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Phys Rev Lett. 2011 Mar 25;106(12):128103. Epub 2011 Mar 23.

Changes in the gradient percolation transition caused by an Allee effect.

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Institute for the Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.


The establishment and spreading of biological populations depends crucially on population growth at low densities. The Allee effect is a problem in those populations where the per capita growth rate at low densities is reduced. We examine stochastic spatial models in which the reproduction rate changes across a gradient g so that the population undergoes a 2D-percolation transition. Without the Allee effect, the transition is continuous and the width w of the hull scales as in conventional (i.e., uncorrelated) gradient percolation, w ∝ g(-0.57). However, with a strong Allee effect the transition is first order and w ∝ g(-0.26).

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