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Population abundance in predator–prey systems with predator’s dispersal between two patches

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  • Huang, Rong
  • Wang, Yuanshi
  • Wu, Hong

Abstract

This paper considers predator–prey systems in which the predator moves between two patches. One patch is a source, where the predator and prey can persist, while the other is a sink where the predator cannot survive. Our aim is to show whether or not the dispersal is beneficial to the predator’s total abundance at equilibrium. Using dynamical systems theory, we demonstrate conditions under which a dispersing predator can persist. Our analysis shows that the predator equilibrium abundance at intermediate dispersal rates can be higher than that without dispersal, while extremely large or small dispersal rates could result in predator’s extinction. Moreover, we find an explicit expression for the total abundance, which clearly shows the role of dispersal rates and asymmetry on the predator’s abundance. Numerical simulations confirm and extend our results.

Suggested Citation

  • Huang, Rong & Wang, Yuanshi & Wu, Hong, 2020. "Population abundance in predator–prey systems with predator’s dispersal between two patches," Theoretical Population Biology, Elsevier, vol. 135(C), pages 1-8.
    • Handle: RePEc:eee:thpobi:v:135:y:2020:i:c:p:1-8
    DOI: 10.1016/j.tpb.2020.06.002
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    References listed on IDEAS

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    1. Arditi, Roger & Lobry, Claude & Sari, Tewfik, 2018. "Asymmetric dispersal in the multi-patch logistic equation," Theoretical Population Biology, Elsevier, vol. 120(C), pages 11-15.
    2. Arditi, Roger & Lobry, Claude & Sari, Tewfik, 2015. "Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation," Theoretical Population Biology, Elsevier, vol. 106(C), pages 45-59.
    3. Wu, Hong & Wang, Yuanshi & Li, Yufeng & DeAngelis, Donald L., 2020. "Dispersal asymmetry in a two-patch system with source–sink populations," Theoretical Population Biology, Elsevier, vol. 131(C), pages 54-65.
    4. Ruiz-Herrera, Alfonso, 2018. "Metapopulation dynamics and total biomass: Understanding the effects of diffusion in complex networks," Theoretical Population Biology, Elsevier, vol. 121(C), pages 1-11.
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    Cited by:

    1. Jiale Ban & Yuanshi Wang & Hong Wu, 2022. "Dynamics of predator-prey systems with prey’s dispersal between patches," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(2), pages 550-569, June.

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