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USING CIRCUIT THEORY TO MODEL CONNECTIVITY IN ECOLOGY, EVOLUTION, AND CONSERVATION
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 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.
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In the citing paper
“Circuit theory connectivity models are generally seen to be robust to coarsening of input data [53], which can enable computation across very large areas at coarse pixel resolution [28], [57].”
From Applying circuit theory for corridor expansion and management at regional scales: tiling, pinch points, and omnidirectional connectivity (2014) · cites this paper as [28]
In the citing paper
“It has already been demonstrated that across long time scales at which genetic mutations can be measured, resistance distance is strongly correlated to the differences between populations [28], [29], [42].”
From Applying circuit theory for corridor expansion and management at regional scales: tiling, pinch points, and omnidirectional connectivity (2014) · cites this paper as [28]
In the citing paper
“In that way, potential movement between different locations in a region is modelled omnidirectionally, as a flow gradient, rather than as a single optimal line, generating corridors beyond optimality whose amplitude and narrowness depend on the conditions of the terrain.”
From Exploring the inherent affordability for movement in past landscapes (2027) · cites this paper as McRae et al., 2008
In the citing paper
“GIS technologies and least-cost analysis tools, such as Linkage Mapper [19] and Circuitscape [20], have demonstrated their potential in diverse fields, from biodiversity conservation to the study of ecological networks [21–25].”
From Tracing neanderthal mobility through the romanian carpathians: a GIS-based least-cost connectivity model (2025) · cites this paper as [21]
In the citing paper
“McRae et al. (2008) illustrated how circuit theory could be used to identify multiple (i.e., redundant) movement pathways or habitat corridors and reveal, for example, critical ‘pinch points’ constraining potential flow between focal areas.”
From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as McRae et al. (2008)
In the citing paper
“Finally, McRae et al. (2008) introduced many readers to the key concepts and metrics used in electrical circuit theory, and how they could be applied to model and map the process of connectivity over extensive landscape, habitat, or population networks (using georeferenced raster grids).”
From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as McRae et al. (2008)
In the citing paper
“The development of accompanying software, such as the open-source program Circuitscape (McRae et al. 2008, 2013; www.circuitscape.org), has provided accessible means of implementing circuit theory concepts across a range of projects and disciplines.”
From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as McRae et al. 2008
In the citing paper
“Circuit theory’s basis in random walk theory results in an implicit assumption that individuals moving across a landscape have no knowledge of relative resistance beyond their immediate surroundings, making it particularly appropriate for modeling natal dispersal paths (McRae et al. 2008).”
From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as McRae et al. 2008
In the citing paper
“Additionally, several assumptions and caveats still need to be addressed, such as modeling long-distance dispersal events (McRae 2006) and asymmetric migration (McRae et al. 2008; but see Hanks 2017).”
From Circuit‐theory applications to connectivity science and conservation (2019) · cites this paper as McRae et al. 2008
In the citing paper
“In the circuittheoretic approach, the landscape is abstracted as a network of current sources, grounds, and resistors.The resulting current flow through the electrical network is then related to the movement or flow intensity of the ecological process of interest.”
From Omniscape.jl: software to compute omnidirectional landscape connectivity (2021) · cites this paper as McRae et al., 2008
In the citing paper
“The circuit-theoretic approach to connectivity modeling was a more recent innovation, and it has been gaining popularity over the past decade (Dickson et al., 2019;McRae, 2006;McRae et al., 2008).”
From Omniscape.jl: software to compute omnidirectional landscape connectivity (2021) · cites this paper as McRae et al., 2008
In the citing paper
“Similarly, McRae et al. (2008) modelled functional connectivity based on electrical circuit theory, which models connectivity across a resistance surface as electric current moving through a circuit.”
From Landscape connectivity for wildlife: development and validation of multispecies linkage maps (2014) · cites this paper as McRae et al. 2008
In the citing paper
“Finally, some methods work by connecting source and destination sites (McRae et al. 2008;Schwartz et al. 2009), which may not be appropriate for all types of questions (Ferrarini 2013).”
From Landscape connectivity for wildlife: development and validation of multispecies linkage maps (2014) · cites this paper as McRae et al. 2008
In the citing paper
“Several authors have alluded to the idea that artificial boundaries might influence the results of least cost path and landscape resistance models [2], [11], [15]–[18], but to our knowledge, no one has directly addressed the issue.”
From The effect of map boundary on estimates of landscape resistance to animal movement (2010) · cites this paper as [11]
In the citing paper
“One of the reasons circuit theory is appealing as a model of gene flow and individual movement is that the incorporation of random walkers on networks to estimate landscape resistance allows resistance to decrease with increasing connectivity, path width, and path redundancy [11], [14].”
From The effect of map boundary on estimates of landscape resistance to animal movement (2010) · cites this paper as [11]
In the citing paper
“Connectivity modelling is an alternate approach to spatial connectivity modelling that is widely used in ecological research (McRae et al., 2008).”
From A spatial connectivity approach to landscapes of conflict: julius caesar and the assault to puig ciutat (NE iberian peninsula) (2022) · cites this paper as McRae et al., 2008
In the citing paper
“Developed by conservation scientist Brad McRae (with a background in electrical engineering) and computer scientist Viral Shah, Circuitscape allows users to apply the logic and mathematics of electrical circuit theory to questions of how genes, animals, or processes flow across heterogeneous landscapes [22,31].”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“However, once the surface is created and used as input for a connectivity analysis, many modeling workflows share the trait of being constrained by computational demand [15,22,25,26], as representing spatial patterns in a cumulative process like connectivity requires extensive calculations, often across millions of pixels.”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“To date, Circuitscape has been most widely applied in landscape genetics, where modelers calculate”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“The Circuitscape algorithm tracks where”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“In contrast, in an animal movement context, producing current flow maps is the goal, with current magnitudes representing the relative use of different pixels by animals (or ecological processes) moving across the landscape (resistance surface) between focal nodes (habitat patches), following the assumption of a random walk [22].”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“The first version [22] was written in Java, followed by version 2.0 in MATLAB.”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“To find Circuitscape applications, we reviewed 1280 papers identified through Web of Science searches (end date for publication, including”
From Circuitscape in julia: empowering dynamic approaches to connectivity assessment (2021) · cites this paper as [22]
In the citing paper
“Furthermore, as noted in21, Circuitscape assumes a directional symmetry of resistance between adjacent pixels, despite movement from an area of higher to lower resistance being much more likely than the reverse.”
From Connectivity modelling in conservation science: a comparative evaluation (2022) · cites this paper as [21]
In the citing paper
“Furthermore, as noted in21, Circuitscape assumes a directional symmetry of resistance between adjacent pixels, despite movement from an area of higher to lower resistance being much more likely than the reverse.”
From Connectivity modelling in conservation science: a comparative evaluation (2022) · cites this paper as [21]
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Metadata
- Authors
- McRae, B. H., Dickson, B. G., Keitt, T. H., & Shah, V. B.
- Affiliations
- National Center for Ecological Analysis and Synthesis (US)
- Northern Arizona University (US)
- The University of Texas at Austin (US)
- University of California, Santa Barbara (US)
- Corresponding author
- McRae, Brad H.
- Venue
- Ecology
- Publisher
- Wiley
- Published
- 2008-10
- Volume
- 89
- Issue
- 10
- Pages
- 2712-2724
- ISSN
- 0012-9658 (ISSN-L)
- OpenAlex
- W2091202128
- Cited by
- 2,244
- References
- 44
- Citations by year
- 2026: 258 · 2025: 233 · 2024: 226 · 2023: 166 · 2022: 209 · 2021: 177 · 2020: 148 · 2019: 148 · 2018: 96 · 2017: 130 · 2016: 93 · 2015: 89 · 2014: 65 · 2013: 69 · 2012: 49
- FWCI
- 21.77
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Ecology (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Environmental Science › Ecology › Wildlife-Road Interactions and Conservation
- Physical Sciences › Environmental Science › Ecology › Wildlife Ecology and Conservation
- Physical Sciences › Environmental Science › Global and Planetary Change › Land Use and Ecosystem Services
- Keywords
- ecological connectivity, circuit theory, random walk hypothesis, resistance surfaces, gene flow, animal movement, dispersal routes, habitat patches, movement corridors, conservation planning, landscape connectivity, population networks
- MeSH terms
- Algorithms, Animals, Conservation of Natural Resources, Ecology, Biological Evolution, Models, Biological, Models, Theoretical, Population Density, Population Dynamics, Ecosystem
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