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Density-dependent migration and synchronism in metapopulations

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Abstract

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.

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Authors and Affiliations

  1. Departamento de Matemática Pura e Aplicada-IM-UFRGS, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre-RS, Brasil, Brazil

    Jacques A. L. Silva & Flávia T. Giordani

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  1. Jacques A. L. Silva
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  2. Flávia T. Giordani
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Correspondence to Jacques A. L. Silva.

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Silva, J.A.L., Giordani, F.T. Density-dependent migration and synchronism in metapopulations. Bull. Math. Biol. 68, 451–466 (2006). https://doi.org/10.1007/s11538-005-9054-8

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