TY - JOUR

T1 - Random dispersal versus fitness-dependent dispersal

AU - Cantrell, Robert Stephen

AU - Cosner, Chris

AU - Lou, Yuan

AU - Xie, Chao

N1 - Funding Information:
We thank Professor Bei Hu for pointing out the reference on Theorem 6.44 of [36]. This research was partially supported by the NSF grants DMS-0816068 (R.S.C., C.C.), DMS-1118623 (R.S.C., C.C.), DMS-1021179 (Y.L.) and has been supported in part by the Mathematical Biosciences Institute and the National Science Foundation under grant DMS-0931642 (Y.L.).

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

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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 -