2014/09/16 by Mike Steel, Steel, Mike
Biochemistry, Genetics and Molecular Biology · Mathematics · #FOS: Biological sciences #FOS: Mathematics #Populations and Evolution (q-bio.PE) #Probability (math.PR) #math.PR #q-bio.PE
paper · pdf · doi:10.48550/arxiv.1409.4713
12 pages, 0 figures
arxiv created 2014/09/16 · arxiv updated 2014/09/17
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.