TY - JOUR
T1 - A type IV functional response with different shapes in a predator–prey model
AU - Köhnke, Merlin C.
AU - Siekmann, Ivo
AU - Seno, Hiromi
AU - Malchow, Horst
N1 - Funding Information:
The Japan Society for the Promotion of Science (JSPS) that provided funding for a stay at Tohoku University for MCK and HM supported this work. MCK acknowledge discussions with Frank M. Hilker about the bifurcation analysis.
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/11/21
Y1 - 2020/11/21
N2 - 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.
AB - 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.
KW - Dome-shaped functional response
KW - Group defense
KW - Type IV functional response
UR - http://www.scopus.com/inward/record.url?scp=85088997415&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85088997415&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2020.110419
DO - 10.1016/j.jtbi.2020.110419
M3 - Article
C2 - 32735991
AN - SCOPUS:85088997415
VL - 505
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
M1 - 110419
ER -