Mathematical Aspects of the Ideal Free Distribution
by
Chris Cosner
University of Miami
Coauthors: R.S. Cantrell, D. DeAngelis, Y. Lou, M. Kshatriya, and V. Padron

The ideal free distribution as formulated by Fretwell and Lucas is a description of the equilibrium spatial distribution of a population that would arise if each individual were able to move to the location where its fitness is highest. Usually the presence of other individuals at a given location is assumed to reduce the fitness of each individual at that location because of crowding effects. This typically results in a situation where all individuals have the same fitness since if some individuals had a lower fitness than others they would move to increase their fitness. This talk will describe some recent work aimed at connecting these ideas to population dynamics. Specific aspects of this work include formulating the ideal free distribution in continuous space, deriving a partial differential equation which can produce that continuum version of the ideal free distribution as an equilibrium, making connections between the ideal free distribution and the idea of balanced dispersal, and showing that ideal free, i.e. balanced, dispersal strategies are sometimes evolutionarily stable in discrete diffusion models. The mathematical analysis uses various ideas and methods from the theory of discrete diffusion systems and reaction-diffusion equations.

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Date received: August 29, 2007