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A multiple phenotype predator–prey model with mutation

Author

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  • Abernethy, Gavin M.
  • Mullan, Rory
  • Glass, David H.
  • McCartney, Mark

Abstract

An existing multiple phenotype predator–prey model is expanded to include mutation amongst the predator phenotypes. Two unimodal maps are used for the underlying dynamics of the prey. A predation strategy is also defined which differs for each of the predators in the model. Results show that the introduction of predator mutation enhances predator survival both in terms of the number of phenotypes and total population for a range of values of the predation rate. In general, the dominant predator phenotype is the one which is most focused on the prey phenotype with the largest population.

Suggested Citation

  • Abernethy, Gavin M. & Mullan, Rory & Glass, David H. & McCartney, Mark, 2017. "A multiple phenotype predator–prey model with mutation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 762-774.
    • Handle: RePEc:eee:phsmap:v:465:y:2017:i:c:p:762-774
    DOI: 10.1016/j.physa.2016.08.037
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    References listed on IDEAS

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    1. Durrett, Rick & Mayberry, John, 2010. "Evolution in predator-prey systems," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1364-1392, July.
    2. Mougi, Akihiko, 2012. "Predator–prey coevolution driven by size selective predation can cause anti-synchronized and cryptic population dynamics," Theoretical Population Biology, Elsevier, vol. 81(2), pages 113-118.
    3. Kevin McCann & Alan Hastings & Gary R. Huxel, 1998. "Weak trophic interactions and the balance of nature," Nature, Nature, vol. 395(6704), pages 794-798, October.
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    Cited by:

    1. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    2. McAllister, A. & McCartney, M. & Glass, D.H., 2023. "Stability, collapse and hyperchaos in a class of tri-trophic predator–prey models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    3. Wu, Daiyong & Zhao, Min, 2019. "Qualitative analysis for a diffusive predator–prey model with hunting cooperative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 299-309.
    4. Lu, Guangqing & Smidtaite, Rasa & Navickas, Zenonas & Ragulskis, Minvydas, 2018. "The Effect of Explosive Divergence in a Coupled Map Lattice of Matrices," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 308-313.

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