Circuit-theory applications to connectivity science and conservation

Article (PDF Available)inConservation Biology 33(2) · October 2018with 907 Reads
DOI: 10.1111/cobi.13230
Cite this publication
Abstract
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. © 2018 Society for Conservation Biology.

Abstract

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 ecosistema. Durante los primeros años de la ciencia de la conservación los ecólogos difundieron los principios de la biografía de islas para evaluar la conectividad con base en la proximidad entre el origen y el fragmento, así como otras medidas derivadas de los mapas binarios de los hábitats. Entre 2006 y 2008 el fallecido Brad McRae introdujo la teoría de circuitos como una estrategia alternativa para modelar el flujo génico y la dispersión o las rutas de movimiento de los organismos. McRae propuso conceptos y medidas de la teoría de circuitos eléctricos como una manera robusta para cuantificar el movimiento a lo largo de múltiples caminos posibles en un paisaje, no solamente a lo largo de un camino o corredor de menor costo. La teoría de circuitos ofrece muchos enlaces teóricos, conceptuales y prácticos con la ciencia de la conservación. Revisamos 459 estudios recientes que citan la teoría de circuitos o el software de fuente abierta Circuitscape. Nos enfocamos en las aplicaciones de la teoría de circuitos a la ciencia y a la práctica de la conservación de la conectividad, incluyendo temas como la genética poblacional y del paisaje, movimiento y caminos de dispersión de los organismos, barreras antropogénicas de la conectividad, comportamiento ante incendios, flujo del agua, y servicios ambientales. La teoría de circuitos probablemente tenga un efecto sobre la ciencia de la conservación y quienes la practican por medio de una percepción mejorada de las dinámicas del paisaje, el movimiento animal, y los estudios de uso de hábitat, y por medio del desarrollo de nuevas herramientas de software para el análisis de datos y su visualización. La influencia de la teoría de circuitos sobre la conservación viene de la base teórica y la elegancia de la estrategia y de las colaboraciones fuertes y la comunidad activa de usuarios que han surgido recientemente. La teoría de circuitos proporciona un trampolín para el entendimiento ecológico y seguirá siendo una importante herramienta de conservación para los investigadores y practicantes en todo el mundo.

Review
Circuit-theory applications to connectivity science
and conservation
Brett G. Dickson ,1,2 Christine M. Albano,1Ranjan Anantharaman,3Paul Beier ,4
Joe Fargione,5Tabitha A. Graves ,6Miranda E. Gray,1Kimberly R. Hall,5Josh J. Lawler,7
Paul B. Leonard,8Caitlin E. Littlefield ,7Meredith L. McClure,1John Novembre,9
Carrie A. Schloss,10 Nathan H. Schumaker,11 Viral B. Shah,3and David M. Theobald1
1Conservation Science Partners Inc., 11050 Pioneer Trail, Suite 202, Truckee, CA, 96161, U.S.A.
2Landscape Conservation Initiative, Northern Arizona University, Box 5694, Flagstaff, AZ, 86011, U.S.A.
3Julia Computing, 45 Prospect Street, Cambridge, MA, 02139, U.S.A.
4School of Forestry, Northern Arizona University, Box 15018, Flagstaff, AZ, 86011, U.S.A.
5The Nature Conservancy – North America Region, 1101 West River Parkway, Suite 200, Minneapolis, MN, 55415, U.S.A.
6U.S. Geological Survey, Northern Rocky Mountain Science Center, 38 Mather Drive, West Glacier, MT, 59936, U.S.A.
7School of Environmental and Forest Sciences, University of Washington, Box 352100, Seattle, WA, 98195, U.S.A.
8U.S. Fish & Wildlife Service, Science Applications, 101 12th Avenue, Number 110, Fairbanks, AK, 99701, U.S.A.
9Department of Human Genetics, Department of Ecology and Evolution, University of Chicago, 920 East 58th Street, Chicago, IL,
60637, U.S.A.
10The Nature Conservancy, 201 Mission Street, San Francisco, CA, 94105, U.S.A.
11U.S. Environmental Protection Agency, 200 Southwest 35th Street, Corvallis, OR, 97330, U.S.A.
Abstract: 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.
Keywords: barriers, corridors, dispersal, ecological flow, electrical current, landscape genetics
Aplicaciones de la Teor´
ıa de Circuitos a la Conservaci´
on y a la Ciencia de la Conectividad
Resumen: Quienes practican la conservaci´
on han reconocido durante mucho tiempo que la conectivi-
dad ecol´
ogica es una prioridad mundial para la preservaci´
on 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.
Paper submitted March 17, 2018; revised manuscript accepted September 30, 2018.
1
Conservation Biology, Volume 0, No. 0, 1–11
C
2018 Society for Conservation Biology
DOI: 10.1111/cobi.13230
2Circuit Theory
ecosistema. Durante los primeros a˜
nos de la ciencia de la conservaci´
on los ec´
ologos difundieron los principios
de la biograf´
ıa de islas para evaluar la conectividad con base en la proximidad entre el origen y el fragmento,
as´
ı como otras medidas derivadas de los mapas binarios de los h´
abitats. Entre 2006 y 2008 el fallecido Brad
McRae introdujo la teor´
ıa de circuitos como una estrategia alternativa para modelar el flujo g´
enico y la
dispersi´
on o las rutas de movimiento de los organismos. McRae propuso conceptos y medidas de la teor´
ıa de
circuitos el´
ectricos como una manera robusta para cuantificar el movimiento a lo largo de m´
ultiples caminos
posibles en un paisaje, no solamente a lo largo de un camino o corredor de menor costo. La teor´
ıa de circuitos
ofrece muchos enlaces te´
oricos, conceptuales y pr´
acticos con la ciencia de la conservaci´
on. Revisamos 459
estudios recientes que citan la teor´
ıa de circuitos o el software de fuente abierta Circuitscape. Nos enfocamos
en las aplicaciones de la teor´
ıa de circuitos a la ciencia y a la pr´
actica de la conservaci´
on de la conectividad,
incluyendo temas como la gen´
etica poblacional y del paisaje, movimiento y caminos de dispersi´
on de los
organismos, barreras antropog´
enicas de la conectividad, comportamiento ante incendios, flujo del agua, y
servicios ambientales. La teor´
ıa de circuitos probablemente tenga un efecto sobre la ciencia de la conservaci´
on
y quienes la practican por medio de una percepci´
on mejorada de las din´
amicas del paisaje, el movimiento
animal, y los estudios de uso de h´
abitat, y por medio del desarrollo de nuevas herramientas de software para
el an´
alisis de datos y su visualizaci´
on. La influencia de la teor´
ıa de circuitos sobre la conservaci´
onvienedela
base te´
orica y la elegancia de la estrategia y de las colaboraciones fuertes y la comunidad activa de usuarios
que han surgido recientemente. La teor´
ıa de circuitos proporciona un trampol´
ın para el entendimiento
ecol´
ogico y seguir´
a siendo una importante herramienta de conservaci´
on para los investigadores y practicantes
en todo el mundo.
Palabras Clave: barreras, corredores, corriente el´
ectrica, dispersi´
on, flujo ecol´
ogico, gen´
etica del paisaje
ddd:dd
,dd,ddd
2006 2008 ,Brad McRae ,dd
dd,
ddd
dCircuitscape459 ,,
ddd
dd,,d
d,dd
,
:;:
:,,,,d,
Introduction
Ecological connectivity is a global priority for preserving
biodiversity and ecosystem function (UNEP 2015; IUCN
2017) and has long been of interest to conservation sci-
entists (Harris 1984). In the early years of conservation
science, ecologists extended principles of island biogeog-
raphy to assess connectivity based on proximity to source
patches (MacArthur & Wilson 1967) and other metrics
derivable from binary maps containing habitat patches
embedded in a nonhabitat matrix (e.g., With et al. 1997).
The introduction of least-cost modeling in the early 1990s
(Knaapen et al. 1992) was a major advancement in con-
nectivity and movement corridor research and quickly
became the dominant paradigm for evaluating connectiv-
ity for animals. However, least-cost paths often have clear
limitations, including an assumption that individuals have
perfect knowledge of the landscape and therefore select
a single optimal route.
In 3 papers published from 2006 to 2008, Brad McRae
introduced circuit theory to many ecologists and con-
servation scientists as an alternative, process-driven ap-
proach to modeling gene flow and the dispersal or
movement routes of organisms (see below). Drawing
from his background in electrical engineering, as well
as the seminal work of Doyle and Snell (1984) and oth-
ers, McRae’s key innovation was recognizing that circuit
theory permitted a robust way to quantify gene flow.
The approach provided a much-needed theoretical basis
for understanding and mapping patterns of connectiv-
ity and has been rapidly adopted in conservation sci-
ence, other ecological disciplines, and beyond. The de-
velopment 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. Additional software and devel-
opment topics are described in Supporting Information.
Conservation Biology
Volume 0, No. 0, 2018
Dickson et al. 3
In the wake of Brad McRae’s untimely death in July
2017 (Lawler et al. 2018), we explored the importance
and key contributions of circuit theory to connectivity
conservation and related issues. We considered the foun-
dations of circuit theory, including key concepts, out-
puts, and comparisons with other approaches to evaluat-
ing connectivity and the theory’s diversity of applications
in conservation and ecology, including a synthesis of rel-
evant publications across a variety of topics and from
multiple geographies. Finally, we considered how new
applications of circuit theory might continue to benefit
conservation theory and practice, particularly in an era
of global change.
Foundations of Circuit Theory in Conservation
Brad McRae posited circuit theory as an elegant alterna-
tive approach to model gene flow and organismal move-
ment in a series of 3 papers published during 2006–2008.
McRae (2006) linked the findings of Doyle and Snell
(1984) and Chandra et al. (1996) to population genet-
ics and landscape ecology. Specifically, Doyle and Snell
(1984) demonstrated that resistance distances from cir-
cuit theory are directly proportional to the movements
of Markovian random walkers on graphs, and Chandra
et al. (1996) related resistance distances to “commute
times,” or the time it takes a random walker to travel
from one point to another and back again. McRae (2006)
described the concept that the genetic distance among
subpopulations of interest can be estimated by represent-
ing the landscape as a circuit board, where each pixel
in a raster depiction of the landscape is a resistor, and
gene flow between any 2 subpopulations occurs via all
possible chains of resistors linking them, not just along
the single chain with the lowest sum of resistances (i.e.,
the least-cost path). He coined this notion “isolation by
resistance” (IBR), which has practical consequences in
the context of conservation. For example, in IBR (but
not least-cost models) increasing the number of paths
always decreases the total resistance and genetic distance
among subpopulations, and habitat degradation increases
genetic distance, even outside the least-cost path. Its theo-
retical foundation and computational efficiency has made
circuit theory a powerful and defensible tool for under-
standing potential gene flow, animal movement routes,
and landscape connectivity.
The second foundational paper (McRae & Beier 2007)
demonstrated that IBR explained genetic patterns of
mammal (wolverine [Gulo gulo]) and plant (bigleaf
mahogany [Swetenia macrophylla]) populations about
50–200% better than 2 conventional approaches, namely
isolation by distance and least-cost paths. The findings
were striking because the species were undergoing rapid
human-caused demographic changes, violating the IBR
model assumption that all populations are in genetic
equilibrium (i.e., based on the response variable, FST).
This robustness suggested that circuit theory could be
applied to the variety of other landscapes experiencing
human-caused changes.
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 (based on georeferenced
raster grids). Two of the most commonly used metrics
include current density and effective resistance. Current
density provides an estimate of the net movement prob-
abilities (or flow) of random walkers through a given
grid cell. Effective resistance permits a pairwise distance-
based measure of isolation among populations or sites
(McRae & Beier 2007). 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 that con-
strain potential flow between focal areas. Redundancy is
a measure of the number of possible pathways between
focal points and reflects a fundamental relationship that
is the ratio of least-cost distance to effective resistance
(see Koen et al. [2012] and Marrotte and Bowman [2017]
for in-depth treatments of this topic). Because circuit the-
ory uses the same underlying landscape resistance data
used by least-cost and other connectivity models, it could
readily be added to the toolkits of conservation planners.
In addition, McRae et al. (2008) introduced many readers
to Circuitscape software, opening the door to diverse
applications.
Applications of Circuit Theory to Conservation
Circuit theory has been applied to a wide range of conser-
vation questions and challenges. Because Circuitscape is
the principal tool that researchers and practitioners use
to apply the method, we reviewed 459 papers identi-
fied through either a Web of Science or Google Scholar
search of work that cited McRae et al. (2008) or the Cir-
cuitscape user guide (McRae & Shah 2009; McRae et al.
2013). Of these studies, 277 directly used the software.
Applications ranged across disciplines from conservation
to evolutionary biology, from anthropology to epidemi-
ology, and more. Circuitscape has been applied on every
continent (including off the coast of Antarctica [Dambach
et al. 2016]), and several applications spanned multiple
continents (e.g., Lawler et al. 2013; Tassi et al. 2015)
(Fig. 1). Whatever the geographic or conservation con-
text, Circuitscape has been most frequently applied to
single, focal species, though studies of 2 or more species
are becoming more common (Fig. 2). The vast majority of
studies addressed animals (n=228), but 10 focused on
plants and 1 on protists (Dong et al. 2016). Mammals were
by far the most common vertebrates studied, followed by
birds, amphibians, reptiles, and fish, though arthropods
have been studied almost as frequently as birds (Fig. 3).
Conservation Biology
Volume 0, No. 0, 2018
4Circuit Theory
Number of studies
1
2–5
6–10
11–25
26–95
Figure 1. Number of peer-reviewed studies that used Circuitscape by nation from January 2009 to February 2018.
Three studies that were continental in their spatial extent are not represented.
0
20
40
60
80
2009 2010 2011 2012 2013 2014 2015 2016 2017
Ye a r
Number of studies
single species
several species
many species
not species specific
other
Figure 2. Number of peer-reviewed studies of 5 types
that used Circuitscape from 2009 to 2017 (several
species, 2–10; many species, >10; not species specific,
specific species not targeted; other, models compared
or physical processes modeled [e.g., hydraulic
resistance in roots [Zeppenfeld et al. 2017]).
At least 5 mammal-focused studies addressed human ge-
nomics or movement patterns.
We examined the impressive range and diversity of
circuit-theoretic and Circuitscape applications and con-
sidered how circuit theory has been used to understand
landscape and population genetics, the movement and
dispersal paths of organisms, anthropogenic barriers to
connectivity, fire behavior, water flow, and ecosystem
services. Additional topic areas and examples are given
in Supporting Information.
Landscape and Population Genetics
The foundational papers on circuit theory energized
the emerging field of landscape genetics (Guillot et al.
2009; Manel & Holderegger 2013). Use of genetic data
to inform models of landscape resistance to movement
with circuit theory has since become standard practice
(Zeller et al. 2012; Simpkins et al. 2018). This informa-
tion has been useful in formalizing the incorporation of
landscape structure and complexity into conservation
plans for many species and ecosystems. For example, the
multispecies Washington Connected Landscapes project
(WWHCWG 2010) incorporated mountain goat (Oream-
nos americanus) connectivity based on genetic circuit-
theory models (Shirk et al. 2010), and the Washington-
British Columbia Climate-Connectivity project (Krosby
Conservation Biology
Volume 0, No. 0, 2018
Dickson et al. 5
Figure 3. Number of peer-reviewed studies that
applied Circuitscape to research questions in the
animal kingdom from January 2009 to February
2018.
et al. 2016) spurred additional research based on genetic
and circuit theoretic approaches for assessing potential
impacts and adaptation actions under climate change
(Parks et al. 2015). Circuit theory has been used in mul-
tiple ways to explore the potential impacts of climate
change on landscape genetics. A few studies explored
how historical changes to Earth’s climate have affected
connectivity, resulting in modern genetic patterns (Bell
et al. 2010; Ortego et al. 2015), or have examined the im-
pact climate change will have on future genetic patterns
(Velo-Anton et al. 2013).
Despite its widespread use and contributions, the ap-
plication of circuit theory in genetics is not yet fully real-
ized. Initial statistical approaches based on comparing in-
terindividual genetic distances with resistance distances
(e.g., with Mantel tests) often led to faulty inferences
by incorrectly assuming linearity, ignoring spatial struc-
ture in the data, and failing to recognize that genetic
distances can be affected by variable local population
density (Legendre & Fortin 2010; Jaqui´
ery et al. 2011;
Graves et al. 2013). Other recent approaches use appro-
priate probability distributions for distance data (Hanks &
Hooten 2013) and newer IBR models accommodate vari-
ation in population sizes to some extent (Petkova et al.
2016). Even if the basic IBR model assumptions are met,
challenges remain in automating procedures for how to
weigh various environmental factors and how to account
for uncertainty in noisy estimates of landscape variables
(Dudaniec et al. 2016). In their comparison of microsatel-
lite genetic data sets with maps of current density derived
using circuit theory, Marrotte et al. (2017) found that
current density was not usually a good predictor of gene
flow for 4 terrestrial mammal species in Ontario, espe-
cially where habitat amount was high or pinch points
were observed. Overall, these and numerous other efforts
to extend circuit theory underscore its foundational and
future importance to landscape genetics.
Identifying and Conserving Pathways and Corridors for Animal Movement
Circuit theory was quickly taken up and applied by
conservation scientists and ecologists not only to pre-
dict population-level patterns of gene flow, but also to
understand how landscape features influence individual
movement paths and thus conservation and restoration
of habitat corridors and targeted studies of movement
(Dickson et al. 2013). The breadth of applications, along
with comparative method studies, has increased under-
standing of the strengths of circuit theory in conserva-
tion and highlights its complementarity with other meth-
ods for predicting movement, including least-cost paths
(e.g., Howey 2011; Mateo-Sanchez et al. 2015; Marrotte
& Bowman 2017). Circuit theory is particularly appropri-
ate when the assumption of moving individuals having
limited knowledge of the surrounding landscape is met
(McClure et al. 2016; Keeley et al. 2017; Maiorano et al.
2017).
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 par-
ticularly appropriate for modeling natal dispersal paths
(McRae et al. 2008). Applications to predicting dispersal
corridors for large, wide-ranging carnivores have been
common (e.g., Proctor et al. 2015; Ahmadi et al. 2017;
Gantchoff & Belant 2017; McClure et al. 2017), but
circuit theory has also been used to model amphib-
ian dispersal via surface water networks of Australia
(Bishop-Taylor et al. 2015), dispersal paths of subter-
ranean beetles via substratum karst systems (Rizzo et al.
2017), marine shrimp larvae dispersal via ocean currents
(Dambach et al. 2016), dispersal of early human pop-
ulations in Africa and the Caucasus (Tassi et al. 2015;
Tarkhnishvili et al. 2016), and even pathways of early
explorers (e.g., Hernando de Soto’s route through the
Appalachian Mountains in 1540 [Thayn et al. 2016]). Ad-
vantages of circuit theory may be less pronounced when
applied to the movements of individuals through known
Conservation Biology
Volume 0, No. 0, 2018
6Circuit Theory
landscapes. For example, circuit theory and least-cost
path models perform comparably in predicting seasonal
ungulate migration routes (Poor et al. 2012; McClure et al.
2016). Still, circuit theory is suitable for characterizing
relative frequency of routine movements along multi-
ple potential paths through urban and other fragmented
landscapes (e.g., Braaker et al. 2014; R¨
odder et al. 2016;
Grafius et al. 2017).
Given its utility for predicting high-use animal move-
ment routes, researchers have applied circuit theory to
evaluate alternatives for establishment of protected areas
to enhance connectivity among populations (e.g., pumas
[Puma concolor] in the Atlantic Forest of southeast Brazil
[Castilho et al. 2015], forest understory birds in Costa
Rica [Fagan et al. 2016], and giant pandas [Ailuropoda
melanoleuca] in China’s Qinling Mountains [Wang et al.
2014]). Circuit theory models have also been used to iden-
tify corridors between occupied and unoccupied habitat
areas to promote recolonization of a species’ historic
range, or to identify areas suitable for habitat restora-
tion (e.g., Jarchow et al. 2016; Zi´
ołkowska et al. 2016;
Gantchoff & Belant 2017). Similarly, other applications
have identified potential pathways for spread of invasive
species, diseases, and pathogens (details given in Sup-
porting Information).
Conservation scientists often wish to protect corridors
that promote movement of more than 1 species and
have used circuit theory to assess the functionality and
efficiency of potential multispecies corridors (e.g., Koen
et al. 2014; Bleyhl et al. 2017; Lechner et al. 2017). Several
studies (e.g., Epps et al. 2011; Breckheimer et al. 2014)
show that corridors designed for wide-ranging umbrella
species enhance connectivity for less vagile organisms
with similar habitat requirements, and Brodie et al. (2015)
found that multispecies corridors tailored to ecologically
similar species (e.g., carnivores and herbivores) can be
highly effective for all species. Dilkina et al. (2017) ex-
plored the cost-effectiveness of grizzly bear (Ursus arc-
tos) and wolverine corridors by optimizing corridor selec-
tion under a constrained budget. Even greater generality
can result from species-agnostic approaches to estimat-
ing ecological flows that base landscape resistance on
the degree to which habitats are unaltered or otherwise
modified by humans (e.g., Bennie et al. 2014; Dickson
et al. 2017).
Anthropogenic Barriers to Connectivity
Circuit theory has been used to determine how humans
impact movement corridors and where mitigating these
impacts might be most crucial to maintaining or restoring
connectivity. Understanding the effects of linear infras-
tructure such as transportation corridors and other bar-
riers (e.g., international boundary structures and fence
lines) on connectivity and gene flow was a primary impe-
tus for McRae’s interest in the theory and development
of Circuitscape (McRae 2006). Examples include work by
Litvaitis et al. (2015) that explores the potential effects
of roads on the movement of wide-ranging carnivores in
New Hampshire and work by Naidoo et al. (2018) exam-
ining barrier effects on movement corridors for African
elephants (Loxodonta africana). Guidance for direct ap-
plication of these approaches with transportation agen-
cies has been provided by Beier et al. (2011), and initial
explorations are underway that explicitly incorporate vol-
ume of traffic on highways into estimates of landscape
permeability (e.g., Theobald et al. 2012). Yet, work inte-
grating connectivity across transportation infrastructure,
particularly within the context of regional transporta-
tion planning, remains understudied (e.g., Mateo-Sanchez
et al. 2014), and this gap is especially important given the
ubiquity of transportation and its strong population and
genetic effects on various animals globally (Trombulak &
Frissell 2000). Beyond the impacts of transportation cor-
ridors, circuit-theory applications have addressed a wide
range of anthropogenic impacts on connectivity, includ-
ing urbanization, agriculture, and energy infrastructure
(Supporting Information).
More recent studies have assessed the vulnerability of
populations to climate change due to fragmentation that
could potentially impede adaptive shifts in distributions
(e.g., Leonard et al. 2017a). A number of studies used
Circuitscape to explicitly plan for climate-driven move-
ments. For example, Lawler et al. (2013) used species
distribution models to map the routes that organisms
might follow to track shifting climates, and Littlefield et al.
(2017) mapped connections between climatic conditions
today and where those conditions will be in the future
(i.e., climate analogs). These and other studies have used
Circuitscape to model climate, sea-level rise, range shifts,
and projections of climate-driven landscape change to
determine or anticipate the impact of climate change on
species and their movements.
Nontraditional and Emergent Applications of Circuit Theory
Fire Spread
Circuit theory has provided an intuitive analogue to the
process of wildfire movement (i.e., spread) across het-
erogeneous landscapes. The approach accommodates
important stochastic properties of wildfire by model-
ing probabilistic spread between adjacent neighbors in a
landscape network (Gray & Dickson 2015). Circuit theory
also accommodates the critical role of spatial context in
estimating fire likelihood because areas on the landscape
can burn far away from an ignition source. In this case,
circuit conductance (the inverse of resistance) is a sur-
rogate for the ease of fire spread across the landscape.
Fuels, topography, and other biophysical variables that
influence the spread of fire may be flexibly integrated into
a conductance surface in a circuit-theoretic model (Gray
Conservation Biology
Volume 0, No. 0, 2018
Dickson et al. 7
& Dickson 2015, 2016). Resulting metrics (e.g., current
density and centrality) and maps of potential fire connec-
tivity can be used to target areas on the landscape where
fuel breaks could most effectively hinder fire movement
through wildlife habitat (Welch et al. 2015) and disrupt
the invasive grass-fire cycle (Gray & Dickson 2016). In
addition, wall-to-wall estimates of fire connectivity can be
useful to identify areas of highest fire likelihood across
a landscape and, consequently, the natural and human
infrastructure at greatest relative risk from wildfire (Gray
& Dickson 2015).
Water Flow
The electronic circuit analogy has been used in a vari-
ety of subdisciplines within the field of hydrology. As
early as 1962, electronic circuit models were seen as
an innovative approach to analyzing groundwater flows
(Robinove 1962). In these early studies, physical cir-
cuit models, often involving the careful placement and
soldering of thousands of resistors for each individual
run, were constructed in the laboratory to simulate the
groundwater system (Miley & Kuelske 1990). With in-
creased computer processing power, this approach was
supplanted by more contemporary node-based numerical
models that are in wide use today (Fetter 2001). The
use of such models has significantly advanced scientists’
understanding of flow connectivity within aquifers as
well as between ground and surface waters (Singh 2014).
Application of resistance-based groundwater models has
provided insights into questions that are highly relevant
to the field of conservation science, including under-
standing water budgets in the midst of rapid human
development (Tillman et al. 2016), the effects of flow
management (Shafroth et al. 2010), groundwater pump-
ing (Falke et al. 2011) on dryland stream habitats and
riparian ecosystems, and the impacts of climate change
on stream summer base flows (Huntington & Niswonger
2012).
Ecosystem Services
In the context of ecosystem services, circuit theory has
been used to examine the landscape genetic structure
and movements of pollinators, especially bees, in re-
sponse to habitat and land-use changes (e.g., Goulson
et al. 2011; Lander et al. 2013; Lozier et al. 2013; Jaffe
et al. 2016a, 2016b). In southeastern Australia, Luck
et al. (2014) used Circuitscape to investigate the poten-
tial movements of Regent Parrots (Polytelis anthopeplus)
through almond orchards, which may benefit from par-
rots foraging on nuts remaining after harvest, reducing
the need for manual or mechanical removal. Koh et al.
(2013) used circuit theory to estimate the potential flow
of agricultural insect predators across habitat networks in
the U.S. Midwest. They quantified the pest-control benefit
of grassland restoration and native prairie remnants and
concluded that the flow of multiple predators on soybean
aphids (Aphis glycines) was improved by the presence of
adjacent, native “conservation plantings” that maximize
such biocontrol services.
Impacts of Circuit Theory and Future Opportunities
Circuit theory’s widespread application across multiple
disciplines (beyond genetics and wildlife ecology) is a tes-
tament to its power and flexibility as a tool for exploring
movement and flow across a range of scales and settings.
For example, novel applications of the theory to under-
standing the spread of fire, water, diseases, and invasive
species, as well as the future impacts of climate change
on natural and human systems, are transforming the way
scientists, planners, managers, and decision makers think
about or incorporate connectivity processes into their
work. From these diverse applications, we anticipate that
new areas of inquiry and tools will emerge that can also
benefit the field of conservation.
We see a variety of opportunities for circuit theory’s
continued development and use in conservation. First, a
new wave of applications is emerging from advances in
how we conceptualize connectivity, such as by recog-
nizing that a range of habitat conditions can serve as a
source for individuals (and genes) moving between pop-
ulations. “Omnidirectional” or “wall-to-wall” approaches
(e.g., Walpole et al. 2012; Koen et al. 2014; Pelletier et al.
2014; Anderson et al. 2016; McRae et al. 2016; Support-
ing Information) avoid the need to arbitrarily define and
delineate discrete areas to connect (e.g., habitat cores or
patches), revealing important areas for connectivity over
continuous landscape gradients. Because circuit theory
extends easily to nontraditional landscapes, efforts to
quantify connectivity in other dynamic systems, such as
seascapes, riverscapes, and belowground environments
(e.g., caves or karst), are expanding. Circuit theory can
also be used to identify key places for mitigating or
restoring connectivity (e.g., McRae et al. 2012; Torrubia
et al. 2014) in areas where new investments in transporta-
tion infrastructure might prioritize crossing structures for
wildlife. Second, tighter coupling between near real-time
data on landscape dynamics (e.g., derived using remotely
sensed images within Google’s Earth Engine environ-
ment) and estimates of landscape resistance and current
flow, as well as increasingly available information (e.g.,
Global Positioning System or other telemetry data) spe-
cific to the movement behaviors or seasonal life-history
traits of a target organism, will greatly improve insights
into or tests of potential connectivity. Third, we expect
that outputs from Circuitscape will be used more fre-
quently as hypotheses to strategically inform the design
and monitoring of habitat-use studies and to strengthen
statistical inferences drawn from field data.
Conservation Biology
Volume 0, No. 0, 2018
8Circuit Theory
Although circuit theory provides a robust and intuitive
framework for analyses of gene flow, animal movement,
and corridor use, IBR may not perform as well as some
other frameworks (e.g., isolation by distance) in less frag-
mented landscapes (Ruiz-Gonzalez et al. 2015) or when
connectivity is being assessed for migration pathways as
opposed to dispersal pathways (e.g., Poor et al. 2012;
McClure et al. 2016). As with any modeling framework,
the assumptions and utility of a circuit-theoretic approach
should always be assessed on a project-by-project ba-
sis. Several assumptions and caveats still need to be ad-
dressed, such as modeling long-distance dispersal events
(McRae 2006) and asymmetric migration (McRae et al.
2008; but see Hanks 2017). Future applications of circuit
theory could account for temporal variation in disper-
sal rates (Anderson et al. 2010; Cushman & Lewis 2010)
and predicting patterns of variation at adaptive loci (e.g.,
Creech et al. 2017).
Since the initial applications of circuit theory in conser-
vation, Circuitscape and other related applications have
undergone rapid and near constant refinement and im-
provement. Increasingly, circuit theory-based analyses
are being conducted on larger and more complex data
sets through recent advances in open-source software
(e.g., gflow [Leonard et al. 2017b]), programing (e.g.,
the Julia numerical computing language [Bezanson et al.
2017]), and cluster- or cloud-based computing resources.
The Julia implementation of Circuitscape (version 5.0)
has greatly improved performance and scalability. Users
are now able to solve for landscape grids that are larger or
derived at finer resolutions than those used in earlier ver-
sions, as well as pairwise resistance calculations between
a higher number of focal points (see also, Supporting
Information).
Similarly, advances in data visualization tools have as-
sisted the communication of circuit theory results to a
broader set of conservation practitioners, stakeholders,
and planning efforts. A leading example is Migrations
in Motion (http://maps.tnc.org/migrations-in-motion),
which uses a dynamic illustration of projected species
migrations under climate change (Lawler et al. 2013) and
has been a powerful and accessible way for The Nature
Conservancy (TNC) to communicate the potential risks
of climate change to a variety of audiences, including
the general public. These advances are often occurring
as scientists around the world apply circuit theory to
inform applications and decision makers. In his work
at TNC, McRae played a major role in the development
of generalized connectivity maps produced with wall-to-
wall (Anderson et al. 2016) and Omniscape (McRae et al.
2016; Supporting Information) versions of Circuitscape
models. These regional-scale flow maps remain a key
component in TNC’s Conserving Nature’s Stage approach
for identifying land protection priorities, which to date
has helped guide decisions on US$38 million in land pro-
tection funding. In India, national policy associated with
the Wildlife Protection Act, which delineates key habitat
areas as tiger reserves, has been informed by Circuitscape-
derived models and maps (Qureshi et al. 2014; Dutta et al.
2016).
We believe the impact of circuit theory and Cir-
cuitscape on conservation has come from not only the
theoretical basis and elegance of the approach, but also
from the powerful collaborations and active user commu-
nity that have emerged. Because circuit theory took root
so quickly and broadly, it can be expected to continue
to provide a springboard for ecological understanding
and remain an important tool for future researchers and
conservation practitioners around the globe.
Acknowledgments
We thank the many supporters of Brad McRae and
his vision for the development of circuit theory and
Circuitscape software for conservation, including
the Wilburforce Foundation, Cougar Fund, National
Aeronautics and Space Administration (NASA), National
Center for Ecological Analysis and Synthesis, The Nature
Conservancy (TNC), University of Washington, and U.S.
Environmental Protection Agency. We also thank T.
Mohapatra and others at Julia Computing for their con-
tributions to the ongoing development of Circuitscape
and related software, funded through a NASA Applied
Sciences-Ecological Forecasting grant (16-ECO4CAST-
0018) to TNC, with matching funds from the Wilburforce
Foundation. We are grateful to the Circuitscape user com-
munity for their creativity and dedication to innovation in
conservation. The comments of M. Burgman, C. Epps, C.
Murcia, T. Nogeire McRae, and 3 anonymous reviewers
greatly improved our manuscript. Any use of trade, firm,
or product names is for descriptive purposes only and
does not imply endorsement by the U.S. Government.
Supporting Information
Additional topic areas and examples of the use of cir-
cuit theory or Circuitscape software and numerical com-
puting methods (Appendix S1) and a sample gallery of
map-based outputs (Appendices S2 and S3) are available
online. The authors are solely responsible for the con-
tent and functionality of these materials. Queries (other
than absence of the material) should be directed to the
corresponding author.
Literature Cited
Ahmadi M, Nezami Balouchi B, Jowkar H, Hemami MR, Fadakar D,
Malakouti-Khah S, Ostrowski S. 2017. Combining landscape suitabil-
ity and habitat connectivity to conserve the last surviving population
of cheetah in Asia. Diversity & Distributions 23:592–603.
Conservation Biology
Volume 0, No. 0, 2018
Dickson et al. 9
Anderson CD, Epperson BK, Fortin MJ, Holderegger R, James P, Rosen-
berg MS, Scribner KT, Spear SF. 2010. Considering spatial and tem-
poral scale in landscape-genetic studies of gene flow. Molecular
Ecology 19:3565–3575.
Anderson MG, Barnett A, Clark M, Prince J, Olivero Sheldon A, Vickery
B. 2016. Resilient and connected landscapes for terrestrial conser-
vation. The Nature Conservancy, Boston.
Beier P, Spencer W, Baldwin RF, McRae B. 2011. Toward best practices
for developing regional connectivity maps. Conservation Biology
25:879–892.
Bell RC, Parra JL, Tonione M, Hoskin CJ, Mackenzie JB, Williams SE,
Moritz C. 2010. Patterns of persistence and isolation indicate re-
silience to climate change in montane rainforest lizards. Molecular
Ecology 19:2531–2544.
Bennie J, Davies TW, Inger R, Gaston KJ. 2014. Mapping artificial
lightscapes for ecological studies. Methods in Ecology and Evolution
5:534–540.
Bezanson J, Edelman A, Karpinski S, Shah VB. 2017. Julia: a fresh ap-
proach to numerical computing. SIAM Review 59:65–98.
Bishop-Taylor R, Tulbure MG, Broich M. 2015. Surface water network
structure, landscape resistance to movement and flooding vital for
maintaining ecological connectivity across Australia’s largest river
basin. Landscape Ecology 30:2045–2065.
Bleyhl B, Baumann M, Griffiths P, Heidelberg A, Manvelyan K, Radeloff
VC, Zazanashvili N, Kuemmerle T. 2017. Assessing landscape con-
nectivity for large mammals in the Caucasus using Landsat 8 seasonal
image composites. Remote Sensing of Environment 193:193–203.
Braaker S, Moretti M, Boesch R, Ghazoul J, Obrist MK, Bontadina F.
2014. Assessing habitat connectivity for ground-dwelling animals in
an urban environment. Ecological Applications 24:1583–1595.
Breckheimer I, Haddad NM, Morris WF, Trainor AM, Fields WR, Jobe RT,
Hudgens BR, Moody A, Walters JR. 2014. Defining and evaluating the
umbrella species concept for conserving and restoring landscape
connectivity. Conservation Biology 28:1584–1593.
Brodie JF, Giordano AJ, Dickson B, Hebblewhite M, Bernard H, Mohd-
Azlan J, Anderson J, Ambu L. 2015. Evaluating multispecies land-
scape connectivity in a threatened tropical mammal community.
Conservation Biology 29:122–132.
Castilho CS, Hackbart VCS, Pivello VR, dos Santos RF. 2015. Evaluat-
ing landscape connectivity for Puma concolor and Panthera onca
among Atlantic Forest Protected Areas. Environmental Management
55:1377–1389.
Chandra A, Raghavan P, Ruzzo W, Smolensky R, Tiwari P. 1996. The
electrical resistance of a graph captures its commute and cover
times. Computational Complexity 6:312–340.
Creech TG, Epps CW, Landguth EL, Wehausen JD, Crowhurst RS,
Holton B, Monello RJ. 2017. Simulating the spread of selection-
driven genotypes using landscape resistance models for desert
bighorn sheep. PLOS ONE 12 (e0176960) http://doi.org/10.
1371/journal.pone.0176960.
Cushman SA, Lewis JS. 2010. Movement behavior explains genetic dif-
ferentiation in American black bears. Landscape Ecology 25:1613–
1625.
Dambach J, Raupach MJ, Leese F, Schwarzer J, Engler JO. 2016. Ocean
currents determine functional connectivity in an Antarctic deep-sea
shrimp. Marine Ecology 37:1336–1344.
Dickson BG, Albano CM, McRae BH, Anderson JJ, Theobald DM, Zach-
mann LJ, Sisk TD, Dombeck MP. 2017. Informing strategic efforts
to expand and connect protected areas using a model of ecological
flow, with application to the western United States. Conservation
Letters 10:564–571.
Dickson BG, Roemer GW, McRae BH, Rundall JM. 2013. Models of
regional habitat quality and connectivity for pumas (Puma con-
color) in the southwestern United States. PLOS ONE 8(e81898)
http://doi.org/10.1371/journal.pone.0081898.
Dilkina B, Houtman R, Gomes CP, Montgomery CA, McKelvey KS,
Kendall K, Graves TA, Bernstein R, Schwartz MK. 2017. Trade-offs
and efficiencies in optimal budget-constrained multispecies corridor
networks. Conservation Biology 31:192–202.
Dong X, Li B, He F, Gu Y, Sun M, Zhang H, Tan L, Xiao W, Liu S, Cai
Q. 2016. Flow directionality, mountain barriers and functional traits
determine diatom metacommunity structuring of high mountain
streams. Scientific Reports 6:24711.
Doyle PG, Snell JL. 1984. Random walks and electrical networks. Math-
ematical Association of America, Washington, D.C.
Dudaniec RY, Worthington Wilmer J, Hanson JO, Warren M, Bell S,
Rhodes JR. 2016. Dealing with uncertainty in landscape genetic re-
sistance models: a case of three co-occurring marsupials. Molecular
Ecology 25:470–486.
Dutta T, Sharma S, McRae BH, Roy PS, DeFries R. 2016. Connecting
the dots: mapping habitat connectivity for tigers in central India.
Regional Environmental Change 16:53–67.
Epps CW, Mutayoba BM, Gwin L, Brashares JS. 2011. An empirical
evaluation of the African elephant as a focal species for connectivity
planning in East Africa. Diversity & Distributions 17:603–612.
Fagan ME, DeFries RS, Sesnie SE, Arroyo-Mora JP, Chazdon RL. 2016.
Targeted reforestation could reverse declines in connectivity for un-
derstory birds in a tropical habitat corridor. Ecological Applications
26:1456–1474.
Falke J, Fausch K, Magelky R, Aldred A, Durnford D, Riley L, Oad R.
2011. The role of groundwater pumping and drought in shaping
ecological futures for stream fishes in a dryland river basin of the
western Great Plains, USA. Ecohydrology 4:682–697.
Fetter C. 2001. Applied hydrogeology. 4th Edition. Prentice Hall, Upper
Saddle River, New Jersey.
Gantchoff MG, Belant JL. 2017. Regional connectivity for recolonizing
American black bears (Ursus americanus) in southcentral USA.
Biological Conservation 214:66–75.
Goulson D, Kaden JC, Lepais O, Lye GC, Darvill B. 2011. Population
structure, dispersal and colonization history of the garden bumble-
bee Bombus hortorum in the Western Isles of Scotland. Conserva-
tion Genetics 12:867–879.
Grafius DR, Corstanje R, Siriwardena GM, Plummer KE, Harris JA.
2017. A bird’s eye view: using circuit theory to study ur-
ban landscape connectivity for birds. Landscape Ecology 32:
1771–1787.
Graves TA, Beier P, Royle JA. 2013. Current approaches using genetic
distances produce poor estimates of landscape resistance to in-
terindividual dispersal. Molecular Ecology 22:3888–3903.
Gray ME, Dickson BG. 2015. A new model of landscape-scale fire con-
nectivity applied to resource and fire management in the Sonoran
Desert, USA. Ecological Applications 25:1099–1113.
Gray ME, Dickson BG. 2016. Applying fire connectivity and centrality
measures to mitigate the cheatgrass-fire cycle in the arid West, USA.
Landscape Ecology 31:1681–1696.
Guillot G, Leblois R, Coulon A, Frantz AC. 2009. Statistical methods in
spatial genetics. Molecular Ecology 18:4734–4756.
Hanks EM. 2017. Modeling spatial covariance using the limiting distri-
bution of spatio-temporal random walks. Journal of the American
Statistical Association 112:497–507.
Hanks EM, Hooten MB. 2013. Circuit theory and model-based infer-
ence for landscape connectivity. Journal of the American Statistical
Association 108:22–33.
Harris LD. 1984. The fragmented forest: island biogeography theory
and the preservation of biotic diversity. University of Chicago Press,
Chicago, Illinois.
Howey M. 2011. Multiple pathways across past landscapes: circuit
theory as a complementary geospatial method to least cost path
for modeling past movement. Journal of Archaeological Science
38:2523–2535.
Huntington JL, Niswonger RG. 2012. Role of surface-water and ground-
water interactions on projected summertime streamflow in snow
dominated regions: an integrated modeling approach. Water Re-
sources Research 48 (11).
Conservation Biology
Volume 0, No. 0, 2018
10 Circuit Theory
International Union for Conservation of Nature (IUCN). 2017. Con-
nectivity conservation. IUCN, Gland, Switzerland. Available from
https://www.iucn.org/theme/protected-areas/wcpa/what-we-do/
connectivity-conservation (accessed July 2018).
Jaff´
e R, Castilla A, Pope N, Imperatriz-Fonseca VL, Metzger JP, Arias MC,
Jha S. 2016a. Landscape genetics of a tropical rescue pollinator.
Conservation Genetics 17:267–278.
Jaff´
e R, et al. 2016b. Beekeeping practices and geographic distance, not
land use, drive gene flow across tropical bees. Molecular Ecology
25:5345–5358.
Jaqui´
ery J, Broquet T, Hirzel AH, Yearsley J, Perrin N. 2011. Inferring
landscape effects on dispersal from genetic distances: How far can
we go? Molecular Ecology 20:692–705.
Jarchow CJ, Hossack BR, Sigafus BH, Schwalbe CR, Muths E. 2016. Mod-
eling habitat connectivity to inform reintroductions: a case study
with the Chiricahua leopard frog. Journal of Herpetology 50:63–69.
Keeley AT, Beier P, Keeley BW, Fagan ME. 2017. Habitat suitability is a
poor proxy for landscape connectivity during dispersal and mating
movements. Landscape & Urban Planning 161:90–102.
Knaapen JP, Scheffer M, Harms B. 1992. Estimating habitat isolation in
landscape planning. Landscape & Urban Planning 23:1–16.
Koen EL, Bowman J, Sadowski C, Walpole AA. 2014. Landscape con-
nectivity for wildlife: development and validation of multispecies
linkage maps. Methods in Ecology & Evolution 5:626–633.
Koen EL, Bowman J, Walpole AA. 2012. The effect of cost surface pa-
rameterization on landscape resistance estimates. Molecular Ecology
Resources 12:686–696.
Koh I, Rowe HI, Holland JD. 2013. Graph and circuit theory connec-
tivity models of conservation biological control agents. Ecological
Applications 23:1554–1573.
Krosby M, Michalak J, Robbins TO, Morgan H, Norheim R, Mauger G,
Murdock T. 2016. The Washington-British Columbia Transboundary
Climate-Connectivity Project: identifying climate impacts and adap-
tation actions for wildlife habitat connectivity in the transboundary
region of Washington and British Columbia. Climate Impacts Group,
University of Washington, Seattle, Washington.
Lander TA, Klein EK, Stoeckel S, Mariette S, Musch B, Oddou-Muratorio
S. 2013. Interpreting realized pollen flow in terms of pollinator
travel paths and land-use resistance in heterogeneous landscapes.
Landscape Ecology 28:1769–1783.
Lawler JJ, Beier P, Dickson BG, Fargione J, Novembre J, Theobald DM.
2018. A tribute to a true conservation innovator, Brad McRae, 1966–
2017. Conservation Biology https://doi.org/10.1111/cobi.13235.
Lawler JJ, Ruesch AS, Olden JD, McRae BH. 2013. Projected climate-
driven faunal movement routes. Ecology Letters 16:1014–1022.
Lechner AM, Sprod D, Carter O, Lefroy EC. 2017. Characterising land-
scape connectivity for conservation planning using a dispersal guild
approach. Landscape Ecology 32:99–113.
Legendre P, Fortin MJ. 2010. Comparison of the Mantel test and alter-
native approaches for detecting complex multivariate relationships
in the spatial analysis of genetic data. Molecular Ecology Resources
10:831–844.
Leonard PB, Duffy EB, Baldwin RF, McRae BH, Shah VB, Mohapatra TK.
2017a. gflow: software for modelling circuit theory-based connec-
tivity at any scale. Methods in Ecology & Evolution 8:519–526.
Leonard PB, Sutherland RW, Baldwin RF, Fedak DA, Carnes RG, Mont-
gomery AP. 2017b. Landscape connectivity losses due to sea level
rise and land use change. Animal Conservation 20:80–90.
Littlefield CE, McRae BH, Michalak JL, Lawler JJ, Carroll C. 2017.
Connecting today’s climates to future climate analogs to facilitate
movement of species under climate change. Conservation Biology
31:1397–1408.
Litvaitis JA, Reed GC, Carroll RP, Litvaitis MK, Tash J, Mahard T, Broman
DJA, Callahan C, Ellingwood M. 2015. Bobcats (Lynx rufus)asa
model organism to investigate the effects of roads on wide-ranging
carnivores. Environmental Management 55:1366–1376.
Lozier JD, Strange JP, Koch JB. 2013. Landscape heterogeneity predicts
gene flow in a widespread polymorphic bumble bee, Bombus bifar-
ius (Hymenoptera: Apidae). Conservation Genetics 14:1099–1110.
Luck GW, Spooner PG, Watson DM, Watson SJ, Saunders ME. 2014.
Interactions between almond plantations and native ecosystems:
lessons learned from north-western Victoria. Ecological Manage-
ment & Restoration 15:4–15.
MacArthur RH, Wilson EO. 1967. The theory of island biogeography.
Acta Biotheoretica 50:133–136.
Maiorano L, Boitani L, Chiaverini L, Ciucci P. 2017. Uncertainties in
the identification of potential dispersal corridors: the importance of
behaviour, sex, and algorithm. Basic & Applied Ecology 21:66–75.
Manel S, Holderegger R. 2013. Ten years of landscape genetics. Trends
in Ecology & Evolution 28:614–621.
Marrotte RR, Bowman J. 2017. The relationship between least-
cost and resistance distance. PLOS ONE 12 (e01742120)
http://doi.org/10.1371/journal.pone.0174212.
Marrotte RR, Bowman J, Brown MGC, Cordes C, Morris KY, Prentice
MB, Wilson PJ. 2017. Multi-species genetic connectivity in a terres-
trial habitat network. Movement Ecology 5:21.
Mateo-S´
anchez MC, Balkenhol N, Cushman S, P´
erez T, Dom´
ınguez A,
Saura S. 2015. Estimating effective landscape distances and move-
ment corridors: comparison of habitat and genetic data. Ecosphere
6:1–16.
Mateo-S´
anchez MC, Cushman SA, Saura S. 2014. Connecting endangered
brown bear subpopulations in the Cantabrian Range (north-western
Spain). Animal Conservation 17:430–440.
McClure ML, Dickson BG, Nicholson KL. 2017. Modeling connectivity
to identify current and future anthropogenic barriers to movement
of large carnivores: a case study in the American Southwest. Ecology
& Evolution 7:3762–3772.
McClure ML, Hansen AJ, Inman RM. 2016. Connecting models to move-
ments: testing connectivity model predictions against empirical mi-
gration and dispersal data. Landscape Ecology 31:1–14.
McRae BH. 2006. Isolation by resistance. Evolution 60:1551–1561.
McRae BH, Beier P. 2007. Circuit theory predicts gene flow in plant
and animal populations. Proceedings of the National Academy of
Sciences of the United States of America 104:19885–19890.
McRae BH, Dickson BG, Keitt TH, Shah VB. 2008. Using circuit theory to
model connectivity in ecology, evolution, and conservation. Ecology
89:2712–2724.
McRae BH, Hall SA, Beier P, Theobald DM. 2012. Where to re-
store ecological connectivity? Detecting barriers and quantifying
restoration benefits. PLOS ONE 7(e52604) https://doi.org/10.1371/
journal.pone.0052604.
McRae BH, Popper K, Jones A, Schindel M, Buttrick S, Hall KR, Unnasch
RS, Platt J. 2016. Conserving nature’s stage: mapping omnidirec-
tional connectivity for resilient terrestrial landscapes in the Pacific
Northwest. The Nature Conservancy, Portland, Oregon. Available
from http://nature.org/resilienceNW (accessed December 2017).
McRae BH, Shah V, Mohapatra T. 2013. Circuitscape 4 user guide.
The Nature Conservancy, Fort Collins, Colorado. Available from
http://www.circuitscape.org (accessed December 2017).
McRae BH, Shah VB. 2009. Circuitscape user’s guide. The University of
California, Santa Barbara, California.
Miley GH, Kuelske KJ. 1990. Groundwater flow analysis of potential
low level radioactive waste disposal sites using electrical circuit
analogies. Pages 229–240 in Heller M, editor. Nuclear simulation.
Springer, Berlin.
Naidoo R, Kilian JW, Du Preez P, Beytell P, Aschenborn O, Taylor
RD, Stuart-Hill G. 2018. Evaluating the effectiveness of local-and
regional-scale wildlife corridors using quantitative metrics of func-
tional connectivity. Biological Conservation 217:96–103.
Ortego J, Gugger PF, Sork VL. 2015. Climatically stable landscapes pre-
dict patterns of genetic structure and admixture in the Californian
canyon live oak. Journal of Biogeography 42:328–338.
Conservation Biology
Volume 0, No. 0, 2018
Dickson et al. 11
Parks LC, Wallin DO, Cushman SA, McRae BH. 2015. Landscape-level
analysis of mountain goat population connectivity in Washington
and southern British Columbia. Conservation Genetics 16:1195–
1207.
Pelletier D, Clark M, Anderson MG, Rayfield B, Wulder MA, Cardille
JA. 2014. Applying circuit theory for corridor expansion and
management at regional scales: tiling, pinch points, and omnidi-
rectional connectivity. PLOS ONE 9(e84135) http://doi.org/10.
1371/journal.pone.0084135.
Petkova D, Novembre J, Stephens M. 2016. Visualizing spatial popula-
tion structure with estimated effective migration surfaces. Nature
Genetics 48:94.
Poor EE, Loucks C, Jakes A, Urban DL. 2012. Comparing habi-
tat suitability and connectivity modeling methods for conserving
pronghorn migrations. PLOS ONE 7(e49390) http://doi.org/10.
1371/journal.pone.0049390.
Proctor MF, Nielsen SE, Kasworm WF, Servheen C, Radandt TG,
Machutchon AG, Boyce MS. 2015. Grizzly bear connectivity map-
ping in the Canada–United States trans-border region. Journal of
Wildlife Management 79:544–558.
Qureshi Q, Saini S, Basu P, Gopal R, Raza E, Jhalam Y. 2014.
Connecting tiger populations for long-term conservation. Na-
tional Tiger Conservation Authority & Wildlife Institute of In-
dia, Dehradun. TR2014-02. Available from http://www.wii.gov.in/
images//images/documents/connecting_tiger.pdf (accessed De-
cember 2017).
Rizzo V, S´
anchez-Fern´
andez D, Alonso R, Pastor J, Ribera I. 2017. Sub-
stratum karstificability, dispersal and genetic structure in a strictly
subterranean beetle. Journal of Biogeography 45:2527–2538.
Robinove CJ. 1962. Ground-water studies and analog models. Geologi-
cal Survey Circular 468. U.S. Department of the Interior, Geological
Survey, Washington, D.C.
R¨
odder D, Nekum S, Cord AF, Engler JO. 2016. Coupling satellite data
with species distribution and connectivity models as a tool for en-
vironmental management and planning in matrix-sensitive species.
Environmental Management 58:130–143.
Ruiz-Gonzalez A, Cushman SA, Madeira MJ, Randi E, G´
omez-Moliner
BJ. 2015. Isolation by distance, resistance and/or clusters? Lessons
learned from a forest-dwelling carnivore inhabiting a heterogeneous
landscape. Molecular Ecology 24:5110–5129.
Shafroth PB, Wilcox AC, Lytle DA, Hickey JT, Andersen DC, Beauchamp
VB, Hautzinger A, McMullen LE, Warner A. 2010. Ecosystem effects
of environmental flows: modelling and experimental floods in a
dryland river. Freshwater Biology 55:68–85.
Shirk AJ, Wallin DO, Cushman SA, Rice CG, Warheit KI. 2010. Inferring
landscape effects on gene flow: a new model selection framework.
Molecular Ecology 19:3603–3619.
Simpkins CE, Dennis TE, Etherington TR, Perry LW. 2018. Assessing
the performance of common landscape connectivity metrics using
a virtual ecologist approach. Ecological Modelling 367:13–23.
Singh A. 2014. Groundwater resources management through the ap-
plications of simulation modeling: a review. Science of the Total
Environment 499:414–423.
Tarkhnishvili D, Gavashelishvili A, Murtskhvaladze M, Latsuzbaia A.
2016. Landscape complexity in the Caucasus impedes genetic as-
similation of human populations more effectively than language or
ethnicity. Human Biology 88:287–300.
Tassi F, Ghirotto S, Mezzavilla M, Vilaca ST, De Santi L, Barbujani G.
2015. Early modern human dispersal from Africa: genomic evidence
for multiple waves of migration. Investigative Genetics 6:13.
Thayn JB, Sampeck K, Spaccapaniccia M. 2016. Refining Hernando de
Soto’s route using electric circuit theory and Circuitscape. Profes-
sional Geographer 68:595–602.
Theobald DM, Reed SE, Fields K, Soule M. 2012. Connecting natu-
ral landscapes using a landscape permeability model to prioritize
conservation activities in the United States. Conservation Letters
5:123–133.
Tillman FD, Wiele SM, Pool DR. 2016. A comparison of estimates of
basin-scale soil-moisture evapotranspiration and estimates of ripar-
ian groundwater evapotranspiration with implications for water
budgets in the Verde Valley, Central Arizona, USA. Journal of Arid
Environments 124:278–291.
Torrubia S, McRae BH, Lawler JJ, Hall SA, Halabisky M, Lang-
don J, Case M. 2014. Getting the most connectivity per
conservation dollar. Frontiers in Ecology & Environment 12:
491–497.
Trombulak SC, Frissell CA. 2000. Review of ecological effects of
roads on terrestrial and aquatic communities. Conservation Biology
14:18–30.
United Nations Environment Programme (UNEP). 2015. UNEP
launches global connectivity conservation project. UNEP,
Nairobi. Available from http://www.unep-wcmc.org/news/unep-
launches-global-connectivity-conservation-project (accessed De-
cember 2017).
Velo-Anton G, Parra JL, Parra-Olea G, Zamudio KR. 2013. Tracking
climate change in a dispersal-limited species: reduced spatial and
genetic connectivity in a montane salamander. Molecular Ecology
22:3261–3278.
Walpole AA, Bowman J, Murray DL, Wilson PJ. 2012. Functional connec-
tivity of Canada lynx at their southern range boundary. Landscape
Ecology 27:761–773.
Wang F, McShea WJ, Wang D, Li S, Zhao Q, Wang H, Lu Z.
2014. Evaluating landscape options for corridor restoration be-
tween giant panda reserves. PLOS ONE 9(e105086) http://doi.org/
10.1371/journal.pone.0105086.
Washington Wildlife Habitat Connectivity Working Group
(WWHCWG). 2010. Washington Connected Landscapes Project:
statewide analysis. Washington Departments of Fish & Wildlife and
Transportation, Olympia. Available from www.waconnected.org
(accessed March 2018).
Welch N, Provencher L, Unnasch RS, Anderson T, McRae BH. 2015.
Designing regional fuel breaks to protect large remnant tracts of
Greater Sage-Grouse habitat in parts of Idaho, Nevada, Oregon, and
Utah. Final report to the Western Association of Fish & Wildlife
Agencies. Contract SG-C-13-02. The Nature Conservancy, Reno,
Nevada.
With KA, Gardner RH, Turner MG. 1997. Landscape connectivity
and population distributions in heterogeneous landscapes. Oikos
78:151–169.
Zeller KA, McGarigal K, Whiteley AR. 2012. Estimating land-
scape resistance to movement: a review. Landscape Ecology 27:
777–797.
Zeppenfeld T, Balkenhol N, K´
ovacs K, Carminati A. 2017. Rhizo-
sphere hydrophobicity: a positive trait in the competition for wa-
ter. PLOS ONE 12 (e0182188) http://doi.org/10.1371/journal.pone.
0182188.
Zi´
ołkowska E, Perzanowski K, Bleyhl B, Ostapowicz K, Kuemmerle
T. 2016. Understanding unexpected reintroduction outcomes: Why
aren’t European bison colonizing suitable habitat in the Carpathians?
Biological Conservation 195:106–117.
Conservation Biology
Volume 0, No. 0, 2018
  • Article
    Full-text available
    Predicting connectivity, or how landscapes alter movement, is essential for understanding the scope for species persistence with environmental change. Although it is well known that movement is risky, connectivity modelling often conflates behavioural responses to the matrix through which animals disperse with mortality risk. We derive new connectivity models using random walk theory, based on the concept of spatial absorbing Markov chains. These models decompose the role of matrix on movement behaviour and mortality risk, can incorporate species distribution to predict the amount of flow, and provide both short‐ and long‐term analytical solutions for multiple connectivity metrics. We validate the framework using data on movement of an insect herbivore in 15 experimental landscapes. Our results demonstrate that disentangling the roles of movement behaviour and mortality risk is fundamental to accurately interpreting landscape connectivity, and that spatial absorbing Markov chains provide a generalisable and powerful framework with which to do so.
  • Article
    Full-text available
    The ability to predict spatial variation in biodiversity is a long-standing but elusive objective of landscape ecology. It depends on a detailed understanding of relationships between landscape and patch structure and taxonomic richness, and accurate spatial modelling. Complex heterogeneous environments such as cities pose particular challenges, as well as heightened relevance, given the increasing rate of urbanisation globally. Here we use a GIS-linked Bayesian Belief Network approach to test whether landscape and patch structural characteristics (including vegetation height, green-space patch size and their connectivity) drive measured taxo-nomic richness of numerous invertebrate, plant, and avian groups. We find that modelled richness is typically higher in larger and better-connected green-spaces with taller vegetation, indicative of more complex vegetation structure and consistent with the principle of 'bigger, better, and more joined up'. Assessing the relative importance of these variables indicates that vegetation height is the most influential in determining richness for a majority of taxa. There is variation, however, between taxonomic groups in the relationships between richness and landscape structural characteristics, and the sensitivity of these relationships to particular predictors. Consequently, despite some broad commonalities, there will be trade-offs between different taxonomic groups when designing urban landscapes to maximise biodiversity. This research demonstrates the feasibility of using a GIS-coupled Bayesian Belief Network approach to model biodiversity at fine spatial scales in complex landscapes where current data and appropriate modelling approaches are lacking, and our findings have important implications for ecologists, conservationists and planners.
  • Article
    Powerful innovations can occur when a concept is taken from one field and used to solve a problem in an unrelated field. In fact, it has been shown that as the distance between a problem solver's field of technical expertise and the focal field of a problem increase, so does the probability of success. This article is protected by copyright. All rights reserved
  • Article
    The global population is increasing rapidly and expected to touch the 9.5 billion mark by 2050 from the current 7.2 billion. The management of the groundwater resources is a challenging task worldwide against the backdrop of the growing water demand for industrial, agricultural, and domestic uses and shrinking resources. Moreover, this task has been hampered significantly due to declining/rising groundwater levels and associated contamination. A broad range of solutions could be considered to address the aforementioned problems of groundwater management, but the effectiveness of all the solutions and their combinations cannot be verified with field experiments. Given their predictive capability, simulation models are often the only viable means of providing input to management decisions, as they can forecast the likely impacts of a particular water management strategy. This paper presents a comprehensive review on the simulation modeling applications for the management of groundwater resources. The past papers on the overview of groundwater simulation models, use of remote sensing and GIS in groundwater modeling, and application of simulation models in arid and semiarid regions are described in detail. Conclusions are drawn where gaps exist and more research needs to be focused.
  • Article
    While corridors in conservation have a long history of use, evaluations of proposed or existing corridors in conservation landscapes are important to avoid the same fate as poorly-functioning “paper parks”. We used resistance surface modeling and circuit theory to evaluate a number of corridors developed at regional and at local scales that aim to improve connectivity for large wildlife in the central part of the Kavango-Zambezi transfrontier conservation area. We used hourly GPS data from 16 collared African elephants (Loxodonta africana), and associated environmental data at used versus available movement paths, to develop a hierarchical Bayesian path selection function model. We used the resulting resistance surface across the study area as an input into circuit theory modeling to assess how well connectivity levels were captured by both types of corridors relative to several alternative scenarios. We found that the majority of regional-scale corridors performed relatively well at capturing elevated levels of connectivity relative to non-corridor comparisons, with 7 of 9 corridors rated as good or better in terms of how they captured electrical current levels (a proxy for connectivity). In contrast, only 14 of 33 smaller-scale, local corridors captured significantly higher levels of connectivity than adjacent non-corridor areas. Our results have practical implications for the design and implementation of wildlife connectivity conservation efforts in the world's largest transfrontier conservation landscape. Modern connectivity science approaches can help evaluate which proposed corridors are likely to function as intended, and which may need further refinement.
  • Article
    Full-text available
    Due to increasing habitat fragmentation and concern about its ecological effects, there has been an upsurge in the use of landscape connectivity estimates in conservation planning. Measuring connectivity is challenging, resulting in a limited understanding of the efficacy of connectivity estimation techniques and the conditions under which they perform best. We evaluated the performance of four commonly used connectivity metrics – Euclidean distance; least-cost paths (LCP) length and cost; and circuit theory’s resistance distance – over a variety of simulated landscapes. We developed an agent-based model simulating the dispersal of individuals with different behavioural traits across landscapes varying in their spatial structure. The outcomes of multiple dispersal attempts were used to obtain ‘true’ connectivity. These ‘true’ connectivity measures were then compared to estimates generated using the connectivity metrics, employing the simulated landscapes as cost-surfaces. The four metrics differed in the strength of their correlation with true connectivity; resistance distance showed the strongest correlation, closely followed by LCP cost, with Euclidean distance having the weakest. Landscape structure and species behavioural attributes only weakly predicted the performance of resistance distance, LCP cost and length estimates, with none predicting Euclidean distance’s efficacy. Our results indicate that resistance distance and LCP cost produce the most accurate connectivity estimates, although their absolute performance under different conditions is difficult to predict. We emphasise the importance of testing connectivity estimates against patterns derived from independent data, such as those acquired from tracking studies. Our findings should help to inform a more refined implementation of connectivity metrics in conservation management.
  • Article
    Full-text available
    Background Habitat fragmentation reduces genetic connectivity for multiple species, yet conservation efforts tend to rely heavily on single-species connectivity estimates to inform land-use planning. Such conservation activities may benefit from multi-species connectivity estimates, which provide a simple and practical means to mitigate the effects of habitat fragmentation for a larger number of species. To test the validity of a multi-species connectivity model, we used neutral microsatellite genetic datasets of Canada lynx (Lynx canadensis), American marten (Martes americana), fisher (Pekania pennanti), and southern flying squirrel (Glaucomys volans) to evaluate multi-species genetic connectivity across Ontario, Canada. Results We used linear models to compare node-based estimates of genetic connectivity for each species to point-based estimates of landscape connectivity (current density) derived from circuit theory. To our knowledge, we are the first to evaluate current density as a measure of genetic connectivity. Our results depended on landscape context: habitat amount was more important than current density in explaining multi-species genetic connectivity in the northern part of our study area, where habitat was abundant and fragmentation was low. In the south however, where fragmentation was prevalent, genetic connectivity was correlated with current density. Contrary to our expectations however, locations with a high probability of movement as reflected by high current density were negatively associated with gene flow. Subsequent analyses of circuit theory outputs showed that high current density was also associated with high effective resistance, underscoring that the presence of pinch points is not necessarily indicative of gene flow. Conclusions Overall, our study appears to provide support for the hypothesis that landscape pattern is important when habitat amount is low. We also conclude that while current density is proportional to the probability of movement per unit area, this does not imply increased gene flow, since high current density tends to be a result of neighbouring pixels with high cost of movement (e.g., low habitat amount). In other words, pinch points with high current density appear to constrict gene flow. Electronic supplementary material The online version of this article (10.1186/s40462-017-0112-2) contains supplementary material, which is available to authorized users.
  • Article
    Full-text available
    The deep subterranean environment is an ideal system to test the effect of physical constraints on the ecology and evolution of species, as it is very homogeneous and with simple communities. We studied the effect of substratum karstificability in the dispersal of the strictly subterranean Troglocharinus ferreri (Reitter) (Coleoptera, Leiodidae) by comparing the genetic diversity and structure of populations in limestone (more soluble) and dolostone (less soluble) in the same karstic system. Troglocharinus ferreri is only known from c. 100 vertical shafts in an area of <500 km2 SW of Barcelona (Spain). We sequenced mitochondrial and nuclear markers of a representative sample to identify main lineages within T. ferreri and estimate their temporal origin, and used mitochondrial data of 129 specimens from 41 caves to reconstruct their demographic history and estimate dispersal among caves. Troglocharinus ferreri diverged from its sister in the Early Pliocene, with an initial divergence of the sampled populations in the Early Pleistocene. The best demographic model was a constant population size with a fast population increase in the middle Pleistocene. The ancestral population was likely in limestone, with a probability of transition from limestone to dolostone triple to that from dolostone to limestone, suggesting a higher permeability of limestone to the transit of individuals. Populations in dolostone caves had lower gene flow between them and a stronger isolation by distance, although the low genetic variability for the studied markers and the lower abundance of dolostone caves decreased the statistical power of the analyses. Our results point to the physical characteristic of the substratum as a determinant of dispersal and gene flow, potentially conditioning the long-term evolution of subterranean biodiversity.
  • Article
    Full-text available
    The ability to acquire water from the soil is a major driver in interspecific plant competition and it depends on several root functional traits. One of these traits is the excretion of gel-like compounds (mucilage) that modify physical soil properties. Mucilage secreted by roots becomes hydrophobic upon drying, impedes the rewetting of the soil close to the root, the so called rhizosphere, and reduces water availability to plants. The function of rhizosphere hydrophobicity is not easily understandable when looking at a single plant, but it may constitute a competitive advantage at the ecosystem level. We hypothesize that by making the top soil hydrophobic, deep-rooted plants avoid competititon with shallow-rooted plants. To test this hypothesis we used an individual-based model to simulate water uptake and growth of two virtual plant species, one deep-rooted plant capable of making the soil hydrophobic and a shallow-rooted plant. We ran scenarios with different precipitation regimes ranging from dry to wet (350, 700, and 1400 mm total annual precipitation) and from high to low precipitation frequencies (1, 7, and 14 days). Plant species abundance and biomass were chosen as indicators for competitiveness of plant species. At constant precipitation frequency mucilage hydrophobicity lead to a benefit in biomass and abundance of the tap-rooted population. Under wet conditions this effect diminished and tap-rooted plants were less productive. Without this trait both species coexisted. The effect of root exudation trait remained constant under different precipitation frequencies. This study shows that mucilage secretion is a competitive trait for the acquisition of water. This advantage is achieved by the modification of the soil hydraulic properties and specifically by inducing water repellency in soil regions which are shared with other species.