Reflections on the extinction–explosion dichotomy

Mike Steel

Theoretical Population Biology, 2015, vol. 101, issue C, 61-66

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.

Keywords: Extinction; Borel–Cantelli lemma; Population size; Coupling; Markov chain (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:101:y:2015:i:c:p:61-66

DOI: 10.1016/j.tpb.2015.03.001

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