Model reduction methods for population dynamics with fast-switching environments: Reduced master equations,...

Area of Science:

• Mathematical Biology
• Statistical Physics
• Computational Science

Background:

• Stochastic population dynamics are crucial in many scientific fields.
• Modeling these dynamics often involves complex environmental interactions.
• Existing methods may struggle with fast environmental switching and population size variations.

Purpose of the Study:

• To develop novel approximation schemes for stochastic population dynamics.
• To incorporate both intrinsic population noise and environmental noise.
• To enable efficient simulation and analytical treatment of these systems.

Main Methods:

• Combining expansions in inverse environmental switching rate.
• Utilizing Kramers-Moyal expansion for inverse population size.
• Developing a series of approximation schemes.

Main Results:

• Achieved efficient simulation of population dynamics in switching environments.
• Derived analytical results for population fluctuations.
• Established connections to piecewise-deterministic and piecewise-diffusive Markov processes.

Conclusions:

• The developed model-reduction methods are accurate and efficient.
• These methods are applicable across diverse research fields, including biology and materials science.
• Provides a powerful framework for analyzing complex stochastic systems.