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

Merlin C Köhnke1, Ivo Siekmann2, Hiromi Seno3

  • 1Institute of Mathematics, School of Mathematics/Computer Science, Osnabrück University, Germany.

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|August 1, 2020
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Summary

Group defense in predator-prey systems can be modeled with a new functional response. Non-monotonic catch rates are key for effective group defense, preventing predator extinction and sometimes creating stable cycles.

Keywords:
Dome-shaped functional responseGroup defenseType IV functional response

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Predator-Prey Dynamics

Background:

  • Group defense is a crucial ecological phenomenon in predator-prey interactions.
  • Existing functional responses may not fully capture the complexities of group defense strategies.

Purpose of the Study:

  • To develop a novel functional response model for group defense using timescale separation.
  • To analyze the impact of prey density on predator-prey dynamics under group defense.

Main Methods:

  • Development of a prey-dependent catch rate model for group defense.
  • Application of timescale separation for functional response derivation.
  • Bifurcation analysis to explore stability and dynamics.

Main Results:

  • The model yields a single parameter controlling saturating or dome-shaped functional responses.
  • Non-monotonic catch rates with increasing prey density are necessary for dome-shaped responses.
  • Higher group defense can paradoxically lead to stable limit cycles or predator extinction.

Conclusions:

  • The developed functional response offers a nuanced representation of group defense.
  • Non-monotonic group defense strategies are often more evolutionarily successful.
  • Understanding functional response shapes is critical for accurate ecological modeling and predicting population dynamics.