2007/06/28 by Rudolf Hanel, R. Hanel, Stefan Thurner +1
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · Environmental Science · Physics and Astronomy · #Origins and Evolution of Life #Plant and animal studies #Sustainability and Ecological Systems Analysis #physics.bio-ph #q-bio.PE
paper · pdf · doi:10.1140/epjb/e2008-00160-7
4 pages, 3 figs
arxiv created 2007/06/28 · openalex publication_date 2008/04/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 approximation for the scalefree case is in perfect agreement with simulation results. We use these solutions to provide a theoretical understanding for experimental data on biodiversity loss in 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 its complete collapse.