Changes in the Gradient Percolation Transition Caused by an Allee Effect

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 proportional to g(-0.57). However, with a strong Allee effect the transition is first order and w proportional to g(-0.26).