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Robust permanence for ecological equations with internal and external feedbacks.

Swati Patel1,2,3, Sebastian J Schreiber4

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This study introduces a mathematical framework for species coexistence, considering internal and external feedbacks. It establishes conditions for robust permanence, ensuring population persistence despite environmental and model changes.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Evolutionary Biology

Background:

  • Species populations are influenced by internal (e.g., trait evolution) and external (e.g., weather) feedbacks.
  • These feedbacks are crucial for population persistence and species coexistence in ecological communities.

Purpose of the Study:

  • To develop a general mathematical framework for analyzing internal and external feedbacks in ecological models.
  • To establish conditions for robust permanence, ensuring species coexistence under perturbations.

Main Methods:

  • Utilized average Lyapunov functions and Morse decompositions.
  • Developed sufficient and necessary conditions for robust permanence in ecological models.

Main Results:

  • Established a general theorem for species coexistence accounting for internal and external feedbacks.
  • Demonstrated conditions for robust permanence, resilient to population density and model structure changes.

Conclusions:

  • The developed framework provides a unified approach to studying species coexistence.
  • Applicable to diverse ecological models, including structured, non-autonomous, and eco-evolutionary dynamics.