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Persistence despite perturbations for interacting populations.

Sebastian J Schreiber1

  • 1Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795, USA. sjschr@wm.edu <sjschr@wm.edu>

Journal of Theoretical Biology
|July 11, 2006
PubMed
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This study defines persistence in population models. Persistence despite frequent small perturbations is equivalent to a positive attractor, while rare large perturbations relate to permanence, impacting model classification robustness.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Dynamical Systems

Background:

  • Understanding population persistence is crucial in ecology.
  • Deterministic models are often used to study population dynamics.
  • Perturbations can significantly alter population trajectories.

Purpose of the Study:

  • To present and analyze two definitions of persistence in deterministic models under perturbations.
  • To establish a classification framework for population models based on their response to perturbations.
  • To evaluate the robustness of these definitions in ecological modeling.

Main Methods:

  • Analysis of persistence despite frequent small perturbations, linked to positive attractors.
  • Analysis of persistence despite rare large perturbations, linked to permanence.

Related Experiment Videos

  • Investigation of the generic robustness of these definitions using dynamical systems theory.

    • Main Results:

    • Persistence despite frequent small perturbations is equivalent to the existence of a positive attractor.
    • Persistence despite rare large perturbations is equivalent to permanence.
    • The classification is generically robust for small perturbations but not for rare large perturbations.

    Conclusions:

    • Two distinct definitions of persistence provide a dichotomy for classifying population models.
    • The robustness of this classification varies depending on the nature and frequency of perturbations.
    • The findings highlight the importance of considering perturbation types in ecological model analysis.