Psychological effect on single-species population models in a polluted environment

Area of Science:

• Ecology
• Mathematical Biology
• Environmental Science

Background:

• Pollution poses a significant threat to biodiversity.
• Understanding population dynamics in contaminated environments is crucial for conservation.
• Mathematical models offer a framework to study ecological responses to environmental stressors.

Purpose of the Study:

• To investigate the psychological effects of single-species population models in polluted environments.
• To determine conditions for local extinction and persistence in the mean for deterministic models.
• To analyze the stochastic permanence and weak persistence in the mean for stochastic models.

Main Methods:

• Formulation of deterministic and stochastic single-species population models.
• Derivation of conditions for local extinction and persistence in the mean.
• Analysis of stochastic permanence and weak persistence in the mean.
• Numerical simulations to validate theoretical findings.

Main Results:

• Established conditions guaranteeing local extinction and persistence in the mean for deterministic models.
• Demonstrated that stochastic single-species populations are weakly persistent in the mean around pollution-free equilibria.
• Identified conditions under which stochastic populations are permanent.

Conclusions:

• The study provides a mathematical framework for understanding population dynamics in polluted environments.
• Results highlight the complex interplay between pollution and population persistence.
• Numerical simulations confirm the theoretical predictions, underscoring the model's efficacy.