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The ideal free distribution: A review and synthesis of the game-theoretic perspective

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  • KÅ™ivan, Vlastimil
  • Cressman, Ross
  • Schneider, Candace

Abstract

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16–32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the “habitat selection game†. Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species.

Suggested Citation

  • KÅ™ivan, Vlastimil & Cressman, Ross & Schneider, Candace, 2008. "The ideal free distribution: A review and synthesis of the game-theoretic perspective," Theoretical Population Biology, Elsevier, vol. 73(3), pages 403-425.
    • Handle: RePEc:eee:thpobi:v:73:y:2008:i:3:p:403-425
    DOI: 10.1016/j.tpb.2007.12.009
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    References listed on IDEAS

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    1. Douglas W. Morris, 2006. "Moving to the ideal free home," Nature, Nature, vol. 443(7112), pages 645-646, October.
    2. Tamara C. Grand, 2002. "Alternative forms of competition and predation dramatically affect habitat selection under foraging--predation-risk trade-offs," Behavioral Ecology, International Society for Behavioral Ecology, vol. 13(2), pages 280-290, March.
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    4. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
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    1. van Leeuwen, E. & Jansen, V.A.A., 2010. "Evolutionary consequences of a search image," Theoretical Population Biology, Elsevier, vol. 77(1), pages 49-55.
    2. Frølich, Emil F. & Thygesen, Uffe H., 2022. "Solving multispecies population games in continuous space and time," Theoretical Population Biology, Elsevier, vol. 146(C), pages 36-45.
    3. Revilla, Tomás A. & Křivan, Vlastimil, 2022. "Prey–predator dynamics with adaptive protection mutualism," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    4. Yong-Chao Su & Cheng-Yu Wu & Cheng-Hong Yang & Bo-Sheng Li & Sin-Hua Moi & Yu-Da Lin, 2021. "Machine Learning Data Imputation and Prediction of Foraging Group Size in a Kleptoparasitic Spider," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    5. Mullon, Christian & Nagurney, Anna, 2012. "A game theoretical approach to the vertical coexistence of small and big fish," Ecological Modelling, Elsevier, vol. 240(C), pages 41-48.
    6. Mark Broom & Jan Rychtář, 2018. "Ideal Cost-Free Distributions in Structured Populations for General Payoff Functions," Dynamic Games and Applications, Springer, vol. 8(1), pages 79-92, March.
    7. Rowell, Jonathan T., 2009. "The limitation of species range: A consequence of searching along resource gradients," Theoretical Population Biology, Elsevier, vol. 75(2), pages 216-227.
    8. Jack W. Bradbury & Sandra L. Vehrencamp & Kenneth E. Clifton, 2015. "The ideal free antelope: foraging dispersions," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(5), pages 1303-1313.
    9. de Villemereuil, Pierre B. & López-Sepulcre, Andrés, 2011. "Consumer functional responses under intra- and inter-specific interference competition," Ecological Modelling, Elsevier, vol. 222(3), pages 419-426.
    10. Varga, Tamás & Garay, József & Rychtář, Jan & Broom, Mark, 2020. "A temporal model of territorial defence with antagonistic interactions," Theoretical Population Biology, Elsevier, vol. 134(C), pages 15-35.
    11. Bell, Adrian V. & Rader, Russell B. & Peck, Steven L. & Sih, Andrew, 2009. "The positive effects of negative interactions: Can avoidance of competitors or predators increase resource sampling by prey?," Theoretical Population Biology, Elsevier, vol. 76(1), pages 52-58.
    12. Menezes, Jorge F.S. & Kotler, Burt P., 2019. "The generalized ideal free distribution model: Merging current ideal free distribution models into a central framework," Ecological Modelling, Elsevier, vol. 397(C), pages 47-54.

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