TY - JOUR

T1 - Ecological and evolutionary dynamics in advective environments

T2 - Critical domain size and boundary conditions

AU - Hao, Wenrui

AU - Lam, King Yeung

AU - Lou, Yuan

N1 - Funding Information:
92D407. Key words and phrases. Reaction-diffusion-advection, persistence, competition, evolutionarily stable strategy, boundary effect, critical domain size. The first author is supported by NSF grant DMS-1818769. The second and third authors are supported by NSF grant DMS-1853561. ∗ Corresponding author: lam.184@math.ohio-state.edu.
Funding Information:
Lewis for stimulating discussions and helpful comments. We thank the three anonymous referees for their comments and suggestions which have substantially improved the presentation of the manuscript. KYL thanks the hospitality of Center for Mathematical Biology, University of Alberta, where part of the research is done. WH was partially supported by the NSF grant DMS-1818769. KYL and YL were partially supported by the NSF grant DMS-1853561.
Publisher Copyright:
© 2021 American Institute of Mathematical Sciences. All rights reserved.

PY - 2021/1

Y1 - 2021/1

N2 - We consider the ecological and evolutionary dynamics of a reactiondi fiusion-advection model for populations residing in a one-dimensional advective homogeneous environment, with emphasis on the effects of boundary conditions and domain size. We assume that there is a net loss of individuals at the downstream end with rate b C 0, while the no-ux condition is imposed on the upstream end. For the single species model, it is shown that the critical patch size is a decreasing function of the dispersal rate when b B 3/2; whereas it first decreases and then increases when b > 3/2. For the two-species competition model, we show that the infinite dispersal rate is evolutionarily stable for b < 3/2 and, when dispersal rates of both species are large, the population with larger dispersal rate always displaces the population with the smaller rate. For certain specific population loss rate b < 3/2, it is also shown that there can be up to three evolutionarily stable strategies. For b > 3/2, it is proved that the infinite random dispersal rate is not evolutionarily stable, and that, for some specific b > 3/2, a finite dispersal rate is evolutionarily stable. Furthermore, for the intermediate domain size, this dispersal rate is optimal in the sense that the species adopting this rate is able to displace its competitor with a similar but different rate. Finally, nine qualitatively different pairwise invasibility plots are obtained by varying the parameter b and the domain size.

AB - We consider the ecological and evolutionary dynamics of a reactiondi fiusion-advection model for populations residing in a one-dimensional advective homogeneous environment, with emphasis on the effects of boundary conditions and domain size. We assume that there is a net loss of individuals at the downstream end with rate b C 0, while the no-ux condition is imposed on the upstream end. For the single species model, it is shown that the critical patch size is a decreasing function of the dispersal rate when b B 3/2; whereas it first decreases and then increases when b > 3/2. For the two-species competition model, we show that the infinite dispersal rate is evolutionarily stable for b < 3/2 and, when dispersal rates of both species are large, the population with larger dispersal rate always displaces the population with the smaller rate. For certain specific population loss rate b < 3/2, it is also shown that there can be up to three evolutionarily stable strategies. For b > 3/2, it is proved that the infinite random dispersal rate is not evolutionarily stable, and that, for some specific b > 3/2, a finite dispersal rate is evolutionarily stable. Furthermore, for the intermediate domain size, this dispersal rate is optimal in the sense that the species adopting this rate is able to displace its competitor with a similar but different rate. Finally, nine qualitatively different pairwise invasibility plots are obtained by varying the parameter b and the domain size.

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U2 - 10.3934/dcdsb.2020283

DO - 10.3934/dcdsb.2020283

M3 - Article

AN - SCOPUS:85101382543

VL - 26

SP - 367

EP - 400

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 1

ER -