A model for a spatially structured metapopulation accounting for within patch dynamics

Andrew G Smith; Ross McVinish; Philip K Pollett

doi:10.1016/j.mbs.2013.11.001

A model for a spatially structured metapopulation accounting for within patch dynamics

Math Biosci. 2014 Jan:247:69-79. doi: 10.1016/j.mbs.2013.11.001. Epub 2013 Nov 23.

Authors

Andrew G Smith¹, Ross McVinish², Philip K Pollett²

Affiliations

¹ School of Mathematics and Physics, University of Queensland, St Lucia 4072, Queensland. Electronic address: a.smith23@uq.edu.au.
² School of Mathematics and Physics, University of Queensland, St Lucia 4072, Queensland.

PMID: 24275018
DOI: 10.1016/j.mbs.2013.11.001

Abstract

We develop a stochastic metapopulation model that accounts for spatial structure as well as within patch dynamics. Using a deterministic approximation derived from a functional law of large numbers, we develop conditions for extinction and persistence of the metapopulation in terms of the birth, death and migration parameters. Interestingly, we observe the Allee effect in a metapopulation comprising two patches of greatly different sizes, despite there being decreasing patch specific per-capita birth rates. We show that the Allee effect is due to the way the migration rates depend on the population density of the patches.

Keywords: Extinction; Markov process; Metapopulation; Partially ordered flow; Spatially structured.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Computer Simulation
Extinction, Biological*
Markov Chains
Models, Theoretical*
Population Dynamics*