Noise driven unlimited population growth

Details Noise driven unlimited population growth Noise driven unlimited population growth

2008-08-28

arxiv.org/abs/0808.3854v2

Biology

Quantitative Biology

Populations and Evolution

4 pages, 2 figures

Scientific paper

10.1103/PhysRevE.78.060103

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes immigration, binary reproduction and death. The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of the population. We develop a systematic WKB theory, complemented by the van Kampen system size expansion, for the MPD and for the decay time. Important signatures of the MPD is a power-law tail (such that all the distribution moments, except the zeroth one, diverge) and the presence in the solution of two different WKB modes.

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