Evolution of dispersal and the ideal free distribution
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1.
Department of Mathematics, University of Miami, P. O . Box 249085, Coral Gables, FL 33124-4250
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Department of Mathematics, The Ohio State State University, Columbus, Ohio 43210
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Received:
01 April 2009
Accepted:
29 June 2018
Published:
01 January 2010
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MSC :
Primary: 35K57, 92D25.
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A general question in the study of the evolution of dispersal
is what kind of dispersal strategies can convey
competitive advantages and thus will evolve.
We consider a two species competition model
in which the species are assumed to have the same population dynamics but different dispersal strategies.
Both species disperse by random diffusion and advection along certain
gradients, with the same random dispersal rates but different advection
coefficients.
We found a conditional dispersal strategy which results in the ideal free distribution of species,
and show that it is a local
evolutionarily stable strategy.
We further show that this strategy
is also a global convergent stable strategy
under suitable assumptions, and our results
illustrate how the evolution of conditional dispersal can lead to an ideal free distribution.
The underlying biological reason is that
the species with this particular dispersal strategy can perfectly match the environmental
resource, which leads to its fitness being equilibrated across the habitats.
Citation: Robert Stephen Cantrell, Chris Cosner, Yuan Lou. Evolution of dispersal and the ideal free distribution[J]. Mathematical Biosciences and Engineering, 2010, 7(1): 17-36. doi: 10.3934/mbe.2010.7.17
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Abstract
A general question in the study of the evolution of dispersal
is what kind of dispersal strategies can convey
competitive advantages and thus will evolve.
We consider a two species competition model
in which the species are assumed to have the same population dynamics but different dispersal strategies.
Both species disperse by random diffusion and advection along certain
gradients, with the same random dispersal rates but different advection
coefficients.
We found a conditional dispersal strategy which results in the ideal free distribution of species,
and show that it is a local
evolutionarily stable strategy.
We further show that this strategy
is also a global convergent stable strategy
under suitable assumptions, and our results
illustrate how the evolution of conditional dispersal can lead to an ideal free distribution.
The underlying biological reason is that
the species with this particular dispersal strategy can perfectly match the environmental
resource, which leads to its fitness being equilibrated across the habitats.
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