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 process based. 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 and to identify important habitat patches and movement corridors for conservation planning.

Abstract. Despite growing interest in the effects of landscape heterogeneity on genetic structuring, few tools are available to incorporate data on landscape composition into population genetic studies. Analyses of isolation by distance have typically either assumed spatial homogeneity for convenience or applied theoretically unjustified distance metrics to compensate for heterogeneity. Here I propose the isolation-by-resistance (IBR) model as an alternative for predicting equilibrium genetic structuring in complex landscapes. The model predicts a positive relationship between genetic differentiation and the resistance distance, a distance metric that exploits precise relationships between random walk times and effective resistances in electronic networks. As a predictor of genetic differentiation, the resistance distance is both more theoretically justified and more robust to spatial heterogeneity than Euclidean or least cost path-based distance measures. Moreover, the metric can be applied with a wide range of data inputs, including coarse-scale range maps, simple maps of habitat and nonhabitat within a species' range, or complex spatial datasets with habitats and barriers of differing qualities. The IBR model thus provides a flexible and efficient tool to account for habitat heterogeneity in studies of isolation by distance, improve understanding of how landscape characteristics affect genetic structuring, and predict genetic and evolutionary consequences of landscape change.Key words. Gene flow, graph theory, isolation by distance, isolation by resistance, landscape connectivity, landscape genetics, resistance distance. The emerging study of how landscape features affect microevolutionary processes (landscape genetics; Manel et al. 2003) will require tools that explicitly incorporate landscape heterogeneity into analyses of gene flow and genetic differentiation. Landscape characteristics may modify gene flow between pairs of subpopulations directly by affecting dispersal rates among them or indirectly by affecting the spatial arrangement of and dispersal rates among intervening subpopulations. Yet, few models are capable of integrating landscape data into predictions of population structure.For example, models of isolation by distance (Wright 1943) are among the most widely applied tools in studies of genetic differentiation in natural populations. These models have provided powerful means to explain population structure (e.g., Rousset 1997Rousset , 2000Sumner et al. 2001;Rueness et al. 2003), investigate departures from migration-drift equilibrium (Slatkin 1993;Hutchison and Templeton 1999), and address ecological questions such as whether dispersal synchronizes the dynamics of populations separated by long distances (Schwartz et al. 2002). Yet, such analyses assume homogeneous, unbounded populations, ignoring effects of range boundaries and of variation in demographic parameters within species' ranges (Maruyama 1970;Slatkin and Maruyama 1975). As Slatkin (1985) noted, most real populations are neither hom...

Maintaining connectivity for broad-scale ecological processes like dispersal and gene flow is essential for conserving endangered species in fragmented landscapes. However, determining which habitats should be set aside to promote connectivity has been difficult because existing models cannot incorporate effects of multiple pathways linking populations. Here, we test an ecological connectivity model that overcomes this obstacle by borrowing from electrical circuit theory. The model vastly improves gene flow predictions because it simultaneously integrates all possible pathways connecting populations. When applied to data from threatened mammal and tree species, the model consistently outperformed conventional gene flow models, revealing that barriers were less important in structuring populations than previously thought. Circuit theory now provides the best-justified method to bridge landscape and genetic data, and holds much promise in ecology, evolution, and conservation planning.Gulo gulo ͉ isolation by resistance ͉ landscape connectivity ͉ Swietenia macrophylla ͉ landscape genetics P reserving and restoring connectivity for broad-scale ecological processes, such as dispersal and gene flow, has become a major conservation priority (1, 2). Conservation organizations are investing considerable resources-and asking governments to do the same-to set aside land to promote connectivity (3). A major impediment to this goal is the difficulty in predicting how different land use, climate change, or reserve design scenarios will affect connectivity, and conservation planning decisions are often made without quantifying benefits for the ecological processes they are meant to conserve. If scarce conservation dollars are to be spent effectively, conservation biologists need clear, efficient, and reliable tools relating landscape composition and pattern to important ecological processes (4).Gene flow is a critical ecological process with conservation benefits ranging from promoting the persistence of small populations to spreading adaptive traits in changing environments (5-8). Because of these important ecological and evolutionary roles, a new and rapidly growing field-landscape genetics-is primarily dedicated to understanding and predicting how landscape characteristics affect gene flow (5). By combining genetic, computational, and spatial analytic tools unavailable a decade ago, the interdisciplinary field has yielded insights relevant not only to conservation (e.g., refs. 8 and 9), but to fields such as evolution (10), infectious disease ecology (11), and population ecology (12).Yet progress in all of these fields has been hampered by a lack of models capable of predicting gene flow from landscape structure. As a result, typical landscape genetic analyses simply detect genetic discontinuities and propose ad hoc explanations based on coincident landscape features, rather than testing a priori predictions of how such features are expected to influence genetic structure. This hinders hypothesis testing and leaves conserva...

Measures of genetic structure among individuals or populations collected at different spatial locations across a landscape are commonly used as surrogate measures of functional (i.e. demographic or genetic) connectivity. In order to understand how landscape characteristics influence functional connectivity, resistance surfaces are typically created in a raster GIS environment. These resistance surfaces represent hypothesized relationships between landscape features and gene flow, and are based on underlying biological functions such as relative abundance or movement probabilities in different land cover types. The biggest challenge for calculating resistance surfaces is assignment of resistance values to different landscape features. Here, we first identify study objectives that are consistent with the use of resistance surfaces and critically review the various approaches that have been used to parameterize resistance surfaces and select optimal models in landscape genetics. We then discuss the biological assumptions and considerations that influence analyses using resistance surfaces, such as the relationship between gene flow and dispersal, how habitat suitability may influence animal movement, and how resistance surfaces can be translated into estimates of functional landscape connectivity. Finally, we outline novel approaches for creating optimal resistance surfaces using either simulation or computational methods, as well as alternatives to resistance surfaces (e.g. network and buffered paths). These approaches have the potential to improve landscape genetic analyses, but they also create new challenges. We conclude that no single way of using resistance surfaces is appropriate for every situation. We suggest that researchers carefully consider objectives, important biological assumptions and available parameterization and validation techniques when planning landscape genetic studies.