Discovering Stochastic Dynamical Equations from Ecological Time Series Data.

Area of Science:

• Ecology
• Dynamical Systems
• Data Science

Background:

• Stochasticity can influence ecosystem dynamics in complex ways.
• Inferring governing equations from data is crucial for understanding these effects.
• Existing methods struggle to identify stochastic influences without known equations.

Purpose of the Study:

• To present a novel methodology for discovering stochastic differential equations from time series data.
• To demonstrate the ability to infer underlying system dynamics and stability structures.
• To apply the method to diverse real-world datasets.

Main Methods:

• Combining stochastic calculus with equation discovery techniques.
• Inputting time series data of state variables to output stochastic differential equations.
• Validating the method on synthetic models with identical steady-state distributions but different governing equations.

Main Results:

• Successfully recovered correct underlying equations from time series data, even for models with similar steady-state distributions.
• Demonstrated accurate inference of system stability structures.
• Applied the methodology to real-world datasets of fish schooling and single-cell migration.

Conclusions:

• The developed equation discovery methodology effectively infers stochastic differential equations from data.
• The approach provides insights into system stability and dynamics across various scales.
• An open-source package, PyDaDDy, is provided for broader application.