Abstract
Fretwell and Lucas [3] introduced the Ideal Free Distribution (IFD) to predict how birds establish themselves among habitats. It has been shown that the IFD is an evolutionarily stable strategy (ESS) of the habitat selection game when fitness is a decreasing function of patch density. We develop a formula for the IFD when there are an arbitrary number of habitats, and fitness functions are linearly decreasing in the population size (i.e., density) in each habitat. We also explore the IFD when fitness functions increase with population size until some maximum threshold is reached (Allee Effect) and examine whether an IFD still is an ESS in this case.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Broom, M., Rychtar, J.: Game-Theoretical Models in Biology. CRC Press, Oxfordshire (2013)
Cressman, R., Krivan, V.: Migration dynamics for the ideal free distribution. Am. Nat. 168, 384–397 (2006)
Fretwell, S., Lucas, H.: On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheor. 19, 16–32 (1969)
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University Press, Cambridge (2010)
Krivan, V.: The Allee-type ideal free distribution. J. Math. Biol. 69, 1497–1513 (2014)
Krivan, V., Cressman, R., Schneider, C.: The ideal free distribution: a review and synthesis of the game-theoretic perspective. Theor. Popul. Biol. 73, 403–425 (2008)
Morris, D.: Measuring the Allee effect: positive density dependence in small mammals. Ecology 83, 14–20 (2002)
Samuelson, L.: Evolutionary Games and Equilibrium Selection. MIT, Cambridge (1997)
Maynard Smith, J.: Evolution and the Theory of Games. Cambridge University Press, Cambridge (1982)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Cressman, R., Tran, T. (2015). The Ideal Free Distribution and Evolutionary Stability in Habitat Selection Games with Linear Fitness and Allee Effect. In: Cojocaru, M., Kotsireas, I., Makarov, R., Melnik, R., Shodiev, H. (eds) Interdisciplinary Topics in Applied Mathematics, Modeling and Computational Science. Springer Proceedings in Mathematics & Statistics, vol 117. Springer, Cham. https://doi.org/10.1007/978-3-319-12307-3_66
Download citation
DOI: https://doi.org/10.1007/978-3-319-12307-3_66
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-12306-6
Online ISBN: 978-3-319-12307-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)