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Converging towards the optimal path to extinction.

Ira B Schwartz1, Eric Forgoston, Simone Bianco

  • 1Nonlinear Systems Dynamics Section, Plasma Physics Division, U.S. Naval Research Laboratory, Washington, DC 20375, USA.

Journal of the Royal Society, Interface
|May 17, 2011
PubMed
Summary
This summary is machine-generated.

Extinction in finite populations, though rare, is driven by random fluctuations. This study links the optimal path to extinction with sensitive dependence on initial conditions in dynamical systems, particularly in epidemic models.

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Area of Science:

  • Stochastic processes
  • Dynamical systems theory
  • Epidemiology

Background:

  • Extinction is a common phenomenon across diverse scientific fields, including population biology and epidemiology.
  • While often viewed as random, extinction in finite populations can be influenced by specific pathways.
  • Understanding the dynamics of extinction is crucial for predicting and managing system collapse.

Purpose of the Study:

  • To identify the optimal pathway that maximizes the probability of extinction in stochastic systems.
  • To explore the connection between sensitive dependence on initial conditions and extinction dynamics.
  • To demonstrate the applicability of dynamical systems concepts to extinction in epidemic models.

Main Methods:

  • Analysis of stochastic models in various fields, focusing on random transitions and population fluctuations.
  • Application of dynamical systems concepts, specifically sensitive dependence on initial conditions.
  • Investigation of optimal paths maximizing extinction probability.

Main Results:

  • The optimal path to extinction is directly associated with maximum sensitive dependence on initial conditions.
  • Dynamical systems naturally evolve towards this optimal extinction path.
  • This equivalence was demonstrated in several stochastic epidemic models.

Conclusions:

  • Sensitive dependence on initial conditions provides a framework for understanding optimal extinction pathways.
  • Dynamical systems theory offers valuable insights into the mechanisms driving extinction events.
  • The findings have implications for managing extinction risks in epidemiological and ecological systems.