Changes in the gradient percolation transition caused by an Allee effect

TL;DR

This paper investigates how the Allee effect influences the nature of the gradient percolation transition in spatial biological models, revealing a shift from continuous to first-order transition with altered scaling behavior.

Contribution

It demonstrates that a strong Allee effect changes the percolation transition from continuous to first order and modifies the scaling of the hull width.

Findings

Without Allee effect, transition is continuous with w ~ g^(-0.57).

With strong Allee effect, transition becomes first order with w ~ g^(-0.26).

Allee effect significantly alters the percolation transition characteristics.

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