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Asymmetric dispersal in the multi-patch logistic equation

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  • Arditi, Roger
  • Lobry, Claude
  • Sari, Tewfik

Abstract

The standard model for the dynamics of a fragmented density-dependent population is built from several local logistic models coupled by migrations. First introduced in the 1970s and used in innumerable articles, this standard model applied to a two-patch situation has never been fully analyzed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated with dispersal is either favorable or unfavorable to total population abundance. We pay special attention to the case of asymmetric dispersal, i.e., the situation in which the dispersal rate from patch 1 to patch 2 is not equal to the dispersal rate from patch 2 to patch 1. We show that this asymmetry can have a crucial quantitative influence on the effect of dispersal.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:120:y:2018:i:c:p:11-15
    DOI: 10.1016/j.tpb.2017.12.006
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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.
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    Cited by:

    1. Auger, Pierre & Kooi, Bob & Moussaoui, Ali, 2022. "Increase of maximum sustainable yield for fishery in two patches with fast migration," Ecological Modelling, Elsevier, vol. 467(C).
    2. 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.
    3. 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.
    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.
    5. 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.
    6. Tan, Chengguan & Wang, Yuanshi & Wu, Hong, 2020. "A consumer–resource system with source–sink populations and asymmetric dispersal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. 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.
    8. Benaïm, Michel & Lobry, Claude & Sari, Tewfik & Strickler, Édouard, 2023. "Untangling the role of temporal and spatial variations in persistence of populations," Theoretical Population Biology, Elsevier, vol. 154(C), pages 1-26.

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