Noise driven unlimited population growth

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.

4 pages, 2 figures

References in corpus (3)

• Rare Events Statistics in Reaction--Diffusion Systems
• Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
• Spectral theory of metastability and extinction in a branching-annihilation reaction

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