, dispersal can destabilize population equilibrium. Conditions are given when this cannot happen, including the case of identical patches.


Competition Dispersal Evolution Habitat selection Ideal free distribution Predator Prey Population dynamics 

Mathematics Subject Classification

34D20 92D25 92D40 92D50 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of MathematicsWilfrid Laurier UniversityWaterlooCanada
  2. 2.Biology CenterAcademy of Sciences of the Czech Republic, and Faculty of Biological SciencesČeské BudějoviceCzech Republic

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