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Modulation of predator–prey interactions by the Allee effect

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  • Verdy, Ariane

Abstract

An Allee effect arising from density-dependent mating success can have significant impacts at the ecosystem level when considered in the context of predator–prey interactions. These are captured by a mathematical model for the exchange of biomass between a structured predator population (continuous weight distribution) and a resource. Because the predator’s mating success affects the amount of resources required for the production of offsprings and their future growth into mature organisms, it influences the flux of biomass between trophic levels. Under simple assumptions, the equations can be reduced to an equivalent unstructured predator–prey model in which the Allee effect modulates the predation rate: the mating probability multiplies the rate of predator growth as well as the rate of resource depletion. Implications of the Allee effect for the bifurcation structure and equilibrium densities are examined. The model is compared to a modified version in which the Allee effect instead modulates the assimilation efficiency, hence the mating probability does not appear in the dynamical equation for the resource density. Both models exhibit qualitatively similar dynamics. However, compared to the model in which the Allee effect modulates predation, the model in which the Allee effect modulates assimilation efficiency predicts (i) unrealistically inefficient resource assimilation when predator density is low, (ii) a higher risk of catastrophic extinction resulting from a change in the parameter controlling the strength of the Allee effect, and (iii) no possibility of an increase in population size when the density dependence is enhanced.

Suggested Citation

  • Verdy, Ariane, 2010. "Modulation of predator–prey interactions by the Allee effect," Ecological Modelling, Elsevier, vol. 221(8), pages 1098-1107.
    • Handle: RePEc:eee:ecomod:v:221:y:2010:i:8:p:1098-1107
    DOI: 10.1016/j.ecolmodel.2010.01.005
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    References listed on IDEAS

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    1. De Roos, André M. & Schellekens, Tim & Van Kooten, Tobias & Van De Wolfshaar, Karen & Claessen, David & Persson, Lennart, 2008. "Simplifying a physiologically structured population model to a stage-structured biomass model," Theoretical Population Biology, Elsevier, vol. 73(1), pages 47-62.
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    Cited by:

    1. Pal, Pallav Jyoti & Mandal, Gourav & Guin, Lakshmi Narayan & Saha, Tapan, 2024. "Allee effect and hunting-induced bifurcation inquisition and pattern formation in a modified Leslie–Gower interacting species system," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    2. Kumar, Udai & Mandal, Partha Sarathi, 2022. "Role of Allee effect on prey–predator model with component Allee effect for predator reproduction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 623-665.
    3. Boli Xie & Zhijun Wang & Yakui Xue & Zhenmin Zhang, 2015. "The Dynamics of a Delayed Predator-Prey Model with Double Allee Effect," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, October.
    4. Iskin da S. Costa, Michel & dos Anjos, Lucas, 2018. "Multiple hydra effect in a predator–prey model with Allee effect and mutual interference in the predator," Ecological Modelling, Elsevier, vol. 373(C), pages 22-24.

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