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A predator–prey refuge system: Evolutionary stability in ecological systems

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  • Cressman, Ross
  • Garay, József

Abstract

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.

Suggested Citation

  • Cressman, Ross & Garay, József, 2009. "A predator–prey refuge system: Evolutionary stability in ecological systems," Theoretical Population Biology, Elsevier, vol. 76(4), pages 248-257.
    • Handle: RePEc:eee:thpobi:v:76:y:2009:i:4:p:248-257
    DOI: 10.1016/j.tpb.2009.08.005
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    References listed on IDEAS

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    1. P. Marrow & U. Dieckmann & R. Law, 1996. "Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective," Working Papers wp96002, International Institute for Applied Systems Analysis.
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    1. Jana, Soovoojeet & Chakraborty, Milon & Chakraborty, Kunal & Kar, T.K., 2012. "Global stability and bifurcation of time delayed prey–predator system incorporating prey refuge," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 85(C), pages 57-77.
    2. Eshel, Ilan & Sansone, Emilia & Shaked, Avner, 2011. "On the evolution of group-escape strategies of selfish prey," Theoretical Population Biology, Elsevier, vol. 80(2), pages 150-157.
    3. Ghanbari, Behzad & Cattani, Carlo, 2020. "On fractional predator and prey models with mutualistic predation including non-local and nonsingular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Gámez, M. & López, I. & Shamandy, A., 2010. "Open- and closed-loop equilibrium control of trophic chains," Ecological Modelling, Elsevier, vol. 221(16), pages 1839-1846.

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