A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability

Edward J. Allen, Linda J.S. Allen, Henri Schurz

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.

Original languageEnglish
Pages (from-to)14-38
Number of pages25
JournalMathematical Biosciences
Volume196
Issue number1
DOIs
StatePublished - Jul 2005

Keywords

  • Birth and death process
  • Environmental variability
  • Logistic equation
  • Markov chain
  • Mathematical model
  • Persistence time
  • Stochastic differential equation

Fingerprint Dive into the research topics of 'A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability'. Together they form a unique fingerprint.

  • Cite this