Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation

E. Éva Kisdi (1)

1 Department of Mathematics and Statistics [Helsinki]

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.

Mots clés: Bifurcation; Coupled map lattice; Discrete-time population dynamics; Dispersal; Mortality; Metapopulation; Stability

E. Éva Kisdi. Costly dispersal can destabilize the homogeneous equilibrium of a metapopulation. Journal of Theoretical Biology, 2009, 262 (2), pp.279. ⟨10.1016/j.jtbi.2009.09.032⟩. ⟨hal-00554650⟩