Resilience and Persistence in the Context of Stochastic Population Models

  • Johan Grasman
  • Onno A. van Herwaarden
  • Thomas J. Hagenaars


The resilience of an ecological system is defined by the velocity of the system as it returns to its equilibrium state after some perturbation. Since the system does not arrive exactly at the equilibrium within a finite time, the definition is based on the time needed to decrease the distance to the equilibrium with some fraction. In this study it is found that for stochastic populations this arbitrarily chosen function disappears because the equilibrium point can be replaced by a small (confidence) domain containing the equilibrium. The size of this domain is a measure for the (local) persistence of the system. This method is fully worked out for the stochastic logistic equation as well as for a prey-predator system.


resilience persistence ecosystem Fokker-Planck equation logistic equation prey-predator system epidemiology 


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Copyright information

© Springer 2005

Authors and Affiliations

  • Johan Grasman
    • 1
  • Onno A. van Herwaarden
    • 2
  • Thomas J. Hagenaars
    • 3
  1. 1.Department of Mathematical and Statistical MethodsWageningen UniversityWageningen
  2. 2.Department of Mathematical and Statistical MethodsWageningen UniversityWageningen
  3. 3.Division of Infectious Diseases, Animal Sciences GroupWageningen UniversityWageningen

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