Abstract
We introduce a minimal agent-based model to understand the effects of the interplay between dispersal and geometric constraints in metapopulation dynamics under the Allee Effect. The model, which does not impose nonlinear birth and death rates, is studied both analytically and numerically. Our results indicate the existence of a survival-extinction boundary with monotonic behavior for weak spatial constraints and a nonmonotonic behavior for strong spatial constraints so that there is an optimal dispersal that maximizes the survival probability. Such optimal dispersal has empirical support from recent experiments with engineered bacteria.
Highlights
The Allee effect is an influential finding named after the ecologist Warder Clyde Allee [1] concerning a phenomenon typically manifested by the departure from the standard logistic growth that enhances the susceptibility to extinction of an already vulnerable sparse population
In spite of the fact that it is known that reaction-diffusion equations with a linear population growth can exhibit a critical diffusion rate guaranteeing the survival of the population [33], we would like to emphasize that our work goes beyond that: we have shown that the relationship between the survivability and dispersal undergoes a transition of monotonicity when a birth-death process with the Allee effect is subjected to the interplay between dispersal and tunable spatial constraints
We have investigated the spectrum of scenarios arising from a metapopulation dynamics under the Allee Effect using a minimal agent-based model which points at describing fundamental mechanisms thereof
Summary
The Allee effect is an influential finding named after the ecologist Warder Clyde Allee [1] concerning a phenomenon typically manifested by the departure from the standard logistic growth that enhances the susceptibility to extinction of an already vulnerable sparse population. C. Allee did not provide a definition of the effect [2], but in general terms it can be defined as “the positive correlation between the absolute average individual fitness in a population and its size over some finite interval”. The strong Allee effect, which is the focus of this work, corresponds to the case when the deviation from the logistic growth includes an initial population threshold below which the population goes extinct [4]. There exists a weak version of the Allee effect which treats positive relations between the overall individual fitness in the population density and does not present population size nor density thresholds
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