Changes in the gradient percolation transition caused by an Allee effect

Abstract

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.