Density-dependent migration and synchronism in metapopulations
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- Silva, J.A.L. & Giordani, F.T. Bull. Math. Biol. (2006) 68: 451. doi:10.1007/s11538-005-9054-8
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A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.