Abstract
We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis.
Highlights
Understanding biological population dynamics provides insight into whether a population will survive or become extinct
The individual-based model (IBM) incorporates agent motility, proliferation, and death, where the individual-level rates vary with local density
The main objective of this work is to determine how individual-level mechanisms are linked to various global Allee effects, which can be approached in two ways
Summary
Understanding biological population dynamics provides insight into whether a population will survive or become extinct Salient features of these population dynamics, such as the growth rate and the maximum population density, can be captured using suitable mathematical modelling frameworks [1,2,3,4,5,6,7,8,9,10,11,12]. The logistic growth model (Fig. 1b) incorporates a linearly decreasing f (C) and is perhaps the most widely used model of biological and ecological population dynamics [1,2,3, 13] This is because the logistic growth model captures two ubiquitous phenomena: (i) nearexponential growth at low density, and; (ii) a finite maximum density, termed the carrying capacity [2,3,4,5, 7, 13, 14]
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