Circuit theory has seen extensive recent use in the field of ecology, where it is often applied to study functional connectivity. The landscape is typically represented by a network of nodes and resistors, with the resistance between nodes a function of landscape characteristics. The effective distance between two locations on a landscape is represented by the resistance distance between the nodes in the network. Circuit theory has been applied to many other scientific fields for exploratory analyses, but parametric models for circuits are not common in the scientific literature. To model circuits explicitly, we demonstrate a link between Gaussian Markov random fields and contemporary circuit theory using a covariance structure that induces the necessary resistance distance. This provides a parametric model for second-order observations from such a system. In the landscape ecology setting, the proposed model provides a simple framework where inference can be obtained for effects that landscape features have on functional connectivity. We illustrate the approach through a landscape genetics study linking gene flow in alpine chamois (Rupicapra rupicapra) to the underlying landscape.
