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CONNECTIVITY MODELS



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McRae et al 2008 In press at Ecology Please do not distribute without permission Running Head CONNECTIVITY MODELS FROM CIRCUIT THEORY Title USING CIRCUIT THEORY TO MODEL CONNECTIVITY IN ECOLOGY EVOLUTION AND CONSERVATION Authors BRAD H MCRAE1 5 BRETT G DICKSON2 TIMOTHY H KEITT3 and VIRAL B SHAH4 1 National Center for Ecological Analysis and Synthesis Santa Barbara California 93101 USA Center for Environmental Sciences and Education Northern Arizona University Flagstaff Arizona 86011 USA 3 Section of Integrative Biology University of Texas at Austin Austin Texas 78712 USA 4 Department of Computer Science University of California Santa Barbara Santa Barbara CA 93106 USA 5 E mail McRae nceas ucsb edu 2 Abstract Connectivity among populations and habitats is important for a wide range of ecological processes Understanding preserving and restoring connectivity in complex landscapes requires connectivity models and metrics that are reliable efficient and processbased We introduce a new class of ecological connectivity models based in electrical circuit theory Although they have been applied in other disciplines circuit theoretic connectivity models are new to ecology They offer distinct advantages over common analytic connectivity models including a theoretical basis in random walk theory and an ability to evaluate contributions of multiple dispersal pathways Resistance current and voltage calculated across graphs or raster grids can be related to ecological processes such as individual movement and gene flow that occur across large population networks or landscapes Efficient algorithms can quickly solve networks with millions of nodes or landscapes with millions of raster cells Here we review basic circuit theory discuss relationships between circuit and random walk theories and describe applications in ecology evolution and conservation We provide examples of how circuit models can be used to predict movement patterns and fates of random walkers in complex landscapes



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