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Dispersal asymmetry in a two-patch system with source–sink populations

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  • Wu, Hong
  • Wang, Yuanshi
  • Li, Yufeng
  • DeAngelis, Donald L.

Abstract

This paper analyzes source–sink systems with asymmetric dispersal between two patches. Complete analysis on the models demonstrates a mechanism by which the dispersal asymmetry can lead to either an increased total size of the species population in two patches, a decreased total size with persistence in the patches, or even extinction in both patches. For a large growth rate of the species in the source and a fixed dispersal intensity, (i) if the asymmetry is small, the population would persist in both patches and reach a density higher than that without dispersal, in which the population approaches its maximal density at an appropriate asymmetry; (ii) if the asymmetry is intermediate, the population persists in both patches but reaches a density less than that without dispersal; (iii) if the asymmetry is large, the population goes to extinction in both patches; (iv) asymmetric dispersal is more favorable than symmetric dispersal under certain conditions. For a fixed asymmetry, similar phenomena occur when the dispersal intensity varies, while a thorough analysis is given for the low growth rate of the species in the source. Implications for populations in heterogeneous landscapes are discussed, and numerical simulations confirm and extend our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:131:y:2020:i:c:p:54-65
    DOI: 10.1016/j.tpb.2019.11.004
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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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    Citations

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    Cited by:

    1. Sadykov, Alexander & Farnsworth, Keith D., 2021. "Model of two competing populations in two habitats with migration: Application to optimal marine protected area size," Theoretical Population Biology, Elsevier, vol. 142(C), pages 114-122.
    2. 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.
    3. Gao, Daozhou & Lou, Yuan, 2022. "Total biomass of a single population in two-patch environments," Theoretical Population Biology, Elsevier, vol. 146(C), pages 1-14.
    4. 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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