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arXiv · 0808.3854

Noise driven unlimited population growth

Baruch Meerson·Pavel V. Sasorov
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Abstract

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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Baruch Meerson, Pavel V. Sasorov. 2008-10-29. Noise driven unlimited population growth. https://doi.org/10.1103/physreve.78.060103

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