The role of dispersal in interacting patches subject to an allee effect

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This article is concerned with a stochastic multipatch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that was recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to ∞, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large, whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, fast long-range dispersal drives the population toward extinction.

Original languageEnglish (US)
Pages (from-to)1182-1197
Number of pages16
JournalAdvances in Applied Probability
Volume45
Issue number4
DOIs
StatePublished - Dec 2013

Fingerprint

Allee Effect
Metapopulation
Patch
Critical value
Stochastic models
Interacting Particle Systems
Geometry
Regular Graph
Complete Graph
Extinction
Expand
Migration
Stochastic Model
Tend
Ring
Necessary
Interaction
Model
Range of data
Simulation

Keywords

  • Allee effect
  • Dispersal
  • Interacting particle system
  • Metapopulation

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability

Cite this

The role of dispersal in interacting patches subject to an allee effect. / Lanchier, Nicolas.

In: Advances in Applied Probability, Vol. 45, No. 4, 12.2013, p. 1182-1197.

Research output: Contribution to journalArticle

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