Population dynamics with threshold effects give rise to a diverse family of Allee effects

BioRxiv : the Preprint Server for Biology
Nabil T Fadai, Matthew J Simpson

Abstract

The Allee effect describes populations that deviate from logistic growth models and arises in applications from ecology to cell biology. A common justification for incorporating Allee effects into population models is that the population in question has altered growth mechanisms at some critical density, often referred to as threshold effects. Despite the ubiquitous nature of threshold effects arising in various biological applications, the explicit link between local threshold effects and global Allee effects has not been considered. In this work, we examine a continuum population model that incorporates threshold effects in the local growth mechanisms. We show that this model gives rise to a diverse family of Allee effects and we provide a comprehensive analysis of which choices of local growth mechanisms give rise to specific Allee effects. This model is then calibrated to a recent set of experimental data known to deviate from logistic growth, which in turn provides an interpretation of the threshold population density and growth mechanisms associated with the population.

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