Allee dynamics: Growth, extinction and range expansion

Indrani Bose, Mainak Pal () and Chiranjit Karmakar ()
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Indrani Bose: Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India
Mainak Pal: Department of Physics, Bose Institute, 93/1, Acharya Prafulla Chandra Road, Kolkata 700009, India
Chiranjit Karmakar: Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781039, Assam, India

International Journal of Modern Physics C (IJMPC), 2017, vol. 28, issue 06, 1-12

Abstract: In population biology, the Allee dynamics refer to negative growth rates below a critical population density. In this paper, we study a reaction-diffusion (RD) model of popoulation growth and dispersion in one dimension, which incorporates the Allee effect in both the growth and mortatility 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 the bifurcation point are computed in the presence of additive noise. For the full RD model, the existence of traveling wave solutions of the population density is demonstrated. The parameter regimes in which the traveling 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.

Keywords: Allee effect; bistability; bifurcation point; early signatures of population extinction transition; traveling wave solution; pulled and pushed waves (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0129183117500747

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