Frontiers in Applied Mathematics and Statistics (Nov 2022)

Prey fear of a specialist predator in a tri-trophic food web can eliminate the superpredator

  • Nabaa Hassain Fakhry,
  • Raid Kamel Naji,
  • Stacey R. Smith?,
  • Mainul Haque

DOI
https://doi.org/10.3389/fams.2022.963991
Journal volume & issue
Vol. 8

Abstract

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We propose an intraguild predation ecological system consisting of a tri-trophic food web with a fear response for the basal prey and a Lotka–Volterra functional response for predation by both a specialist predator (intraguild prey) and a generalist predator (intraguild predator), which we call the superpredator. We prove the positivity, existence, uniqueness, and boundedness of solutions, determine all equilibrium points, prove global stability, determine local bifurcations, and illustrate our results with numerical simulations. An unexpected outcome of the prey's fear of its specialist predator is the potential eradication of the superpredator.

Keywords