期刊
JOURNAL OF THEORETICAL BIOLOGY
卷 404, 期 -, 页码 391-397出版社
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jtbi.2016.06.010
关键词
Metapopulation dynamics; Persistence; Mean time to extinction; Generating function approach
资金
- Porter School of Environmental Studies at Tel Aviv University
- Australian Research Council [DP150102472]
A simple discrete generation Markov metapopulation model is formulated for studying the persistence and extinction dynamics of a species in a given region which is divided into a large number of sites or patches. Assuming a linear site occupancy probability from one generation to the next we obtain exact expressions for the time evolution of the expected number of occupied sites and the mean-time to extinction (MTE). Under quite general conditions we show that the MTE, to leading order, is proportional to the logarithm of the initial number of occupied sites and in precise agreement with similar expressions for continuous time-dependent stochastic models. Our key contribution is a novel application of generating function techniques and simple asymptotic methods to obtain a second order asymptotic expression for the MTE which is extremely accurate over the entire range of model parameter values. (C) 2016 Elsevier Ltd. All rights reserved.
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