Investigating the interactions between Allee effect and harvesting behaviour of a single species model: An evolutionary dynamics approach

Yanwei Liu, Tonghua Zhang and Xia Liu

Physica A: Statistical Mechanics and its Applications, 2020, vol. 549, issue C

Abstract: In this study, we propose an ecological model, which is based on the Smith growth model and subject to multiplicative Allee effect. We then investigate the equilibrium bifurcation induced by the harvesting behaviour and the Allee effect, and pitch fork bifurcation and saddle node bifurcation may occur. Assuming that the carrying capacity and harvesting rate obey a Gaussian distribution, we then consider the evolutionary dynamics by using continuous strategy evolutionary game theory. Our study shows that strong Allee effect and low harvesting rate can induce bistability. It also suggests that evolution prevents extinction even if population has strong Allee effect. Numerical analysis shows that the evolutionary model can admit up to nine equilibrium points including up to four Evolutionary Stable Strategy equilibria.

Keywords: Allee effect; Pitch fork bifurcation; Saddle node bifurcation; Evolutionarily stable strategy (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437120301060

DOI: 10.1016/j.physa.2020.124323

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