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Weak-form inference for hybrid dynamical systems in ecology.

Daniel Messenger1, Greg Dwyer2, Vanja Dukic1

  • 1Department of Applied Mathematics, University of Colorado, Boulder, CO, USA.

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|December 17, 2024
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Summary

This study introduces a new data-driven method to model population dynamics with both short-term continuous changes and long-term discrete shifts. It helps predict population booms and busts by understanding multi-scale ecological effects.

Keywords:
WSINDydata-driven modellinghybrid systemsmulti-scale modelparameter estimationsystem identification

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Area of Science:

  • Ecological modeling
  • Population dynamics
  • Mathematical biology

Background:

  • Species exhibit population fluctuations due to predation and environmental factors.
  • Predicting these population booms and busts is challenging due to complex, multi-scale dynamics.

Purpose of the Study:

  • To develop a data-driven method for extracting hybrid governing equations for population dynamics.
  • To estimate parameters for coupled short-term continuous and long-term discrete population models.
  • To assess interdependencies between different timescales in ecological systems.

Main Methods:

  • Utilizing weak-form equation learning to extract hybrid dynamical systems.
  • Coupling short-term continuous dynamics with long-term discrete updates.
  • Parameter estimation using sparse, intermittent measurements of population variables.

Main Results:

  • Successfully extracted short-term continuous dynamical system equations parametrized by long-term variables.
  • Derived long-term discrete equations parametrized by short-term variables.
  • Demonstrated method utility across various ecological scenarios, including North American spongy moth epizootics.

Conclusions:

  • The developed method effectively models multi-scale population dynamics.
  • It allows for direct assessment of interdependencies between short-term and long-term ecological factors.
  • Provides a robust framework for predicting population booms and busts in variable environments.