IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v106y2015icp45-59.html
   My bibliography  Save this article

Is dispersal always beneficial to carrying capacity? New insights from the multi-patch logistic equation

Author

Listed:
  • 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 completely analysed. Here, we complete this analysis and we delineate the conditions under which fragmentation associated to dispersal is either beneficial or detrimental to total population abundance. Therefore, this is a contribution to the SLOSS question. Importantly, we also show that, depending on the underlying mechanism, there is no unique way to generalize the logistic model to a patchy situation. In many cases, the standard model is not the correct generalization. We analyse several alternative models and compare their predictions. Finally, we emphasize the shortcomings of the logistic model when written in the r-K parameterization and we explain why Verhulst’s original polynomial expression is to be preferred.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:thpobi:v:106:y:2015:i:c:p:45-59
    DOI: 10.1016/j.tpb.2015.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580915001021
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2015.10.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Wang, Yuanshi, 2019. "Asymmetric diffusion in a two-patch consumer-resource system," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 258-273.
    4. D.L. DeAngelis & Bo Zhang & Wei-Ming Ni & Yuanshi Wang, 2020. "Carrying Capacity of a Population Diffusing in a Heterogeneous Environment," Mathematics, MDPI, vol. 8(1), pages 1-12, January.
    5. 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.
    6. Wang, Yuanshi & DeAngelis, Donald L., 2019. "Energetic constraints and the paradox of a diffusing population in a heterogeneous environment," Theoretical Population Biology, Elsevier, vol. 125(C), pages 30-37.
    7. Jiapeng Qu & Zelin Liu & Zhenggang Guo & Yikang Li & Huakun Zhou, 2021. "A System Dynamics Model for Assessing the Efficacy of Lethal Control for Sustainable Management of Ochotona curzoniae on Tibetan Plateau," Sustainability, MDPI, vol. 13(2), pages 1-11, January.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:106:y:2015:i:c:p:45-59. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.