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Risk of Population Extinction Due to Demographic Stochasticity in Population Models

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The risk of population extinction in stochastic models due to demographic variation is reviewed in some basic population models. Theoretical results pertaining to the probability of population extinction and expected time to extinction in discrete and continuous-time Markov chain models are presented along with some numerical examples illustrating these results. We begin with the simplest type of stochastic population model, the exponential growth model, then discuss the logistic growth model, a model with an Allee effect, and a spatially implicit metapopulation model. All of these stochastic models are continuous in time, but the state space is discrete. It is shown that similar methods of analysis apply to all of these models. In addition, some nonlinear structured models are considered. These models are formulated as branching processes, discrete-time Markov chain models. The extinction dynamics for all of these models are compared.
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Keywords: Markov chain; age structure; branching process; demographic stochasticity; metapopulation

Document Type: Research Article

Affiliations: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, USA

Publication date: July 1, 2003

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