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Evolution of Dispersal in Advective Patchy Environments

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Abstract

We study a two-species competition model in a patchy advective environment, where the species are subject to both directional drift and undirectional random dispersal between patches and there are losses of individuals in the downstream end (e.g., due to the flow into a lake or ocean). The two competing species are assumed to have the same growth rates but different advection and random dispersal rates. We focus our studies on the properties of an associated eigenvalue problem which characterizes the extinction/persistence dynamics of the underlying patch population model. We also derive conditions on the advection and random dispersal rates under which a mutant species can or cannot invade the resident species.

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Data Availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

The authors thank two anonymous reviewers for their insightful suggestions that led to improvement of the paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Weihai, 264209, Shandong, People’s Republic of China

    Shanshan Chen

  2. Department of Mathematics, William & Mary, Williamsburg, VA, 23187-8795, USA

    Junping Shi

  3. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Zhisheng Shuai

  4. Department of Mathematics, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Yixiang Wu

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  1. Shanshan Chen

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  2. Junping Shi

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Correspondence toJunping Shi.

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Communicated by Paul Newton.

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S. Chen is supported by National Natural Science Foundation of China (Nos. 12171117, 11771109) and Shandong Provincial Natural Science Foundation of China (No. ZR2020YQ01), J. Shi is supported by US-NSF Grant DMS-1715651 and DMS-1853598, and Z. Shuai is supported by US-NSF Grant DMS-1716445.

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