RT Journal Article
SR Electronic
T1 Allee dynamics: growth, extinction and range expansion
JF bioRxiv
FD Cold Spring Harbor Laboratory
SP 098418
DO 10.1101/098418
A1 I Bose
A1 M Pal
A1 C Karmakar
YR 2017
UL http://biorxiv.org/content/early/2017/01/05/098418.abstract
AB 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.