Allee dynamics: Growth, extinction and range expansion

TL;DR

This paper models population dynamics with Allee effects using reaction-diffusion equations, analyzing extinction, growth, and range expansion, and compares findings with experimental data on yeast populations.

Contribution

It introduces a reaction-diffusion model incorporating Allee effects in growth and mortality, analyzing bifurcations, traveling waves, and regime transitions.

Findings

Identification of parameter regimes for population expansion and retreat

Demonstration of traveling wave solutions in the model

Agreement with experimental observations on yeast populations

Abstract

In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this Letter, we study a reaction-diffusion (RD) model of population growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortality rates. In the absence of diffusion, the bifurcation diagram displays regions of both finite population density and zero population density, i.e., extinction. The early signatures of the transition to extinction at a bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of travelling wave solutions of the population density is demonstrated. The parameter regimes in which the travelling wave advances (range expansion) and retreats are identified. In the weak Allee regime, the transition from the pushed to the pulled wave is shown as a function of the mortality rate constant. The results obtained are in agreement with the recent experimental observations on budding yeast populations.