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Title: Approximating measures of persistence in a general class of population processes.

Authors: B.J. Cairns and P.K. Pollett.

Reference: Theoretical Population Biology 68: 77-90.

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Abstract: We provide a general framework for estimating persistence in populations which may be affected by catastrophic events, and which are either unbounded or have very large ceilings. We model the population using a birth–death process modified to allow for downward jumps of arbitrary size. For such processes, it is typically necessary to truncate the process in order to make the evaluation of expected extinction times (and higher-order moments) computationally feasible. Hence, we give particular attention to the selection of a cut-off point at which to truncate the process, and we present a simple method for obtaining quantitative indicators of the suitability of a chosen cut-off.

Keywords. Population process, Catastrophes, Hitting time, Extinction.

Acknowledgement. The authors would like to thank the referees, whose comments and suggestions greatly improved the presentation of the paper. The support of the Australian Research Council is gratefully acknowledged (Grant No. A00104575). The work of the first author is supported by a Ph.D. Scholarship from the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems.

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