Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

I investigate the stability of the homogeneous equilibrium of a discrete-time metapopulation assuming costly dispersal with arbitrary (but fixed) spatial pattern of connectivity between the local populations. First, I link the stability of the metapopulation to the stability of a single isolated pop...

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Bibliographic Details
Published in:Journal of theoretical biology 2010-01, Vol.262 (2), p.279-283
Main Author: Kisdi, Eva
Format: Article
Language:English
Subjects:
Bifurcation
Computer Simulation
Coupled map lattice
Discrete-time population dynamics
Dispersal
Humans
Metapopulation
Models, Biological
Mortality
Population Density
Population Dynamics
Stability
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Summary:I investigate the stability of the homogeneous equilibrium of a discrete-time metapopulation assuming costly dispersal with arbitrary (but fixed) spatial pattern of connectivity between the local populations. First, I link the stability of the metapopulation to the stability of a single isolated population by proving that the homogeneous metapopulation equilibrium, provided that it exists, is stable if and only if a single population, which is subject to extra mortality matching the average dispersal-induced mortality of the metapopulation, has a stable fixed point. Second, I demonstrate that extra mortality may destabilize the fixed point of a single population. Taken together, the two results imply that costly dispersal can destabilize the homogeneous equilibrium of a metapopulation. I illustrate this by simulations and discuss why earlier work, arriving at the opposite conclusion, was flawed.
ISSN:0022-5193
1095-8541
DOI:10.1016/j.jtbi.2009.09.032