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Competition And Predation In A Three Species Model

Author

Listed:
  • JANUSZ SZWABIǸSKI

    (Institute of Theoretical Physics, Wrocław University, pl. Maxa Borna 9, 50-204 Wrocław, Poland)

  • ANDRZEJ PȨKALSKI

    (Institute of Theoretical Physics, Wrocław University, pl. Maxa Borna 9, 50-204 Wrocław, Poland)

  • KAMIL TROJAN

    (Institute of Theoretical Physics, Wrocław University, pl. Maxa Borna 9, 50-204 Wrocław, Poland)

Abstract

A model of dynamics of three interacting species is presented. Two of the species are prey and one is predator, which feeds on both prey, however with some preference to one type. Prey compete for space (breeding) although they always have access to food. Predators in order to survive and reproduce must catch prey, otherwise they die of hunger. The dynamics of the model is found via differential equations in the mean-field like approach and through computer simulations for agent-based method. We show that the coexistence of the three species is possible in the mean-field model, provided the preference of the predators is small, whereas from simulation it follows that the stochastic fluctuations drive, generally, one of the prey populations into extinction. We have found a different type of behavior for small and large systems and a rather unexpected dependence of the coexistence chance of the preference parameter in bigger lattices.

Suggested Citation

  • Janusz Szwabiǹski & Andrzej Pȩkalski & Kamil Trojan, 2006. "Competition And Predation In A Three Species Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(11), pages 1629-1645.
    • Handle: RePEc:wsi:ijmpcx:v:17:y:2006:i:11:n:s0129183106010078
    DOI: 10.1142/S0129183106010078
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