Bulletin of Mathematical Biology

, Volume 69, Issue 1, pp 135–156

The Impact of the Allee Effect in Dispersal and Patch-Occupancy Age on the Dynamics of Metapopulations

Original Article

DOI: 10.1007/s11538-006-9075-y

Cite this article as:
Martcheva, M. & Bolker, B.M. Bull. Math. Biol. (2007) 69: 135. doi:10.1007/s11538-006-9075-y

Abstract

In this paper, we introduce a Levins-type metapopulation model with empty and occupied patches, and dispersing population. We structure the proportion of occupied patches according to the patch-occupancy age. We observe that patch-occupancy age may destabilize the metapopulation, leading to persistent oscillations. We also allow for the dispersal rate to vary with the proportion of empty patches in a monotone or unimodal way. The unimodal dependence leads to multiple non-trivial equilibria and bistability when the reproduction number of the metapopulation R <1 but greater than a lower critical value R* . We show that the metapopulation will persist independently of its initial status if R > 1.

Keywords

Metapopulations Patch-occupancy age Allee effect in dispersal Oscillatory dynamics Persistence 

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Zoology DepartmentUniversity of FloridaGainesvilleUSA

Personalised recommendations