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Reflections on the extinction–explosion dichotomy

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  • Steel, Mike

Abstract

A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is an elegant and classical theorem that explains why this dichotomy must hold under certain assumptions concerning the process. In this note, I explore how these assumptions might be relaxed further in order to obtain the same, or a similar conclusion, and obtain both positive and negative results.

Suggested Citation

  • Steel, Mike, 2015. "Reflections on the extinction–explosion dichotomy," Theoretical Population Biology, Elsevier, vol. 101(C), pages 61-66.
    • Handle: RePEc:eee:thpobi:v:101:y:2015:i:c:p:61-66
    DOI: 10.1016/j.tpb.2015.03.001
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    References listed on IDEAS

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    1. Lambert, Amaury & Stadler, Tanja, 2013. "Birth–death models and coalescent point processes: The shape and probability of reconstructed phylogenies," Theoretical Population Biology, Elsevier, vol. 90(C), pages 113-128.
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