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.

A spatial genetics approach to inform vector control of tsetse flies (Glossina fuscipes fuscipes) in Northern Uganda

“…The population genetic data are used to estimate genetic differentiation in the software ARLEQUIN v.3.5 (Excoffier & Lischer, 2010; Figure 2: M 1 ), which outputs a pairwise F ST matrix among sampling sites (Figure 2: O 1 ). The environmental data are used to create a resistance‐based landscape model in the program Circuitscape v.4.0.5 (McRae et al., 2008, 2013; Figure 2: M 2 ), which outputs a circuit map for each environmental variable that is then used to estimate pairwise landscape resistance matrices among sampling sites (Figure 2: O 2 ). We then used multiple matrix regression with randomization (MMRR; Figure 2: M 3 ) in the R (R Development Core Team, 2011) package “PopGenReport” (Adamack and Gruber, 2014) to test for correlation between these two outputs (Figure 2: O 1 and O 2 ) for each environmental variable, while accounting for geographic distance and linear spatial autocorrelation.…”

Model explorations of ecological network performance under conditions of global change

“…Because invasive species are generally not yet established in an area, a metapopulation model would be difficult to parameterize. Therefore, such simulations often make use of electric circuit models (McRae et al 2008), which combine principles of graph theory and metapopulation theory. Such models apply circuit theory to movement ecology via random-walk theory, and appear to be particularly useful for simulating the initial spread of (invasive) species into a landscape from source populations, before a viable population has been established.…”

Functional connectivity within conservation networks: Delineating corridors for African elephants

“…Circuit theory is based on a random walk, with connectivity between habitat patches increasing with the number of alternative routes and decreasing with distance (McRae et al 2008). Circuit theory uses the principles of an electric circuit, where a current (animal) flows through nodes and resistors (habitat patches and matrix) with voltage (probability of animal travel) and resistance (permeability of habitat types; McRae et al 2008).…”

“…Circuit theory uses the principles of an electric circuit, where a current (animal) flows through nodes and resistors (habitat patches and matrix) with voltage (probability of animal travel) and resistance (permeability of habitat types; McRae et al 2008). The resulting product is a prediction of 'current density' or a probability of movement across each pixel of the landscape.…”