Stochastic plant-herbivore interaction model with Allee effect.

Area of Science:

• Mathematical Biology
• Ecology
• Stochastic Modeling

Background:

• Environmental stochasticity is a key factor influencing population dynamics.
• Real-world ecological systems are inherently random, necessitating stochastic models.
• Previous deterministic models may not fully capture ecological complexity.

Purpose of the Study:

• To develop and analyze a stochastic extension of a plant-herbivore model.
• To investigate the impact of environmental noise on population dynamics.
• To assess the implications for land management and wildlife conservation.

Main Methods:

• Formulation and analysis of a simplified stochastic plant-herbivore model, including global Lipschitz continuity and existence/uniqueness of solutions.
• Extension of the analysis to a more complex and realistic model.
• Numerical simulations using the Euler-Maruyama method to explore long-term dynamics.

Main Results:

• The stochastic model exhibits properties like global Lipschitz continuity and unique solutions.
• Noise introduced to the herbivore population had a greater effect on dynamics than noise in the plant population.
• Numerical simulations demonstrated significant long-term dynamic changes due to stochasticity.

Conclusions:

• Stochastic models are essential for accurately representing ecological systems with environmental noise.
• The distribution of noise (herbivore vs. plant) critically affects population dynamics.
• Ignoring environmental noise in ecological models can jeopardize conservation and land management objectives.