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Disturbed nonlinear multispecies models in ecology.

D Summers1, Z Y Wu, G C Sabin

  • 1Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Canada.

Mathematical Biosciences
|May 1, 1991
PubMed
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This study estimates ecosystem population dynamics under disturbances using control theory. We developed methods to determine the full range of possible population sizes for interacting species.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Control Theory

Background:

  • The Lotka-Volterra model is a fundamental tool for studying species interactions.
  • Real-world ecosystems experience unpredictable disturbances affecting species' intrinsic growth rates.
  • Estimating the full range of population dynamics under such uncertainty is crucial for ecological management.

Purpose of the Study:

  • To develop methods for estimating the set of all possible population densities in a disturbed Lotka-Volterra ecosystem.
  • To provide both numerical and analytical solutions for these population dynamics.
  • To demonstrate the applicability of these methods to other nonlinear ecological models.

Main Methods:

  • Utilizing Lyapunov techniques and the concept of "reachable set" from control theory.

Related Experiment Videos

  • Developing numerical methods involving global optimization to estimate the reachable set.
  • Deriving an explicit analytical expression for the reachable set in the general m-dimensional case.

    • Main Results:

    • Successful estimation of reachable sets for 2, 3, and 4 species Lotka-Volterra models.
    • An explicit, conservative analytical estimate for the reachable set in the m-dimensional case was derived.
    • The developed methods are applicable to other nonlinear ecosystem models beyond Lotka-Volterra.

    Conclusions:

    • The study provides robust tools for analyzing the impact of bounded, unknown disturbances on ecological models.
    • Both numerical and analytical approaches offer valuable insights into ecosystem resilience and potential population states.
    • This work contributes to a better understanding of ecological dynamics under uncertainty, with implications for conservation and management.