Single-species population models with stage structure and partial tolerance in polluted environments

Area of Science:

• Ecology
• Mathematical Biology
• Environmental Science

Background:

• Population dynamics are influenced by environmental pollution and internal psychological factors.
• Understanding species' responses to pollution is crucial for conservation and management.
• Stage-structured models offer a detailed approach to population dynamics.

Purpose of the Study:

• To develop and analyze stage-structured population models incorporating psychological effects and partial tolerance in polluted environments.
• To investigate the conditions and timing of population extinction.
• To determine population persistence and the existence of periodic solutions.

Main Methods:

• Development of mathematical models for single-species population dynamics.
• Analysis of extinction conditions and time to extinction.
• Derivation of conditions for weak persistence in the mean and stochastic permanence.
• Investigation of periodic solutions for the population model.
• Numerical simulations to validate theoretical findings.

Main Results:

• Extinction time is inversely related to psychological effect intensity.
• Conditions for weak persistence in the mean and stochastic permanence were established.
• The existence of a periodic solution for the population model was proven.
• Numerical simulations confirmed the accuracy of the derived theoretical results.

Conclusions:

• Psychological effects significantly impact population extinction dynamics in polluted environments.
• The models demonstrate the potential for population persistence and stable periodic behavior under specific conditions.
• The study provides a robust mathematical framework for analyzing complex population dynamics influenced by environmental and psychological factors.