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

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.