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Changes in the gradient percolation transition caused by an Allee effect.

Michael T Gastner1, Beata Oborny, Alexey B Ryabov

  • 1Institute for the Chemistry and Biology of the Marine Environment, Carl von Ossietzky Universität, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany.

Physical Review Letters
|April 27, 2011
PubMed
Summary

The Allee effect, a reduction in population growth at low densities, significantly alters how populations spread. This study reveals that a strong Allee effect changes population spread from a continuous to a first-order transition.

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Area of Science:

  • Ecology
  • Population Dynamics
  • Mathematical Biology

Background:

  • Population establishment and spread are vital for ecological dynamics.
  • The Allee effect describes reduced per capita growth rates at low population densities, posing challenges for species survival and expansion.
  • Understanding population dynamics under varying densities is crucial for conservation and management.

Purpose of the Study:

  • To investigate the impact of the Allee effect on population spread dynamics.
  • To analyze how a strong Allee effect modifies 2D-percolation transitions in stochastic spatial models.
  • To compare the scaling behavior of population hull width with and without the Allee effect.

Main Methods:

  • Utilizing stochastic spatial models with a gradient in reproduction rate to simulate population spread.
  • Analyzing 2D-percolation transitions under varying environmental conditions.
  • Quantifying the scaling relationship between hull width (w) and the gradient parameter (g) in the presence and absence of the Allee effect.

Main Results:

  • Without the Allee effect, the population transition is continuous, with hull width scaling as w ∝ g(-0.57).
  • With a strong Allee effect, the transition becomes first-order.
  • The presence of a strong Allee effect alters the hull width scaling to w ∝ g(-0.26).

Conclusions:

  • The Allee effect fundamentally changes the nature of population spread transitions.
  • Population spread dynamics are significantly influenced by density-dependent growth limitations.
  • The distinct scaling behaviors highlight the critical role of the Allee effect in ecological spatial dynamics.