Abstract. Population size and landscape connectivity are key determinants of population viability, yet no methods exist for simultaneously estimating density and connectivity parameters. Recently developed spatial capture-recapture (SCR) models provide a framework for estimating density of animal populations but thus far have not been used to study connectivity. Rather, all applications of SCR models have used encounter probability models based on the Euclidean distance between traps and animal activity centers, which implies that home ranges are stationary, symmetric, and unaffected by landscape structure. In this paper we devise encounter probability models based on ''ecological distance,'' i.e., the least-cost path between traps and activity centers, which is a function of both Euclidean distance and animal movement behavior in resistant landscapes. We integrate least-cost path models into a likelihood-based estimation scheme for spatial capture-recapture models in order to estimate population density and parameters of the least-cost encounter probability model. Therefore, it is possible to make explicit inferences about animal density, distribution, and landscape connectivity as it relates to animal movement from standard capture-recapture data. Furthermore, a simulation study demonstrated that ignoring landscape connectivity can result in negatively biased density estimators under the naive SCR model.

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.

Landscape resistance reflects how difficult it is for genes to move across an area with particular attributes (e.g. land cover, slope). An increasingly popular approach to estimate resistance uses Mantel and partial Mantel tests or causal modelling to relate observed genetic distances to effective distances under alternative sets of resistance parameters. Relatively few alternative sets of resistance parameters are tested, leading to relatively poor coverage of the parameter space. Although this approach does not explicitly model key stochastic processes of gene flow, including mating, dispersal, drift and inheritance, bias and precision of the resulting resistance parameters have not been assessed. We formally describe the most commonly used model as a set of equations and provide a formal approach for estimating resistance parameters. Our optimization finds the maximum Mantel r when an optimum exists and identifies the same resistance values as current approaches when the alternatives evaluated are near the optimum. Unfortunately, even where an optimum existed, estimates from the most commonly used model were imprecise and were typically much smaller than the simulated true resistance to dispersal. Causal modelling using Mantel significance tests also typically failed to support the true resistance to dispersal values. For a large range of scenarios, current approaches using a simple correlational model between genetic and effective distances do not yield accurate estimates of resistance to dispersal. We suggest that analysts consider the processes important to gene flow for their study species, model those processes explicitly and evaluate the quality of estimates resulting from their model.

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