Using Circuit Theory to Design Connected Landscapes

Dispersal is a key process in maintaining healthy and viable animal populations. Maintaining movement and connectivity across landscapes can help to reduce inbreeding, rescue small populations from extinction, and/or colonize new habitat. But with limited funding and constant threats of habitat loss, how do we choose which habitats to protect so that landscapes will stay well-connected for wild animal species? We've been working on these questions with some novel twists: we're applying ideas from electrical engineering to the study of connectivity in landscapes.

So what do animals and electrons have in common? Plenty, according to the mathematics behind electronic circuits on the one hand and random walk theory on the other. Commonalities between the theories have been exploited in other disciplines, like the study of neural and social networks, but their use in ecology and evolution is new. Because of these connections, powerful computing tools developed in engineering can be used to analyze connectivity in large and complex landscapes. For example, by simultaneously taking into account multiple dispersal pathways, circuit theory can be used to explain patterns of gene flow and genetic differentiation among animal populations, and to predict how these patterns might change under future land use or climate change scenarios. Or, if current flows across a model landscape, the density of flow in different areas can be used to predict which portions of the landscape are most important for  dispersing animals, thus identifying critical connective habitats. The goals are to understand how landscape heterogeneity structures populations, and to efficiently prioritize habitats for conservation so that we can maintain well-connected landscapes into the future.

Press Coverage:

Conservation Magazine: Circuitous Routes: Circuit Theory Guides Wildlife Corridor Design by Eric Wagner

Wired Magazine: Scientist Employs 'Circuit Theory' to Protect Endangered Species by Carl Zimmer

Convergence Magazine:  Where the Wild Things Are by Anna Davison

Earthtimes.org: Where Mountain Lions Roam: Star-P Helps Decipher Threatened Wildlife Migration

Some new applications of circuit theory:

(A) Map of an example landscape, with landscape resistances ranging from 1 (white) to infinity (black).  (B) Results from conventional least-cost modeling between habitat patches in lower-left and upper-right corners of the map.  (C) Circuitscape output for the same two habitat patches.  Circuitscape efficiently identifies “pinch points,” or critical habitat linkages, as well as features important for redundancy.  Unlike least-cost methods, circuit theory doesn't highlight habitat cul-de-sacs or corridors that don't contribute to connectivity (such as the one leading off the top of the map).  Work with Brett Dickson and Tim Keitt to appear soon in Ecology.

Connectivity for mountain lions moving between core habitat areas in southern California.  Blue shows areas of low current density, which are expected to have low densities of dispersing mountain lions; yellow designates movement bottlenecks, where connectivity is most vulnerable to habitat destruction.  This is an example analysis only; better dispersal routes to the South were cut off by map edges.  In general, high current flow indicates high priority areas for conservation or restoration.  Research Collaborators: Brett Dickson and Rick Hopkins, Live Oak Associates, with generous support from Vicki Long.