Limit theorems for discrete-time metapopulation models

Phil Pollett

(Joint work with Fionnuala Buckley, University of Queensland)

Abstract: I will examine a simple discrete-time model for a population that occupies geographically separated habitat patches and for which there are distinct phases of colonization and local patch extinction. By exploiting results on weak convergence of sequences of time-inhomogeneous Markov chains I will establish that, when the number of patches is large, the proportion of occupied patches can be approximated by Gaussian Markov chain whose parameters can be written down explicitly in terms of the extinction and colonization rates.

Acknowledgement: This work is supported by the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems

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Last modified: 3rd October 2009