Can I read Extinction Dynamics in Mainland–Island Metapopulations: An N-patch Stochastic Model on EtoBox?

Extinction Dynamics in Mainland–Island Metapopulations: An N-patch Stochastic Model by David Alonso; Alan McKane is a Biochemistry, Genetics and Molecular Biology article available to read on EtoBox.

What is Extinction Dynamics in Mainland–Island Metapopulations: An N-patch Stochastic Model about?

A generalization of the well-known Levins' model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability Ps(n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for Ps(0) and P(0,t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field ap

Who reads Extinction Dynamics in Mainland–Island Metapopulations: An N-patch Stochastic Model?

Author

David Alonso; Alan McKane

Publisher

Springer; Springer-Verlag; Springer New York LLC; Mathematical Biology, Inc; Springer Science and Business Media LLC; Society for Mining, Metallurgy and Exploration Inc. (ISSN 1522-9602)

Published

2002

Language

EN

Field

Biochemistry, Genetics and Molecular Biology (Life Sciences)