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

Köhnke, MC, Siekmann, I, Seno, H and Malchow, H (2020) A type IV functional response with different shapes in a predator-prey model. Journal of Theoretical Biology, 505. ISSN 0022-5193

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Abstract

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.

Item Type: Article
Uncontrolled Keywords: 01 Mathematical Sciences, 06 Biological Sciences, 08 Information and Computing Sciences
Subjects: Q Science > QA Mathematics
Q Science > QH Natural history
Divisions: Computer Science & Mathematics
Publisher: Elsevier
Related URLs:
Date Deposited: 12 Aug 2020 09:18
Last Modified: 12 Aug 2020 09:30
DOI or Identification number: 10.1016/j.jtbi.2020.110419
URI: https://researchonline.ljmu.ac.uk/id/eprint/13486

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