Adaptive behaviour and multiple equilibrium states in a predator-prey model.

Area of Science:

• Ecology
• Mathematical Biology
• Behavioral Ecology

Background:

• Ecological systems can exhibit multiple stable equilibrium states, challenging simple models.
• Existing models often use complex functional responses without clear biological justification.
• The role of prey behavioral adaptation in generating ecosystem stability is underexplored.

Purpose of the Study:

• To investigate if prey behavioral adaptation to predation pressure can cause multiple stable ecological equilibria.
• To develop a parsimonious predator-prey model incorporating prey behavioral plasticity.
• To provide a biological justification for complex ecological dynamics beyond predator functional responses.

Main Methods:

• Extension of the classic Lotka-Volterra predator-prey model.
• Introduction of prey behavioral modes ('safe' vs. 'risky') with a 'cost of policy'.
• Analysis of a simplified two-dimensional model to identify stable equilibria and basins of attraction.

Main Results:

• The model demonstrates two stable co-existing equilibrium states.
• Basins of attraction for these states are separated by a saddle point separatrix.
• The model avoids complex functional responses or predator behavioral changes.

Conclusions:

• Prey behavioral adaptation is a viable mechanism for generating multiple stable states in ecological systems.
• This adaptive behavioral model offers a biologically plausible alternative to complex functional responses.
• The findings highlight the importance of considering prey plasticity in ecological modeling and conservation.