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Is dispersal always beneficial to carrying capacity? New insights from 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 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
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Wang, Yuanshi, 2019. "Asymmetric diffusion in a two-patch consumer-resource system," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 258-273.
    10. 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.
    11. 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.

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