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

JOURNAL OF THEORETICAL BIOLOGY

卷:505

Article

Koenke, Merlin C.¹  Siekmann, Ivo²  Seno, Hiromi³  Malchow, Horst¹ 

[1] Osnabruck Univ, Sch Math Comp Sci, Inst Math, Osnabruck, Germany

[2] Liverpool John Moores Univ, Dept Appl Math, Liverpool L3 3AF, Merseyside, England

[3] Tohoku Univ, Res Ctr Pure & Appl Math, Grad Sch Informat Sci, Aoba Ku, Aramaki Aza Aoba 6-3-09, Sendai, Miyagi 9808579, Japan

关键词: Type IV functional response;    Dome-shaped functional response;    Group defense;   

DOI  :  10.1016/j.jtbi.2020.110419

来源: Elsevier

【 摘 要 】

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. (C) 2020 Elsevier Ltd. All rights reserved.

【 授权许可】

Free