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From the Lotka–Volterra model to a spatialised population-driven individual-based model

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  • Thierry, Hugo
  • Sheeren, David
  • Marilleau, Nicolas
  • Corson, Nathalie
  • Amalric, Marion
  • Monteil, Claude

Abstract

The modelling of predator–prey dynamics is of great importance in ecology. Models based on differential equations aim to understand the interactions between populations of prey and predators at population scale, but they are unable to handle spatial and individual behaviour heterogeneities (individual scale). In this study, a population-driven individual-based model is proposed that has been developed from the archetypical Lotka–Volterra model. The population scale was retained for processes with slower dynamics, such as reproduction for both species and the natural death of predators. The individual scale was only used for the predation process, defining local rules for individual movements of prey and predators (related to a perception distance of predators and the presence of shelters for prey in the spatial environment) and to locate births and deaths. This model was compared with the Lotka–Volterra model. Simulations were able to exhibit the overall classic periodic evolution of population sizes with local variations. The effects of spatial heterogeneity were then explored through a range of prey refuge densities. The model was implemented on the Netlogo platform. This work illustrates how both individual and population scales may be linked through methodological choices in order to focus on the impacts of spatialisation and take into account the effects of spatial and individual heterogeneities.

Suggested Citation

  • Thierry, Hugo & Sheeren, David & Marilleau, Nicolas & Corson, Nathalie & Amalric, Marion & Monteil, Claude, 2015. "From the Lotka–Volterra model to a spatialised population-driven individual-based model," Ecological Modelling, Elsevier, vol. 306(C), pages 287-293.
    • Handle: RePEc:eee:ecomod:v:306:y:2015:i:c:p:287-293
    DOI: 10.1016/j.ecolmodel.2014.09.022
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    References listed on IDEAS

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    1. Trojan, Kamil & Pȩkalski, Andrzej, 2003. "Dynamics of a predator–prey model in a habitat with cover," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 330(1), pages 130-138.
    2. Salau, Kehinde & Schoon, Michael L. & Baggio, Jacopo A. & Janssen, Marco A., 2012. "Varying effects of connectivity and dispersal on interacting species dynamics," Ecological Modelling, Elsevier, vol. 242(C), pages 81-91.
    3. Karsai, Istvan & Kampis, George, 2011. "Connected fragmented habitats facilitate stable coexistence dynamics," Ecological Modelling, Elsevier, vol. 222(3), pages 447-455.
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    Cited by:

    1. Kumar, Sunil & Kumar, Ranbir & Cattani, Carlo & Samet, Bessem, 2020. "Chaotic behaviour of fractional predator-prey dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Marilleau, Nicolas & Lang, Christophe & Giraudoux, Patrick, 2018. "Coupling agent-based with equation-based models to study spatially explicit megapopulation dynamics," Ecological Modelling, Elsevier, vol. 384(C), pages 34-42.

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