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Competition, predation and coexistence in a three trophic system

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  • Florencia Carusela, M.
  • Momo, Fernando R.
  • Romanelli, Lilia

Abstract

Simple ecological models that mostly operate with population densities using continuous variables, explain quite well the behavior of real populations. In this work we propose and discuss the continuous dynamics of a system of three species, which belongs to the well-known family of Lotka–Volterra models. In particular, the proposed model includes direct effects such as predation and competition among species, and indirect effects such as refuge. The model is proposed to explain recent studies about a group of crustacean (amphipods of genus Hyallela) found in all the plain streams and shallow lakes of the American continent. The studied system includes three compartments: algae, a strictly herbivore amphipod and an omnivore (herbivore and carnivore) one. The analysis of the model shows that there are stable extinction equilibria throughout all the parameters’ space. There are also equilibria with stable coexistence of the three species and two interesting binary equilibria: one with stable coexistence of algae and herbivore and other with coexistence between algae and omnivore amphipods. The presence of Allee effect in the algae growth and the existence of refuge for the herbivore amphipod (prey) determine a bottom-up control.

Suggested Citation

  • Florencia Carusela, M. & Momo, Fernando R. & Romanelli, Lilia, 2009. "Competition, predation and coexistence in a three trophic system," Ecological Modelling, Elsevier, vol. 220(19), pages 2349-2352.
    • Handle: RePEc:eee:ecomod:v:220:y:2009:i:19:p:2349-2352
    DOI: 10.1016/j.ecolmodel.2009.06.008
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    References listed on IDEAS

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    1. Naji, R.K. & Balasim, A.T., 2007. "On the dynamical behavior of three species food web model," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1636-1648.
    2. Naji, Raid Kamel & Balasim, Alla Tariq, 2007. "Dynamical behavior of a three species food chain model with Beddington–DeAngelis functional response," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1853-1866.
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    Cited by:

    1. Li, Junmin & Huang, Ping & Zhang, Renduo, 2010. "Modeling the refuge effect of submerged macrophytes in ecological dynamics of shallow lakes: A new model of fish functional response," Ecological Modelling, Elsevier, vol. 221(17), pages 2076-2085.
    2. Renato Colucci & Érika Diz-Pita & M. Victoria Otero-Espinar, 2021. "Dynamics of a Two Prey and One Predator System with Indirect Effect," Mathematics, MDPI, vol. 9(4), pages 1-22, February.

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