Abstract.
We solve the Unanimity Rule on networks with exponential, uniform and scalefree degree distributions. In particular we arrive at equations relating the asymptotic number of nodes in one of two states to the initial fraction of nodes in this state. The solutions for exponential and uniform networks are exact, the analytical approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for biodiversity loss in experimental data of foodwebs, which is available for the three network types discussed. The model allows in principle to estimate the critical value of species that have to be removed from the system to induce a complete diversity collapse.
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Hanel, R., Thurner, S. Solution of the unanimity rule on exponential, uniform and scalefree networks: A simple model for biodiversity collapse in foodwebs. Eur. Phys. J. B 62, 327–330 (2008). https://doi.org/10.1140/epjb/e2008-00160-7
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DOI: https://doi.org/10.1140/epjb/e2008-00160-7