A type IV functional response with different shapes in a predator–prey model

Merlin C. Köhnke, Ivo Siekmann, Hiromi Seno, Horst Malchow

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Group defense is a phenomenon that occurs in many predator–prey systems. Different functional responses with substantially different properties representing such a mechanism exist. Here, we develop a functional response using timescale separation. A prey-dependent catch rate represents the group defense. The resulting functional response contains a single parameter that controls whether the group defense functional response is saturating or dome-shaped. Based on that, we show that the catch rate must not increase monotonically with increasing prey density to lead to a dome-shaped functional response. We apply bifurcation analysis to show that non-monotonic group defense is usually more successful. However, we also find parameter regions in which a paradox occurs. In this case, higher group defense can give rise to a stable limit cycle, while for lower values, the predator would go extinct. The study does not only provide valuable insight on how to include functional responses representing group defense in mathematical models, but it also clarifies under which circumstances the usage of different functional responses is appropriate.

Original languageEnglish
Article number110419
JournalJournal of Theoretical Biology
Publication statusPublished - 2020 Nov 21


  • Dome-shaped functional response
  • Group defense
  • Type IV functional response

ASJC Scopus subject areas

  • Statistics and Probability
  • Modelling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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