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Evolutionarily stable dispersal strategies in a two-patch advective environment

  • * Corresponding author: Yihao Fang

    * Corresponding author: Yihao Fang
Jing-jing Xiang is partially supported by the Research Foundation of Education Bureau of Shaanxi Province (15JK1433), "The mathematical modeling and analysis of disease spreading in media". Yihao Fang is partially supported by the National Natural Science Foundation of China(11571364).
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  • Two-patch models are used to mimic the unidirectional movement of organisms in continuous, advective environments. We assume that species can move between two patches, with patch 1 as the upper stream patch and patch 2 as the downstream patch. Species disperse between two patches with the same rate, and species in patch 1 is transported to patch 2 by drift, but not vice versa. We also mimic no-flux boundary conditions at the upstream and zero Dirichlet boundary conditions at the downstream. The criteria for the persistence of a single species is established. For two competing species model, we show that there is an intermediate dispersal rate which is evolutionarily stable. These results support the conjecture in [6], initially proposed for reaction-diffusion models with continuous advective environments.

    Mathematics Subject Classification: Primary: 37X75; Secondary: 92D40.


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  • Figure 1.  Illustration of Lemma 3.6 for $0\leq q < 1$

    Figure 2.  Illustration of Lemma 3.7 for $1\leq q < 5/4$

    Figure 3.  PIP for $0<q < 1$ with the sign of $\lambda_1$

    Figure 4.  PIP for $1\leq q < 5/4$ with the sign of $\lambda_1$

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