Conservation practitioners have long recognized ecological connectivity as a global priority for preserving biodiversity and ecosystem function. In the early years of conservation science, ecologists extended principles of island biogeography to assess connectivity based on source patch proximity and other metrics derived from binary maps of habitat. From 2006 to 2008, the late Brad McRae introduced circuit theory as an alternative approach to model gene flow and the dispersal or movement routes of organisms. He posited concepts and metrics from electrical circuit theory as a robust way to quantify movement across multiple possible paths in a landscape, not just a single least-cost path or corridor. Circuit theory offers many theoretical, conceptual, and practical linkages to conservation science. We reviewed 459 recent studies citing circuit theory or the open-source software Circuitscape. We focused on applications of circuit theory to the science and practice of connectivity conservation, including topics in landscape and population genetics, movement and dispersal paths of organisms, anthropogenic barriers to connectivity, fire behavior, water flow, and ecosystem services. Circuit theory is likely to have an effect on conservation science and practitioners through improved insights into landscape dynamics, animal movement, and habitat-use studies and through the development of new software tools for data analysis and visualization. The influence of circuit theory on conservation comes from the theoretical basis and elegance of the approach and the powerful collaborations and active user community that have emerged. Circuit theory provides a springboard for ecological understanding and will remain an important conservation tool for researchers and practitioners around the globe.Aplicaciones de la Teoría de Circuitos a la Conservación y a la Ciencia de la Conectividad Resumen: Quienes practican la conservación han reconocido durante mucho tiempo que la conectividad ecológica es una prioridad mundial para la preservación de la biodiversidad y el funcionamiento del * email: brett@csp-inc.org Article impact statement: Uses of circuit theory to understand connectivity have had a durable and global impact on conservation science and practice.

Summary1. Increasing habitat connectivity is important for mitigating the effects of climate change, landscape fragmentation and habitat loss for biodiversity conservation. However, modelling connectivity at the relevant scales over which these threats occur has been limited by computational requirements. 2. Here, we introduce the open-source software GFLOW, which massively parallelizes the computation of circuit theory-based connectivity. The software is developed for high-performance computing, but scales to consumergrade desktop computers running modern Linux or Mac OS X operating systems. 3. We report high computational efficiency representing a 1739 speedup over existing software using highperformance computing and a 8Á49 speedup using a desktop computer while drastically reducing memory requirements. 4. GFLOW allows large-extent and high-resolution connectivity problems to be calculated over many iterations and at multiple scales. We envision GFLOW being immediately useful for large-landscape efforts, including climate-driven animal range shifts, multitaxa connectivity, and for the many developing use-cases of circuit theorybased connectivity.

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A fundamental problem in landscape ecology is understanding the isolating effects of different patterns of habitat loss and fragmentation on species and ecosystems. In the 21st century, urban development and sea level rise (SLR) are predicted to affect large areas of the United States, further exacerbating already fragmented and densely populated landscapes. Increasing or restoring habitat connectivity may ameliorate these effects, but the broad-reaching efforts required to assess current and future changes to connectivity, especially in low-lying areas vulnerable to SLR, are still under development. To address these issues, we strategically identified a small group of regionally significant species that represent a range of characteristics and ecological requirements useful for examining landscape connectivity. We used expert opinion to parameterize divergent species responses (i.e. resistance) to landscape features and to assess permeability of the landscape. From this, we estimated contemporary and future low-resistance habitat cores in the year 2100. We modeled six species for habitat connectivity using a multiscaled circuit theory-based approach and analysed them collectively to indicate landscape connectivity across the Southeastern United States. Using this approach, we were able to forecast changing connectivity patterns based on predicted urbanization and SLR. Our results suggest that there will be a 41% reduction in the number of low-resistance cores and a 35% decrease in mean area of remaining cores. In addition, current areas of high landscape connectivity will become more fragmented as future connectivity values indicate a more homogenized landscape structure. In the future landscape, pathways for connectivity are likely to move inland and northward as sea level and urbanization pressures increase. Our results may inform more comprehensive planning initiatives regionally or nationally, while simultaneously providing a multiscaled context for localized planning efforts.

Conservation decisions should be evaluated for how they meet conservation goals at multiple spatial extents. Conservation easements are land use decisions resulting from a combination of social and environmental conditions. An emerging area of research is the evaluation of spatial distribution of easements and their spatial correlates. We tested the relative influence of interacting social and environmental variables on the spatial distribution of conservation easements by ownership category and conservation status. For the Appalachian region of the United States, an area with a long history of human occupation and complex land uses including public-private conservation, we found that settlement, economic, topographic, and environmental data associated with spatial distribution of easements (N = 4813). Compared to random locations, easements were more likely to be found in lower elevations, in areas of greater agricultural productivity, farther from public protected areas, and nearer other human features. Analysis of ownership and conservation status revealed sources of variation, with important differences between local and state government ownerships relative to non-governmental organizations (NGOs), and among U.S. Geological Survey (USGS) GAP program status levels. NGOs were more likely to have easements nearer protected areas, and higher conservation status, while local governments held easements closer to settlement, and on lands of greater agricultural potential. Logistic interactions revealed environmental variables having effects modified by social correlates, and the strongest predictors overall were social (distance to urban area, median household income, housing density, distance to land trust office). Spatial distribution of conservation lands may be affected by geographic area of influence of conservation groups, suggesting that multi-scale conservation planning strategies may be necessary to satisfy local and regional needs for reserve networks. Our results support previous findings and provide an ecoregion-scale view that conservation easements may provide, at local scales, conservation functions on productive, more developable lands. Conservation easements may complement functions of public protected areas but more research should examine relative landscape-level ecological functions of both forms of protection.