Bifurcations and hydra effects in Bazykin's predator-prey model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Bazykin's model is used to study predator-prey dynamics.
• Harvesting can significantly alter population stability and dynamics.
• Hydra effects, where removing a species leads to an increase in its population, are a key phenomenon in some ecological models.

Purpose of the Study:

• To analyze harvesting-induced stability exchanges in Bazykin's model.
• To investigate the occurrence of hydra effects under different harvesting strategies (prey vs. predator).
• To understand the role of predator functional response and interference in inducing complex dynamics.

Main Methods:

• Bifurcation analysis of Bazykin's model.
• Examination of population stock patterns under varying harvesting rates.
• Simulation of ecological dynamics to observe stability and bifurcations.

Main Results:

• Prey harvesting does not induce hydra effects in this model.
• Predator harvesting can lead to multiple hydra effects and bistability, particularly with a type II functional response and predator interference.
• Various bifurcations (Hopf, saddle-node) occur with increasing predator harvesting, but over-exploitation does not generate these.
• Maximum sustainable yield (MSY) is found at a globally stable state.

Conclusions:

• Predator harvesting strategies are crucial for managing ecological stability and preventing extinctions.
• The interplay of functional response and inter-predator interference drives complex population dynamics.
• Findings provide a theoretical basis for developing effective conservation policies and sustainable fishery management practices.