Generalist predator dynamics under kolmogorov versus non-Kolmogorov models

Area of Science:

• Ecology
• Mathematical Biology
• Theoretical Ecology

Background:

• Ecosystems feature complex interactions across multiple trophic levels.
• Generalist predators utilize diverse food sources, influencing community dynamics.

Purpose of the Study:

• To compare the ecological dynamics of two generalist predator models: predator-two prey and predator-prey-subsidy.
• To determine which model, under specific parameters, favors predator survival and coexistence.
• To analyze non-equilibrium dynamics and model stability.

Main Methods:

• Developed and non-dimensionalized two classes of mathematical models: predator-two prey (Kolmogorov system) and predator-prey-subsidy (non-Kolmogorov).
• Utilized Type II response functions for predator-prey interactions.
• Analyzed model dynamics, including steady states, limit cycles, and multistability.

Main Results:

• The predator-prey-subsidy model exhibits more regular dynamics, including steady states and a single limit cycle type.
• The predator-two prey model demonstrates richer dynamics, featuring multiple limit cycle types and multistability.
• Multistability in the predator-two prey model leads to strong sensitivity to initial conditions.

Conclusions:

• Generalist predator models, both Kolmogorov and non-Kolmogorov, reveal distinct dynamical behaviors.
• The predator-prey-subsidy model offers more predictable population dynamics.
• The predator-two prey model's complexity can lead to unpredictable outcomes and coexistence of different stable states.