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Title: A comparison of models for predicting population persistence

Authors: B.J. Cairns, J.V. Ross and T. Taimre.

Reference: Ecological Modelling 201(1): 19-26 .

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Abstract:


We consider a range of models that may be used to predict the future persistence of populations, particularly those based on discrete-state Markov processes. While the mathematical theory of such processes is very well-developed, they may be difficult to work with when attempting to estimate parameters or expected times to extinction. Hence we focus on diffusion and other approximations to these models, presenting new and recent developments in parameter estimation for density dependent processes, and the calculation of extinction times for processes subject to catastrophes. We illustrate these and other methods using data from simulated and real time series. We give particular attention to a procedure, due to Ross et al. (2006), for estimating the parameters of the stochastic SIS logistic model, and demonstrate ways in which these parameters may be used to estimate expected extinction times. Although the stochastic SIS logistic model is strictly density dependent and allows only for birth and death events, it nonetheless may be used to predict extinction times with some accuracy even for populations that are only weakly density dependent, or that are subject to catastrophes.

Keywords. Extinction, population model, parameter estimation, catastrophes.

Acknowledgement. This work was supported by PhD scholarships to each of the authors from the Australian Research Council Centre of Excellence for Mathematics and Statistics of Complex Systems. The work of BC was also funded by the BBSRC. The authors would like to thank Phil Pollett for providing code to compute the mean time to extinction for the OU approximation, and the referees for their helpful suggestions.


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Cancer Epidemiology Unit, University of Oxford, Richard Doll Building, Roosevelt Drive, Oxford OX3 7LF, U.K.