A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability |
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Authors: | Allen Edward J Allen Linda J S Schurz Henri |
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Affiliation: | Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA. |
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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. |
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Keywords: | Persistence time Mathematical model Birth and death process Environmental variability Markov chain Stochastic differential equation Logistic equation |
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