Abstract
This work extends previous work (Cantrell et al., 2008 [9]) on fitness-dependent dispersal for a single species to a two-species competition model. Both species have the same population dynamics, but one species adopts a combination of random and fitness-dependent dispersal and the other adopts random dispersal. Global existence of smooth solutions to the time-dependent quasilinear parabolic system is studied. When a single species has a strong tendency to move up its fitness gradient, it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution (Cantrell et al., 2008 [9]). For the two-species competition model, if one species has strong tendency to move up its fitness gradient, such approximately ideal free dispersal is advantageous relative to random dispersal. Bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 2905-2941 |
| Number of pages | 37 |
| Journal | Journal of Differential Equations |
| Volume | 254 |
| Issue number | 7 |
| DOIs | |
| State | Published - Apr 1 2013 |
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Keywords
- 35K57
- 92D25
- Fitness-dependent dispersal
- Random dispersal
- Reaction-diffusion-advection
ASJC Scopus subject areas
- Analysis
Cite this
Random dispersal versus fitness-dependent dispersal. / Cantrell, Robert; Cosner, George; Lou, Yuan; Xie, Chao.
In: Journal of Differential Equations, Vol. 254, No. 7, 01.04.2013, p. 2905-2941.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Random dispersal versus fitness-dependent dispersal
AU - Cantrell, Robert
AU - Cosner, George
AU - Lou, Yuan
AU - Xie, Chao
PY - 2013/4/1
Y1 - 2013/4/1
N2 - This work extends previous work (Cantrell et al., 2008 [9]) on fitness-dependent dispersal for a single species to a two-species competition model. Both species have the same population dynamics, but one species adopts a combination of random and fitness-dependent dispersal and the other adopts random dispersal. Global existence of smooth solutions to the time-dependent quasilinear parabolic system is studied. When a single species has a strong tendency to move up its fitness gradient, it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution (Cantrell et al., 2008 [9]). For the two-species competition model, if one species has strong tendency to move up its fitness gradient, such approximately ideal free dispersal is advantageous relative to random dispersal. Bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate.
AB - This work extends previous work (Cantrell et al., 2008 [9]) on fitness-dependent dispersal for a single species to a two-species competition model. Both species have the same population dynamics, but one species adopts a combination of random and fitness-dependent dispersal and the other adopts random dispersal. Global existence of smooth solutions to the time-dependent quasilinear parabolic system is studied. When a single species has a strong tendency to move up its fitness gradient, it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution (Cantrell et al., 2008 [9]). For the two-species competition model, if one species has strong tendency to move up its fitness gradient, such approximately ideal free dispersal is advantageous relative to random dispersal. Bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate.
KW - 35K57
KW - 92D25
KW - Fitness-dependent dispersal
KW - Random dispersal
KW - Reaction-diffusion-advection
UR - http://www.scopus.com/inward/record.url?scp=84873247000&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84873247000&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2013.01.012
DO - 10.1016/j.jde.2013.01.012
M3 - Article
AN - SCOPUS:84873247000
VL - 254
SP - 2905
EP - 2941
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 7
ER -