Evolution of dispersal and the ideal free distribution

Research output: Contribution to journalArticle

66 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)17-36
Number of pages20
JournalMathematical Biosciences and Engineering
Volume7
Issue number1
DOIs
StatePublished - Jan 2010

Fingerprint

Distribution-free
Population Dynamics
Advection
Ecosystem
evolutionarily stable strategy
Population dynamics
population dynamics
biogeography
habitats
Evolutionarily Stable Strategy
Competition Model
advection
Fitness
Strategy
Gradient
Resources
Coefficient

Keywords

  • Evolution of dispersal
  • Ideal free distribution
  • Reaction-diffusion-advection

ASJC Scopus subject areas

  • Applied Mathematics
  • Modeling and Simulation
  • Computational Mathematics
  • Agricultural and Biological Sciences(all)
  • Medicine(all)

Cite this

Evolution of dispersal and the ideal free distribution. / Cantrell, Robert; Cosner, George; Lou, Yuan.

In: Mathematical Biosciences and Engineering, Vol. 7, No. 1, 01.2010, p. 17-36.

Research output: Contribution to journalArticle

@article{46e938ec465d442a8a91210f7c1f752e,
title = "Evolution of dispersal and the ideal free distribution",
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.",
keywords = "Evolution of dispersal, Ideal free distribution, Reaction-diffusion-advection",
author = "Robert Cantrell and George Cosner and Yuan Lou",
year = "2010",
month = "1",
doi = "10.3934/mbe.2010.7.17",
language = "English (US)",
volume = "7",
pages = "17--36",
journal = "Mathematical Biosciences and Engineering",
issn = "1547-1063",
publisher = "Arizona State University",
number = "1",

}

TY - JOUR

T1 - Evolution of dispersal and the ideal free distribution

AU - Cantrell, Robert

AU - Cosner, George

AU - Lou, Yuan

PY - 2010/1

Y1 - 2010/1

N2 - 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.

AB - 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.

KW - Evolution of dispersal

KW - Ideal free distribution

KW - Reaction-diffusion-advection

UR - http://www.scopus.com/inward/record.url?scp=77954650698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954650698&partnerID=8YFLogxK

U2 - 10.3934/mbe.2010.7.17

DO - 10.3934/mbe.2010.7.17

M3 - Article

VL - 7

SP - 17

EP - 36

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 1

ER -