Reflections on the extinction-explosion dichotomy

Mike Steel

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arXiv · 1409.4713

Reflections on the extinction-explosion dichotomy

Mike Steel

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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 a 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.

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Mike Steel. 2014-09-16. Reflections on the extinction-explosion dichotomy. https://arxiv.org/abs/1409.4713

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