Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1497–1513 | Cite as

The Allee-type ideal free distribution

  • Vlastimil KřivanEmail author


The ideal free distribution (IFD) in a two-patch environment where individual fitness is positively density dependent at low population densities is studied. The IFD is defined as an evolutionarily stable strategy of the habitat selection game. It is shown that for low and high population densities only one IFD exists, but for intermediate population densities there are up to three IFDs. Population and distributional dynamics described by the replicator dynamics are studied. It is shown that distributional stability (i.e., IFD) does not imply local stability of a population equilibrium. Thus distributional stability is not sufficient for population stability. Results of this article demonstrate that the Allee effect can strongly influence not only population dynamics, but also population distribution in space.


Dispersal Evolutionary game theory Habitat selection game Logistic equation Non-smooth analysis Population dynamics Optimal foraging 

Mathematics Subject Classification

26A27 92D25 92D40 92D50 



I thank Ross Cressman and two anonymous reviewers for their thoughtful suggestions. Institutional support RVO:60077344 is acknowledged.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Biology Center, Academy of Sciences of the Czech Republic, and Faculty of ScienceUniversity of South BohemiaCeske BudejoviceCzech Republic

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