Forest Service Rocky Mountain Research Station General Technical Report RMRS-GTR-333 June 2015

United States Department of Agriculture

Resistance-Surface-Based Wildlife 

Conservation Connectivity Modeling:

Summary of Efforts in the United States and Guide for Practitioners

Alisa A. Wade, Kevin S. McKelvey, Michael K. Schwartz
Wade, Alisa A.; McKelvey, Kevin S.; Schwartz, Michael K. 2015. Resistance-surface-based wildlife 

conservation connectivity modeling: Summary of efforts in the United States and guide for 

practitioners. Gen. Tech. Rep. RMRS-GTR-333. Fort Collins, CO: U.S. Department of Agriculture, 

Forest Service, Rocky Mountain Research Station. 93 p.

Abstract

 Resistance-surface-based connectivity modeling has become a widespread tool for conservation 

planning. The current ease with which connectivity models can be created, however, masks the numerous untested assumptions underlying both the rules that produce the resistance surface and the 

algorithms used to locate low-cost paths across the target landscape. Here we present a process to 

guide map creation, from conceptualization through validation, that seeks to better consider the complex 

biological issues inherent to connectivity modeling. Following this organized approach to connectivity 

modeling will help analysts prevent a plethora of issues common in recently created models, such as 

the failure to specify the temporal domain, purpose of the mapped connectivity, or the biological rationales for assigned pixel-level resistances. Following these steps will improve both the understanding 

and biological relevance of constructed connectivity maps.

Keywords: connectivity, resistance surface, least-cost path, cost distance modeling, validation, 

models, conservation.

Authors

Alisa A. Wade is a private consultant conservation scientist and an affiliate faculty with the University 

of Montana, Department of Geosciences, Missoula, Montana.

Kevin S. McKelvey and Michael K. Schwartz are research ecologists, U.S. Forest Service, Rocky 

Mountain Research Station, Wildlife and Terrestrial Ecosystems, Missoula, Montana.

Cover—Connectivity modeling of greater sage-grouse leks (black dots) in southwest 

Montana. Resistance of land cover to gene flow is hypothesized and connectivity models 

are generated by comparing landscape attributes to measures of genetic connectivity. The 

connectivity map is provided courtesy of Todd Cross (tbcross@fs.fed.us, 406-209-8633). The 

sage grouse photo is provided courtesy of John Carlson: Photo Copyright - John Carlson.
Table of Contents

Chapter 1: Introduction ........................................................................................... 1

Chapter 2: Ecological Framework and Key Definitions for 

Modeling Connectivity ......................................................................................... 5

Chapter 3: Resistance-Surface-Based Connectivity Modeling: 

Defining a Process and Reviewing the Literature ........................................... 15

Chapter 4: The Importance of Validating Wildlife Connectivity Models ........... 43

Chapter 5: Practitioner Efforts ............................................................................. 53

Chapter 6: Guiding Questions for Practitioners ................................................. 65

Chapter 7: Conclusions and Synthesis ............................................................... 69

Literature Cited ...................................................................................................... 71

Appendices ............................................................................................................ 82

USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 1

Chapter 1. Introduction 

“Corridors are a hot topic, perhaps even a fad, in conservation planning these 

days. ... Planners...are busy drawing...habitat corridors...sometimes with only a vague 

awareness of the biological issues underlying the corridor strategy” (Noss 1987). 

Despite originating in a seminal paper dating back a quarter century, Reed Noss’s 

comment remains relevant today. During that time, the initial controversy surrounding 

whether wildlife corridors are cost or ecologically effective (the “corridor controversy” 

reviewed in Anderson and Jenkins 2006) has given way to general acceptance of the 

importance of landscape connectivity (Hilty and others 2006). Yet, there remains a lack 

of consensus about exactly what landscape connectivity entails (Crooks and Sanjayan 

2006), how it should be modeled and quantified (Beier and others 2008; Kindlmann and 

Burel 2008; Huber and others 2010; Sawyer and others 2011; Zeller and others 2012), 

and whether sufficient biological understandings underlie current landscape linkage 

designs (Bélisle 2005; Chetkiewicz and others 2006; Beier and others 2009; Lowe 

and Allendorf 2010; Parks and others 2012). Here we primarily focus on connectivity 

defined as the degree to which a landscape facilitates wildlife movement (sensu Taylor 

and others 2006).

In the face of increasing habitat loss and fragmentation (Wilcove and others 1998), 

as well as the potential need for species range shifts under novel climates (Heller and 

Zavaleta 2009; Carroll and others 2010), the debate surrounding the definition, modeling, 

and implementing of connectivity has not stopped an explosion of research concerning 

connectivity for wildlife conservation (Crooks and Sanjayan 2006), nor has it slowed 

efforts amongst land use planners and managers to design connectivity projects. Implementing connectivity on-the-ground, however, has high political and economic costs, as 

well as large opportunity costs: finite resources invested in protecting a putative linkage 

will not be available for protecting other areas. Thus, it is imperative that linkages be 

modeled carefully; modeling should be rooted in the principles of both wildlife ecology 

and model uncertainty. Planning linkage-based conservation should follow a clearly 

defined process to ensure that the problems are properly framed, landscapes are properly 

modeled, and the correct methods and metrics have been applied. 

Early in the process, conservation practitioners must clearly define their conservation 

goals and consider whether increasing connectivity is the highest priority management 

approach. Connectivity is not a panacea and is just one of many tools available to land 

managers (Simberloff and Cox 2005). Other landscape management options (reviewed 

in Lindenmayer and others 2008) include maintaining large patches of native vegetation, managing for structurally complex and heterogeneous habitats, and creating buffers 

surrounding sensitive and core habitat areas. Further, certain forms of connectivity may 

not be ecologically feasible or cost-effective for some species and landscapes (Simberloff and others 1992; Hannon and Schmiegelow 2002). However, recent studies have 

provided additional data to support thoughtfully planned connectivity (Collinge 1998; 

Tewksbury and others 2002; Damschen and others 2006; Worboys and others 2010; 

Gilbert-Norton and others 2010).

A clearly defined conservation goal supporting the decision to increase connectivity 

will guide practitioners in selecting from a large suite of connectivity modeling methods. Each method has its own unique set of assumptions and best practices, and each 

produces slightly different types of maps. Connectivity modeling is not a one-size-fitsall endeavor. For example, if the goal is to measure whether a landscape is connected, 
2 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

construction of landscape graphs between habitat patches may be sufficient (reviewed in 

Galpern and others 2011). Similarly, for some very coarse scale connectivity mapping, 

where connectivity is modeled at regional to continental scales, expert opinion may 

be the only option due to data limitations (e.g., Jongman 1995; process summarized in 

Beier and others 2011). At the other end of a complexity spectrum are spatially explicit 

population models (SEPM). These models link population processes and landscape 

features to assess demographic consequences of connecting populations, and may be 

particularly helpful in assessing scenarios of land cover or climate change (reviewed 

in Carroll 2006). 

If spatially explicit connections are required—e.g., the goal is to design and implement linkages by purchasing or otherwise protecting specific areas—there remain many 

options. For example, individual Based Models (IBM) that simulate animal movement 

using species-specific behavioral rules (e.g., movement angles) and mortality risks in 

response to landscape elements can be applied. There are also IBM-like approaches that 

use observed animal movement data to assess landscape connectivity (e.g., “morphological image mapping,” Vogt and others 2009). 

However, the most common type of spatially explicit connectivity modeling uses 

resistance surfaces. Resistance-surface-based connectivity modeling is a relatively 

accessible method that does not require excessive data or computational resources. 

Resistance surfaces represent the degree to which some landscape feature impedes or 

facilitates some movement process (Adriaensen and others 2003), typically represented 

as a cell (pixel) value in a grid (raster) within a Geographic Information System (GIS). 

Linkages are then modeled in areas with lowest resistance to the movement process 

considered. The models are relatively easy to apply given existing data, and the approach 

offers the flexibility to develop models ranging from simple to complex, tailored to the 

specific conservation needs, and able to be refined as better data become available. A 

resistance surface is conceptually related to the idea of travel costs from behavioral 

ecology, and can therefore be designed to integrate ecological concepts important to 

successful wildlife movement such as an organism’s perceptual range and susceptibility 

to competition and predation (Bélisle 2005). 

Resistance-surface connectivity modeling assumes a relationship between surficial 

proxy measures and ease of animal movement. Unlike a SEPM—which requires specification of the biological needs and behaviors of the modeled organism—resistance surfaces 

can be posited without clear links to specific biological processes. It is common, for 

example, to equate resistance to habitat quality (e.g., Wikramanayake and others 2004; 

Beazley and others 2005; Kindall and Van Manen 2007; Gavashelishvili and Lukarevskiy 

2008; Thatcher and others 2009; Castilho and others 2011; Atwood and others 2011). 

However, it is often not clearly stated whether the presumed low resistance through high 

quality habitat is due to ease of movement, ease of food acquisition, behavioral familiarity, predator avoidance, or any of a multitude of other potential biological factors. Given 

this, it is important that resistance surfaces be considered hypotheses reflecting a solid 

consideration of causal biology. Similarly, resistance modeling generally implies that an 

organism has a specific directional movement goal, which may or may not be biologically reasonable. In some resistance-surface approaches, such as when connectivity 

is modeled using circuit theory (McRae and Beier, 2007; McRae and others 2008, see 

Chapter 3), organisms are modeled as electrons being pulled from a source (anode) to 

a destination (cathode). In other methods, such as least-cost path (LCP) analysis (see 

Chapter 3), an organism’s knowledge of landscape resistance is assumed to be perfect; 

the organism always knows the right path choice to minimize the overall cost and takes 

it. LCP analyses, like circuit analogies, generally assume a single goal: to travel from 

one cell to another, generally distant, one. The biological realism of these connectivity 

algorithms is largely unknown, but these levels of knowledge and motivation would 

surely be rare amongst organisms.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 3

There is, however, nothing in the process of modeling resistance-surface-based connectivity that forces one to confront these biological issues explicitly, and the ease of 

creating resistance-surface models therefore presents a potential trap. Data layers in a 

GIS can easily be transformed into resistance surfaces through simple manipulations, 

and user-friendly software exists to apply common algorithms to build corridors. It is 

easy to build a resistance-based connectivity map. However, due to the abstractions and 

hidden assumptions associated with this process, we assert that it is difficult to build a 

good one; it remains largely unknown whether the current connectivity models or designs will meet conservation goals and reduce biodiversity loss (Vos and others 2002; 

Goodwin 2003; Sawyer and others 2011; Zeller and others 2012).

The primary objective of this report is to provide a thorough, yet concise and accessible, information summary and guidance for land managers seeking to employ 

resistance-surface-based connectivity modeling for terrestrial wildlife conservation. We 

note that connectivity for aquatic species is also critically important, but the methods 

for modeling connectivity in ocean (e.g., Treml and others 2008) or riverine (e.g., Fagan 

2002) environments may not lend themselves to resistance-surface-based approaches 

(but see Landguth and others 2012). 

There are several helpful reviews in the primary literature covering topics such as 

best uses for connectivity metrics (Calabrese and Fagan 2004; Kindlmann and Burel 

2008; Rayfield and others 2011), best practices for modeling resistance surfaces (Spear 

and others 2010; Zeller and others 2012), and corridor and conservation network design 

guidelines (Beier and others 2008, 2011; Sawyer and others 2011). We synthesize, update, 

and expand on these efforts to achieve five goals: (1) briefly summarize the theoretical ecological concepts that underlie connectivity modeling and planning, (2) review 

connectivity modeling efforts in the primary literature, (3) review applied connectivity 

planning efforts in the United States, (4) detail the process of validating connectivity 

models, and (5) build on past and current connectivity modeling efforts and provide 

guiding questions to assist practitioners in modeling robust, ecologically grounded, 

resistance-surface-based wildlife connectivity. We note that these are not proscriptive 

guidelines because landscape connectivity is context dependent, depending on the species 

of concern, the landscape, and the conservation goal. What we provide is an organized 

approach to the problem of constructing resistance-based connectivity models. Each 

stage in this process is motivated by key critical questions that should be considered to 

ensure that connectivity designs are as ecologically relevant as possible. 

Throughout this report, we direct practitioners to other key resources that provide 

helpful details. There are other general frameworks for connectivity planning available, 

providing guidance on steps from assembling the planning team, determining the goals 

of the project, establishing collaborative arrangements, selecting the study area, through 

assessing opportunities and limiting factors of the modeled linkages (Hilty and others 

2006; see Anderson and Jenkins 2006; Beier and others 2011; summarized in Aune 

and others 2011). While some of these frameworks tend towards coarse scale regional 

connectivity modeling, many of the guidelines are helpful at any scale. Similarly, there 

exist in-depth reviews of theoretical foundations for connectivity modeling (e.g., Forman 1995; Bennett 2003; Hilty and others 2006; Lindenmayer and Fisher 2006) and 

technical details on specific steps in the larger process (e.g., Adriaensen and others 2003; 

Theobald 2005; Beier and others 2009; Spear and others 2010; Huber and others 2010; 

Parks and others 2012; Zeller and others 2012); we urge readers to consult these helpful 

works as necessary. Here, we seek to find the balance between detail and accessibility, 

providing a summary of existing efforts and detailed questions for modeling resistancesurface-based, spatially explicit linkage designs for terrestrial wildlife conservation. To 

accomplish our goal, we reviewed 47 recent publications that used resistance modeling 

and 31 recent efforts by planners and practitioners in the United States.
4 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 5

Chapter 2. Ecological Framework and Key 

Definitions for Modeling Connectivity 

The Foundations of Resistance-Based Connectivity Modeling

Land cover conversion leading to habitat loss is one of the greatest threats to global 

biodiversity (Wilcove and others 1998; Sala and others 2000; Foley and others 2005; 

Cushman 2006) (see “Connectivity Terminology” at the end of Chapter 2 for definitions 

of words in bold). Associated with habitat loss is habitat fragmentation, the breaking apart of large contiguous blocks of habitat into multiple smaller patches. Habitat 

fragmentation has numerous negative effects on ecosystems (for a thorough treatment 

of the topic, see Saunders and others 1991; Lindenmayer and Fisher 2006). Fragmentation changes the shape and pattern of habitats throughout the landscape and tends to 

decrease habitat quality more than areal losses would indicate: fragmentation in and 

of itself reduces the amount of structural core area, where edge effects and external 

disturbances do not permeate. Fragmentation, and particularly “dissection” of habitats 

by roads and other human-built barriers, reduces landscape connectivity (Franklin and 

Forman 1987; Forman and Alexander 1998). Ultimately, habitat loss and fragmentation 

can lead to declines in wildlife populations (Ricketts 2001; Wiegand and others 2005; 

Hansen and DeFries 2007).

Reduced landscape connectivity leads to isolation of individuals or populations via 

reduced foraging, dispersal and reproduction, or migration movements (Lindenmayer 

and Fischer 2006). These effects of reduced landscape connectivity span multiple spatial 

and temporal scales affecting processes as varied as daily foraging, annual migrations, 

rates of genetic mixing, and population persistence. Reduced landscape connectivity may 

also alter food webs (Holyoak 2000) and ecosystem processes including microclimatic 

shifts and nutrient cycling (Collinge 1996). The degree of impacts from fragmentation depends on whether the organism in question is a habitat specialist or generalist, 

whether it prefers habitat core or edge areas (Bender and others 1998; Fahrig 2003), 

and the species’ evolutionary predilection to cross “gaps” or barriers in the landscape 

(Lindenmayer and Fischer 2006).

Because land cover conversion, fragmentation, and habitat loss are prevalent, maintaining or restoring landscape connectivity is widely accepted as necessary, but not 

sufficient, for sustaining daily habitat, demographic, and genetic processes that support 

the persistence of local and peripheral populations and their evolutionary potential 

(Debinski and Holt 2000; Bennett 2003; Crooks and Sanjayan 2006; Taylor and others 

2006; Pressey and others 2007). Connectivity may be particularly critical for species 

seeking suitable habitat under a changing climate (Lawler and others 2008; Heller and 

Zavaleta 2009; Carroll and others 2010; McKelvey and others 2011). 

The term landscape connectivity was originally coined by Merriam (1984) and defined by Taylor and others (1993) as “the degree to which the landscape facilitates or 

impedes movement among resource patches.” A landscape therefore only has functional 

connectivity relative to a single species’ perspective. Functional connectivity is also 

dependent on the specific organisms’ scale of movement (Wiens 1997), perception of 

the landscape (Lima and Zollner 1996), resource needs, and behavioral responses to 

landscape elements and patterns (Lima and Zollner 1996; Wiens 1997; Tischendorf and 

Fahring 2000; D’Eon and others 2002). In practice, because behavioral responses to the 
6 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

landscape are not always known for a specific species, connectivity models often focus 

only on the physical patterns, or structural connectivity, of the landscape. However, 

structural connectivity in no way ensures functional connectivity, and a functionally 

connected landscape may not appear on a map as having structurally contiguous habitat 

considered suitable for a species’ movement (Taylor and others 2006). 

Fundamentally, the concept of landscape connectivity is grounded in three primary 

ecological fields: island biogeography, metapopulation, and landscape ecology. Although 

the original development of the first theory, island biogeography (MacArthur and Wilson 

1967), was related to actual islands, the theory later came to represent a general view 

of the landscape as habitat patches with high quality habitat that supported organisms 

surrounded by an inhospitable landscape of other, unsuitable habitats, commonly referred to as the matrix. The theory holds that biodiversity is positively related to size 

and proximity of patches (specifically, the theory developed functions to calculate the 

theoretical equilibrium number of organisms on an island in response to island size and 

distance from the mainland). Biologists eventually recognized that this theory was not 

a perfect fit for most terrestrial systems because patch/matrix differences are seldom as 

extreme as the original ocean/land dichotomy. In short, the matrix matters (reviewed in 

Franklin and Lindenmayer 2009), and the theory breaks down to the degree to which 

it matters. Nevertheless, the theory set up the view of the landscape as a binary “patch 

or matrix” system. 

The second theoretical foundation for connectivity is metapopulation theory (Levins 

1968, 1969a; Hanski 1998). The theory holds that local populations of organisms are 

connected by individuals moving (dispersing) between other local populations to create a 

larger, interconnected system of populations (metapopulation). In the simplest of terms, 

metapopulation theory quantifies the proportion of patches occupied as a function of the 

ratio of patch-level extinction and recolonization (Levins 1969a, 1970). Importantly, 

for all of the patches to be occupied, colonization rates need to be orders of magnitude 

higher than extinction rates; when extinction rates equal colonization rates, the entire 

metapopulation goes to extinction (Levins 1969a, 1970). Lande’s (1987) individual occupancy model, which is a precise discretization of Levins’ model (Noon and McKelvey 

1996), examines the effects of metapopulation dynamics in the case where patches 

represent individual home ranges. Lande (1987) theoretically demonstrated that, for 

territorial organisms, sufficient fragmentation, even in environments with unlimited 

habitat, will lead to extinction. 

The concepts of proximity and size of patches from island biogeography combined with 

the critical element of dispersal rates from metapopulation theory were incorporated into 

the third foundation of landscape connectivity, the growing field of landscape ecology. 

This field of study tends toward a patch-corridor-matrix view of the landscape (Forman 

1995). In the terminology of landscape ecology, a patch is a relatively discrete area that 

differs from the surrounding matrix, where matrix is the primary, most extensive (and 

often most contiguous) land cover type. Patches may be connected through the matrix 

via corridors, linear landscape elements that differ from the land cover on either side 

(dissimilar from the matrix). Landscape ecologists see the pattern of patches, corridors, 

and matrix forming a hierarchy of landscape mosaics, that in turn, affect (and are affected 

by) ecological processes across a range of scales (Turner 1989). These landscape mosaics have more recently been viewed by landscape ecologists and conservation biologists 

as being made up of a series of patches along a gradient of habitat quality (Fischer and 

others 2004). Given a gradient of patchily distributed habitat qualities, in this paradigm 

habitat patches are subjectively defined for management convenience (Bennett 2003), 

and the matrix may be equally important for conservation (Ricketts 2001; Jules and 

Shahani 2003; Prevedello and Vieira 2010). However, while this paradigm does not 

formalize landscapes into arrangements of habitat islands in a sea of matrix, the flavor 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 7

of the older island-biogeographic concept is often retained: animals are assumed to live 

within and move between patches of most preferred habitat seeking paths through a 

matrix of less preferred habitat. The physical paths taken through the matrix represent 

functional linkages, spatially explicit paths of any shape and form through the matrix 

that provide functional connectivity across the landscape. 

Connectivity modeling naturally followed this trajectory of ideas: early connectivity 

modeling focused on creating narrow links between patches as suggested by the patchmatrix-corridor model. As the field evolved, however, and with landscapes increasingly 

viewed as containing gradients of habitat quality, the issue changed from the maintenance or creation of structural linkages in the shape of corridors, to nuanced linkages, 

identified using the perceptual scale of a given conservation target (Wiens and Milne 

1989). Thus, connectivity was no longer understood in terms of the presence or absence 

of a single thin corridor (Bennett and others 2006), but rather a network of optional 

paths (that may or may not consist of a highly visible contiguous swath of habitat) to 

facilitate movement under different scenarios, responding directly to a clearly articulated 

conservation goal. Thus, connectivity modeling efforts have recently moved to mapping 

potential linkages (sensu Fagan and Calabrese 2006), which represent hypotheses about 

paths that provide functional connectivity. Potential linkages are determined by evaluating the spatial landscape structure given knowledge of an organism’s likely behavioral 

response to the specific area’s landscape elements. 

The analysis of connectivity within complex habitat quality gradients requires assumptions about how landscape patterns affect and direct organismal movement and 

dispersal. Formalizing these relationships as resistance surfaces allows the application 

of flow algorithms to identify structural or functional linkages. Conceiving connectivity 

as flow rates across a variably resistant surface makes this approach extremely flexible: 

many things can flow. Thus, resistance (or cost) surfaces can represent the hypothesized 

relationships between landscape features and a variety of ecological flows, such as movement of organisms, genes, or processes. It provides a facile approach to determining 

the location and shape of functional linkages given the landscape-ecological paradigm 

of landscapes being mosaics of patches with different habitat qualities. Mapping patch 

qualities to resistance levels and thereby enabling the use of flow algorithms, makes the 

problem of determining how organisms might move across complex patchy landscapes 

tractable. 

The Ecological Consequences of Connectedness

Although the consequences of habitat fragmentation and lost connectivity receive 

more attention, practitioners must be aware of the potential negatives to increased connectedness. In particular, there is a concern that increased connectivity for target organisms may also lead to increased connectedness for unintended organisms and processes, 

spreading invasive species, changing competition and metapopulation dynamics, and 

introducing disease (Bennett 2003; Crooks and Suarez 2006; McCallum and Dobson 

2006; Blowes and Connolly 2012). As a result, practitioners should assess the potential 

for negative effects of connectivity, particularly in the presence of invasive species, and 

integrate specific mitigation measures into the planning process (Aune and others 2011). 

Further, higher movement rates may be associated with higher mortality rates for some 

species (Biro and others 2003; Frair and others 2005; Grilo and others 2011). However, 

there is growing evidence that, in most cases, the benefits outweigh the risks, and that 

thoughtfully designed or restored connectivity increases biodiversity in increasingly 

fragmented landscapes (Beier and Noss 1998; Bennett 2003; Worboys and others 2010; 

Gilbert-Norton and others 2010; Beckmann and others 2010). 
8 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

First Principles for Modeling Wildlife Connectivity

Connectivity is species-specific. A forest may provide connectivity for squirrels, but 

may represent a barrier for meadow voles. Not only is habitat species-specific, but species also respond to landscapes at very different spatial and temporal scales depending 

on their size, mobility, sensory acuity, and the purpose of their movements. A road may 

present an impassable barrier or a minor nuisance depending on the size of an organism and whether their biological needs require successful road crossing once a day or 

once a decade. Therefore, one of the most critical ecological concepts to consider when 

modeling connectivity is that of scale.

The importance of the grain and extent of both temporal and spatial scales has long 

been recognized as critical for conservation biology (Wiens 1989; Levin 1992; Frankham 

and Brook 2004). Specifically, connectivity modeling results may be very sensitive to 

grain size and the extent of analysis (Graves and others 2007; Pascual-Hortal and Saura 

2007), thus it is critical that the modeling be conducted at a spatial and temporal scale 

that matches the organism’s perceptual scale (Wiens and Milne 1989; Baguette and Van 

Dyck 2007; Pe’er and Kramer-Schadt 2008; Galpern and Manseau 2013). Thus, the 

optimal scale of functional connectivity analysis arises from the intersection of speciesspecific traits and the type of connectivity being modeled. For example, Squires and 

others (2007) estimated a total population size of approximately 13 wolverines (Gulo 

gulo) occupying four mountain ranges in Montana. Any one of these mountain ranges, 

however, contains tens of thousands of chipmunks (Neotamias spp.). The spatial extent 

and grain of connectivity modeling to meet the daily needs of an individual wolverine 

would clearly be larger than those required for a chipmunk. Additionally, the wolverine 

population is so small that it requires both genetic and demographic connectivity to persist, and analysis would require a spatial extent of multiple mountain ranges. Betweenmountain-range demographic and genetic connectivity is much less important for the 

larger chipmunk populations and, due to their comparatively small size and reduced 

mobility, is unlikely to occur with any frequency.

Temporal scaling is at least as important as spatial scaling in connectivity modeling. 

Temporal scaling affects both movement and population processes. In the wolverine/

chipmunk example, wolverine’s small population size within a range mandates nearly 

continuous movements between mountain ranges to avoid extinction due to chance events 

and to rapidly recolonize areas to avoid range shrinkage. These needs are demographic 

in nature, and temporally scale to years to decades. Chipmunks, on the other hand can 

persist in isolated mountain ranges for thousands of years. In the Spring Mountains, 

Nevada, a separate species, Palmer’s chipmunk (Neotamias palmeri), has likely persisted 

in isolation since the Pleistocene, but retains levels of genetic variability not dissimilar to 

widely distributed species (McKelvey and others 2013). Thus, where local populations 

are larger and extirpation is not a frequent concern, the primary connectivity requirements may be to alleviate genetic rather than demographic stochasticity, and dispersal 

rate requirements scale to generation times rather than to population sizes (Lowe and 

Allendorf 2010). Both demographic and genetic processes, however, are short term 

when compared to the ebb and flow of climatic conditions that can render large areas 

that were habitat unsuitable and open up new areas of habitat in previously unsuitable 

landscapes. Connectivity at these time scales controls current ranges of species, and the 

process of speciation itself. These broad-scale and long-term connectivity needs have 

not been the historical focus of conservation biology. However, with the potential for 

rapid directional climate change in the near future, connectivity that allows movements 

at the regional to continental scale may be most critical for long-term population and 

species persistence (Heller and Zavaleta 2009; Shoo and others 2013). 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 9

Species-specific traits and the biological requirements facilitated by connectivity also 

determine the characteristics of potential linkages (Harrison 1992). If an organism moves 

rapidly, or if the biological requirements require short distance movements, connectivity 

may be achieved by a landscape whose only property is that it does not impede these 

movements. However, if movement is slower, or across greater distances, connectivity will require a landscape that provides food, water, and shelter or resting habitat in 

addition to allowing movement. If it takes generations to move across the space, then 

connectivity requires a landscape that provides for the entire life history needs of a species and is of sufficient areal extent and quality so as to support contiguous populations. 

When planning for connectivity, careful consideration of species’ needs and capabilities 

should be evaluated at a hierarchy of spatial and temporal scales. Further, the biological 

needs and associated movement requirements should be identified. We formalize these 

ideas by identifying six types of landscape connectivity: Structural Connectivity and five 

additional types of functional connectivity that are closely related to spatial and temporal 

scales of movement, Daily Habitat, Seasonal Migration, Demographic, Genetic, and 

Range Shift. We include brief definitions for these terms in “Connectivity Terminology” 

at the end of Chapter 2, but because these ideas are developed in this report, rather than 

being general to the literature, we discuss each of these ideas in detail. 

 1. Daily Habitat. This represents wildlife movement to meet daily food, water, and 

shelter needs, and it is the smallest temporal and spatial scale we consider. Daily 

movement connectivity is particularly important for species that shelter or breed 

in one habitat and forage in another type(s) of habitat separated by less suitable 

habitat, or for wide-ranging species that have home ranges that span a mosaic of 

habitat suitability (Bennett 2003). Improving daily habitat connectivity may be 

an important conservation goal for species or populations that have high mortality because of barriers (for example, roads) that hamper meeting basic resource 

needs. Because daily habitat movements occur at small spatial scales, they often 

follow tortuous paths (Crist and others 1992; Johnson and others 1992) and need 

to be modeled at an appropriately fine grain. 

 2. Seasonal Migration. This type of movement has many of the same motivations as 

Daily Habitat movement, but generally occurs at broader spatial extents (relative 

to each species’ daily movements) and does not occur for all species. To separate 

this from Demographic movement (below), we define this as round-trip, seasonal 

movements. For species such as ungulates that require seasonal movements to 

obtain forage, seasonal migration routes may be some of the most critical to 

identify for conservation actions. 

 3. Demographic. Demographic movement is defined as being between sub-populations

and occurring at relatively broad extents. These are dispersals from one subpopulation to another rather than seasonal loops. Demographic movement rates 

that provide stability across sub-populations scale as the proportion of the census 

population, whereas genetic connectivity scales to the total number of migrants 

(Lowe and Allendorf 2010). In practice, this means that necessary rates of movement are at least an order of magnitude greater than are required to achieve genetic 

stability. 

 4. Genetic. Genetic movement, like demographic movement, occurs between subpopulations and happens at the same spatial scale. However, the temporal scale is 

much different. Genetic movement serves to maintain genetic variability across 

sub-populations by transferring genes at rates equal to rates of loss caused by 

genetic drift. So while demographic stability occurs if the number of migrants is 

sufficient to maintain a constant population on an annual basis, genetic stability 
10 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

occurs if the number of migrants is sufficient for the next generation to have equal 

genetic variability when compared to the current generation (Mills and Allendorf 

1996). 

 5. Range shift. Historical variability in climate, topography, and plant and animal 

communities has necessitated that species shift range for long-term species 

persistence. These are not movements made on an annual or even generational 

basis. However, with the possibility of rapid directional climate change (see 

Loarie and others 2009), introductions of exotic species, and other anthropogenic 

global changes, the rates of this type of movement may increase. Planned linkages between distant patches (such as pole-ward or elevational range shifts) may 

be required to help species adapt to unprecedented rates of change (Harris and 

Scheck 1991; Hobbs and Hopkins 1991; Tiebout III and Anderson 1997).

 6. Structural. Landscape structure connectedness is assumed to increase long-term 

persistence of species without specifically defining a movement type or even 

which species are targeted. Although other connectivity requirements would 

generally be evaluated for a target organism, landscape structure is often evaluated for an unspecified group of organisms and includes broad concepts such 

as assumptions that biodiversity is increased when there are few human-built 

barriers (e.g., Theobald and others 2012). Therefore, in many cases, structural 

connectivity actually refers to lack of physical structures such as houses, roads, 

and parking lots. However, it can also refer to landscape features such as “facets” 

(Beier and Brost 2010), defined as landscape units with uniform topographic 

and soil attributes. This approach is well-suited for assessing general scenarios 

of land cover or ecosystem change (e.g., Wade and Theobald 2009; Brost and 

Beier 2012; Baldwin and others 2012).

These connectivity types are not independent; in a global sense, all are important for 

the long term conservation of a species. However, formal consideration of each type 

should lead to better and more comprehensive connectivity models and designs. For 

example, if the primary goal of a connectivity plan is to increase the likelihood that an 

organism can acquire its daily needs of food, water, and shelter, then these goals should 

be formally identified. A design that achieved this while also maintaining some level 

of between-population genetic connectivity would, however, be more likely to succeed 

in maintaining the species in that portion of its range. 

In conclusion, resistance based connectivity modeling is the direct outgrowth of the 

fields of island biogeography and metapopulation dynamics when applied to complex, 

patchy, habitat gradients, the landscape-ecological view of landscapes. Transforming 

these quality gradients into resistance gradients allows the application of flow algorithms 

and makes computing connectivity tractable. However, because this transformation 

is intrinsically integrative and abstract, it can be accomplished without links to the 

specific biological behaviors, needs, and limitations of a target organism. To properly 

relate putative resistance factors to organism biology requires evaluating the spatial and 

temporal scales of the connectivity process in terms of the organism’s own perceptual 

scale, density, and vagility. Further, it requires specificity concerning the type of movement being modeled. In the remainder of this report, we narrow our focus to the specific 

process of developing resistance-surface-based connectivity models, first providing a 

literature survey of published analyses, and then outlining an 8-step process which, if 

followed, will guide the analysis and avoid common pitfalls. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 11

Connectivity Terminology

Connectivity

•	 Landscape Connectivity: Also called ecological connectivity (although usually 

applied to diffusion of ecological processes not movement of organisms), landscape 

permeability, (inverse of) isolation. This is a general term to represent the degree 

to which the landscape facilitates or impedes movement of organisms or processes 

(Crooks and Sanjayan 2006; Taylor and others 2006). Landscape connectivity can 

be represented as functional or structural connectivity. We note that some previous 

authors consider the term “landscape connectivity” to represent the connectivity of 

vegetation patterns or habitat, and to be a synonym of structural connectivity (e.g., 

Lindenmayer and Fischer 2006); however, we use the term as originally defined, 

above, as a general, umbrella term. We identify six total types of connectivity, 

one structural and five functional:

□ Structural Connectivity: Also called landscape pattern connectivity, habitat 

connectivity. Structural connectivity is the degree of physical, spatial contiguity of habitat types or elements in the landscape, assumed to increase 

flow of some processes, but generally considered independent of any specific 

organism (Collinge 1998). 

□ Functional Connectivity: Also called actual connectivity. Functional connectivity is an emergent property of species-landscape interactions whereby 

the landscape, whatever its structure, allows sufficient organismal movement 

to provide some or all functional types of connectivity:

•	 Daily Habitat: movement between resource patches to meet daily 

food, water, and shelter needs;

•	 Seasonal Migration: annual or seasonal departure and return to breeding areas (Sinclair 1983);

•	 Demographic: movement that leads to successful recruitment in new 

population (Lowe and Allendorf 2010) ;

•	 Genetic: movement between populations that affects genetic structure, 

minimizes losses of genetic variability, and influences the evolutionary 

processes (Lowe and Allendorf 2010);

•	 Range Shift: movement that allows species to track the shifting range 

of habitat availability resulting from factors such as climate change, 

large scale disturbances, novel pathogens, etc.

•	 Connectedness: Quantitative measure of connectivity; many metrics exist for 

quantifying connectedness (Calabrese and Fagan 2004; Kindlmann and Burel 

2008; Magle and others 2009; Laita and others 2011). Connectivity is measured 

uniquely for a given type of functional or structural connectivity.

Conservation Target: Broadly, anything that one wishes to conserve. In this context, 

a biological element selected for conservation; this can be a single species or guild, at 

any level of biodiversity (e.g., individual, population, metapopulation, etc.).

Core Area: An area that is assumed to be vital to a specified conservation target. Often 

identified core areas represent specific types of habitat that are unique or rare in their 

abilities to provide habitat needs (e.g., foraging/prey, cover, reproduction), areas of 

particularly high productivity for the target, or simply large contiguous areas of habitat 

considered vital for metapopulation persistence. This idea differs from a habitat patch 

core that is more tightly defined as the center of a habitat patch, surrounded by a protective buffer, so that the core is not affected by edge effects or permeated by external 

disturbances. 
12 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Corridor: Originally defined as a relatively narrow strip of land cover that differs from 

the matrix on either side (Forman 1995); in its original meaning, the term represented 

only structural connectivity between patches and was not related to organism movement, 

but the term now refers to a human-built or naturally occurring linkage that is relatively 

short, usually linear, and dissimilar from the surrounding matrix and that may allow 

organisms to move between habitat patches (Beier and Noss 1998). In resistance modeling, corridors are associated with paths of low resistance that lie between predefined 

nodes representing source and destination locations for a specified conservation target.

Edge: The portion of a habitat patch near its perimeter where environmental conditions 

are more affected by the surrounding matrix as compared to the patch core (Turner and 

others 2001).

Habitat Fragmentation: Splitting of a single habitat patch into multiple, smaller patches; 

also generally entails habitat loss.

Habitat Loss: Reduction in total area of habitat.

Linkage: A spatially explicit representation of a physical path in the landscape, of any 

shape or form, through a landscape matrix. Linkages are not limited to narrow, linear 

connections between habitat patches (Bennett 2003). There are three primary types of 

linkages:

•	 Structural Linkage: a linkage drawn on a map based solely on structural vegetation or habitat patterns; does not consider species-specific behavioral responses 

to the landscape.

•	 Functional Linkage: a linkage that is empirically shown to provide a specific 

type of functional connectivity;

•	 Potential Linkage: often modeled as a structural element in the landscape (e.g., 

continuous swath of habitat) that, given assumed or known organismal behavioral 

response to landscape elements, is hypothesized to provide a functional linkage. 

Matrix: In the terminology of landscape ecology, a matrix was originally defined as the 

primary, most extensive background land cover type (Forman 1995) and was generally 

considered the inhospitable binary opposite of habitat. Ecologists now view the matrix 

as a heterogeneous mix of land cover along a gradient from high quality, core habitat 

to completely inhospitable barriers; it is generally agreed that even less-than-suitable 

matrix is often used as habitat (Haila 2002; Berry and others 2005).

Patch: Also called habitat patch. A patch is a relatively contiguous land cover that differs 

from the surrounding land cover (Forman 1995); a habitat patch is a contiguous area in 

the landscape that meets specified habitat requirements for a given species.

Perceptual Scale: The grain and extent of an organism’s response to heterogeneity in 

the landscape (Wiens 1989).

Resistance Surface: Also called cost surface. The resistance surface is the foundation 

of the modeling process, whereby land areas are assigned resistance (or cost) values 

representing the hypothesized relationship between ecological variables and the difficulty of animal movement across that cell. In common practice, these maps are GIS 

raster surfaces. Resistance values are proxies for ecological cost (also called functional 

cost, cost distance) and are generally assumed to represent either time (travel time), or 

fitness (physiological expenditure or likelihood of mortality) associated with traversing a specific area. However, in practice the ecological underpinnings of resistance are 

often poorly defined. Thus, resistance is often based on perceptions of habitat quality, 

correlations with known animal movements, or assumed impediments to movement 

(e.g., anthropogenic structures). In the case of structural connectivity (see Chapter 3), 

resistance is generally not formally linked to ecological cost.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 13

Scale (Grain, Extent): Scale is the spatial or temporal dimension of an object or process; 

there are two primary attributes of scale: grain is the finest level of resolution (e.g., in 

a GIS, the size of a cell, for time minutes vs. hours) and extent is the size of the study 

area or duration of time under consideration (Turner and others 2001).
14 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 15

Chapter 3. Resistance-Surface-Based 

Connectivity Modeling: Formalizing the 

Process and Reviewing the Literature

“There are known knowns. These are things we know that we know. There are 

known unknowns. That is to say, there are things that we know we don’t know. But 

there are also unknown unknowns. There are things we don’t know we don’t know.”

Donald Rumsfeld 

Building a resistance-surface-based connectivity model based in actual functional connectivity requires both structured thinking concerning the ecological concepts discussed 

in Chapter 2 and a formalized process to make sure that important considerations have 

not been neglected. As noted both in the introduction and Chapter 2, there is nothing 

intrinsic to the process that forces one to address the issues that Donald Rumsfeld so 

pithily expressed. However, without formalizing our state of knowledge regarding the 

biological and ecological processes we seek to model, the chances of developing an 

accurate connectivity map are low. To provide a structure to help to achieve this, we 

identify eight critical steps for modeling resistance-surface-based linkage designs for 

terrestrial wildlife conservation (Figure 1; see Figure 2 for mapped examples of steps 2, 

3, 4, and 5):

 1. Define the type of connectivity to be modeled;

 2. Create resistance layer(s);

 3. Define what is being connected;

 4. Calculate ecological distance;

 5. Map potential linkages;

 6. Validate potential linkages;

 7. Assess climate change effects (optional); 

8. Quantify connectedness (optional).

Assessing the uncertainty involved with each step is also a critical element of successful 

connectivity modeling (see more detailed discussion in Chapter 4). Although we discuss 

these steps in a linear fashion for convenience, the modeling process is seldom linear; 

decisions at each step may require that a decision made at a previous step be revisited.

Here, we focus on the modeling process, not the planning or implementation phases 

of linkage design. We do not consider pre-modeling planning, which includes clearly 

defining the conservation issue or problem, choosing conservation targets, and identifying collaborators, budgets, and timelines (Groves and others 2002). We also do not 

consider post-modeling implementation, which includes assessing feasibility of linkage 

designs, prioritizing linkages for protection, and estimating economic costs (Bennett 

2003; Hilty and others 2006; for more details on these steps see Aune and others 2011; 

Beier and others 2011). 
16 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Figure 1—Resistance-surface modeling workflow. Workflow proceeds from top to bottom, but steps are not linear as 

decisions at each step may require revisiting previous steps; particularly, uncertainty analysis may suggest need to 

revamp methods. Methods from left to right reduce uncertainty in final mapped linkages. Step 8, quantifying connectivity, does not necessarily affect uncertainty.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 17

Figure 2—Example of steps 2 (top left; create resistance layer), 3 (top right; define what is being connected), 4 

(bottom left; calculate ecological distance; here, least cost distance), and 5 (bottom right; map potential linkages; 

here using normalized least cost) in the process of resistance-surface-based connectivity modeling (here, for Elk; 

Figure ES.1 in WHCWG 2010; see Chapter 5 for a discussion of this project). (Permission to reprint figure granted 

by the Washington Wildlife Habitat Connectivity Working Group).
18 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

For each step, we include findings from a review of two types of literature: (1) papers

seeking to provide guidance, critiques, or reviews for connectivity modeling and 

(2) papers that describe examples of resistance-surface connectivity modeling for conservation purposes. Although some papers covered both types of literature, we used our 

best judgment to determine their primary intent. The former papers are referenced in 

the discussion of each modeling step, below. The latter type of papers, those that describe 

connectivity modeling for conservation purposes, are summarized by each modeling

step and listed in Appendix 1 (47 papers). In this report and in the table, we include 

several papers that did not have a primary intent of mapping linkages, but instead 

sought to more generally assess or quantify connectivity (17 papers, highlighted in 

grey in Appendix 1). We included these papers because they contribute something 

unique in their approach to modeling connectivity. To identify the papers discussed 

herein, we searched Web of Science and Google Scholar1, followed citation leads, 

and relied on our own knowledge of the literature. 

Steps for Modeling Resistance-Surface-Based Linkage Designs 

for Terrestrial Wildlife Conservation

Step 1. Define Type of Connectivity to Be Modeled

The conservation problem must be clearly defined in the pre-planning stages, and this 

in turn suggests the type of connectivity that should be modeled: in Chapter 2 we identified six movement types (also see “Connectivity Terminology” at the end of Chapter 2). 

Many of the papers we reviewed, however, did not explicitly state the type of connectivity being modeled, but we were often able to infer the type from the stated intent. 

Several of the papers modeled more than one type of connectivity. The majority of 

papers’ stated intent was to model “dispersal” (18 papers). This appeared to represent 

a combination of the second and fourth most commonly modeled connectivity types: 

genetic (specifically stated or intended in 10 papers) and demographic connectivity 

(9 papers). Structural connectivity was the third most commonly modeled (8 papers). 

Three papers sought to model daily habitat connectivity, and two sought to model migration connectivity. No authors stated or clearly implied they were modeling connectivity 

associated with range shifts. Two papers stated they were modeling “functional” connectivity, without further defining what that meant. In four of the papers we reviewed, 

the type of connectivity was not stated and could not be inferred (Appendix 1). In our 

view, this review identifies a clear deficiency in connectivity modeling to date. If the 

type of connectivity being modeled is not clearly specified, it becomes impossible to 

evaluate the quality of the resulting model either through direct validation (see Chapter 4) or even in the less demanding context of comparing the resulting linkage map to 

other constructs based on different resistance values, grain sizes, path algorithms, or 

nodal structures (below). Without specifying precisely what is trying to be achieved, 

there can be no related metric to judge success.

1 We searched Web of Science for documents between January 1, 2002, and August 31, 2012, for the 

terms: Title = (linkage* OR corridor* OR landscape permeability OR conservation network OR connectivity OR landscape resistance ) AND Topic = (least cost path OR least-cost OR least cost OR cost distance 

OR ecological distances OR resistance surface OR permeability OR isolation by resistance). This resulted 

in 425 citations. We reviewed abstracts to select the top 100 papers that most likely concerned resistancesurface connectivity modeling. We searched Google Scholar to identify any papers we may have missed 

with the terms: habitat connectivity, resistance layer, impedance layer, inverse of suitability, least cost path, 

least cost corridor, least cost distance, conservation area design, corridor map, Circuitscape, linkage mapper, FunConn, CorridorDesigner, Connectivity Analysis Toolkit, UNICOR, landscape integrity, MaxEnt 

connectivity, modeling connectivity, and functional connectivity.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 19

Step 2. Create the Resistance Layer

The resistance layer is the foundation of the modeling process, whereby cells in a GIS 

raster surface are assigned a value representing the hypothesized relationship between 

ecological variables and the difficulty of animal movement across that cell. Zeller and 

others (2012) provide a comprehensive recent review of this critical step, and we recommend that practitioners refer to their manuscript for more detailed discussion of potential 

pitfalls. Here, we identify four sub-steps to creating the resistance layer: (a) determine 

the scale of the resistance layer, (b) identify ecological variables, (c) assign resistance 

values based on chosen ecological variables, and (d) validate the resistance surface. 

Step 2a. Resistance layer extent and grain. The extent of the resistance layer should 

extend well beyond the area of interest. Mapping errors can occur at the edges of the 

resistance layer due to artificial truncation of landscape features, but more importantly, 

linkages will be artificially limited by the map edges (Koen and others 2010), which 

will be modeled as de facto barriers. Buffering beyond the area of interest reduces the 

likelihood that these errors will affect modeled potential linkages or that important 

potential linkages will be missed. Unfortunately, artificial boundaries constrain both 

political realities and data. Thus, if buffering the study area is intractable, it must be 

understood that connectivity analyses near the study area border are likely deformed 

and less dependable. Analysis extent must also reflect the level of organismal structure 

under consideration. For example, the extent of analysis for modeling demographic connectivity between multiple populations is very different from a model of daily habitat 

connectivity for a single organism. 

The grain of the resistance surface, represented as the cell size in GIS, should reflect 

the perceptual grain of the species or conservation target given the type of connectivity 

being modeled. Often, however, there is a tradeoff between grain and extent for computational reasons (Lima and Zollner 1996), and commonly grain size is constrained 

non-biologically by the granularity of the available data.

Very few of the papers we reviewed specifically addressed the biological rationale 

associated with extent and grain. It was, for example, difficult to determine whether 

researchers extended analysis areas beyond the primary study extent to avoid mapping 

errors. For spatial grain, the majority of papers appear to set analysis grain on the basis 

of the resolution of available data rather than the perceptual grain of the conservation 

target. Therefore, the majority of researchers used between a 30 m – 100 m cell size, 

although several papers that modeled movement of smaller organisms used more finely 

resolved cell sizes (e.g., Stevens and others 2006; Driezen and others 2007; Wang and 

others 2009; Decout and others 2012) or larger cell sizes for larger animals (e.g., Falcucci 

and others 2008; Huck and others 2011; Carroll and others 2012; Ziółkowska and others 

2012), in an effort to reflect an organism’s perceptual grain. A few papers mention that 

cell size was chosen in response to computational limitations (e.g., Bunn and others 

2000; Carroll and others 2012).

Several papers discussed scale mismatches associated with convenience-scaled 

resistance surfaces. For example, Pullinger and Johnson (2010) specifically discuss 

the potential implications arising from a mismatch between the inferred paths from 

telemetry (taken for caribou at >3 hour recurrence intervals) and modeled paths (using 

environmental variables with 25 m cell resolution). When cell resolution is arbitrary or 

differs from the scale of related occurrence data, a sensitivity test in which the analysis 

is run using a range of cell resolutions is a reasonable approach (Broquet and others 

2006). Only five of the papers reviewed, however, considered various cell resolutions 

in their studies. For example, Walpole and others (2012) looked at correlation between 

resistance-surface cell size and occurrence data for lynx; they found that correlations 

existed for all cell sizes examined, and chose the finest resolution data for use in the 
20 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

remainder of the analysis. This level of analysis, although commendable, may not be 

sufficient to fully understand the sensitivities of putative corridors to cell size (Graves 

and others 2007; Pascual-Hortal and Saura 2007). For example, Schadt and others (2002) 

found that the size and shape of habitat patches were sensitive to grain size, and Carroll 

and others (2012) found the final modeled links were sensitive to analysis resolution. 

An alternative to conducting a sensitivity analysis may be to use genetic (e.g., Cushman 

and Lewis 2010) or occurrence data (e.g., Janin and others 2009) in a model selection 

framework. Because organisms respond differently to various physical environmental 

properties at different scales, Zeller and others (2012) suggest that it may be best to 

determine an optimal grain for each ecological variable, rather than trying to find an 

optimum for all variables combined. This idea applies to temporal scales, as well. For 

example, Lowe and Allendorf (2010) reviewed the differences between demographic 

and genetic connectivity, noting the temporal mismatch in using genetic data to estimate 

resistance surfaces for modeling demographic connectivity.

It should be noted that grain size of the resistance surface is not the only way to 

reflect the perceptual grain of a species, and several of the papers we reviewed applied 

other approaches, such as defining patches, accumulating ecological costs, or mapping 

potential links on the basis of a species’ assumed perceptual grain. We discuss those 

approaches below. 

Step 2b. Determine ecological variables. Selection of ecological variables should be 

guided by state-of-the-science knowledge about a species’ habitat relationships if the 

goal is to model a type of functional connectivity. For evaluating landscape structure, 

this isn’t formally possible, as putative connectivity is not associated with specific organisms. However, the variables should still represent something thought to influence 

ecological flows, and the rationales for the choices should be clear. When assigning 

resistance levels to structural elements, this assignment unavoidably contains implicit 

understandings concerning the relationship between the element and organismal biology. For example, giving urban areas high resistance values implicitly indicates that the 

resulting connectivity models are not appropriate when applied to organisms common 

in urban areas. Inherently, even if guided by biological studies, variables are chosen 

using expert opinion and, from a practical standpoint, are driven by data availability. 

Optimally, the choice of variables should be comprehensive (Beier and others 2008), 

but there is no way to guarantee that all potential factors affecting species movement 

will be included, and, in truth, a relatively small subset of possible variables will be 

available as continuous spatial data. For this reason, almost all of the studies considered some form of land use or land cover (41), and many included a measure of human 

population density or locations (18), and/or road density (32). Ideally, studies should 

choose variables more specifically related to assumed relationship between an organism 

and potential for movement but, data availability generally dictate that rough proxies 

be used. Given this, if possible, a number of potential connectivity models should be 

compared within a coherent model selection framework. Of the 47 papers we reviewed, 

14 used model selection to compare potential ecological variables. 

In addition to considering the biological rationale for choosing a particular environmental variable, it is also important to consider data accuracy; restricting data layers to 

those with high accuracy rates is desirable (Zeller and others 2012). At a minimum, data 

sources should be listed and data accuracy should be incorporated into the discussion of 

the likely accuracy of the resulting modeled linkages. Only two of the papers reviewed 

explicitly considered uncertainty associated with data sources. 

In many cases data reliability is affected by the scaling decisions associated with 

Step 2a, above. Different types of data are variably sensitive to scaling decisions. In 

general, classified data, such as the areal extent of forest cover, tend to be highly sensitive to scale when classification is based on achieving threshold value, and particularly 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 21

when a classified type is rare on a landscape. For example, if a cell needs to be >50% 

tree covered to be classified “Forest,” and forested areas are scattered within a largely 

agricultural landscape, as cell size increases, the area classified as Forest will predictably decrease—at some large cell size none of the cells will be 50% tree covered. Thus, 

when evaluating the accuracy of any mapped environmental variable, it is important 

to ascertain the degree to which its assumed value is dependent on scaling decisions.

Step 2c. Assign resistance values. In this step, each cell in the resistance surface is 

assigned a value denoting the ease of movement across that cell. This is generally the 

most critical step because the resistance values control the general nature of the final 

product. Zeller and others (2012) describe either a one or two stage process. The first step 

in either case is to assign initial resistance values either on the basis of expert opinion 

or empirical data. In the second stage, model selection, which requires empirical data, 

is used to finalize resistance values. 

Fifty-four percent of the papers we reviewed were also reviewed by Zeller and others (2012); we both found an over-reliance on expert opinion to guide resistance value 

assignment. Three papers we reviewed used “landscape integrity,” a Structural Connectivity metric associated with anthropogenic features coupled with expert opinion to 

quantify resistance values. The remaining papers sought to reflect (generally, the inverse 

of) “habitat suitability” in the resistance surface. Twenty papers modeled habitat suitability (and therefore resistance) using exclusively expert opinion.

The importance of resistance value assignment in connectivity analyses cannot be 

overstated. While other steps will define the spatial arrangement and exact locations 

of connection paths (Steps 3 and 4, respectively, below), the resistance surface defines 

landscape connectivity and all results are highly sensitive to the method of identifying 

resistance values (Sawyer and others 2011). Not surprisingly, expert opinion has not been 

shown to be a robust method for parameterization of resistance surfaces (e.g., Pullinger 

and Johnson 2010; and see discussion in Zeller and others 2012). While there are cases 

where the exigencies associated with a perceived conservation crisis may require the 

use of expert opinion (e.g., Compton and others 2007), a connectivity plan built on expert opinion must be viewed with circumspection absent further testing and refinement 

(see Chapter 4 on model validation). At a minimum, it is important to define who is an 

“expert” (Krueger and others 2012), and expert opinion should be questioned as being 

useful beyond a local range of knowledge (Murray and others 2009). Four papers that 

we reviewed used a clearly defined method for surveying and compiling expert opinion 

(such as Analytical Hierarchy Process), which is more likely to properly quantify expert 

opinion. However, properly investigating what people believe should not be confused 

with properly investigating the likelihood that their beliefs are correct.

Following Zeller and others (2012), we define resistance surfaces based on empirical data as any model that yields estimates of resistance based on patterns observed in 

biological data. When evaluating the nature of empirical support for resistance surface 

construction, Zeller and others (2012) defined the following categories: 

1. Point selection function (PSF): correlation between presence data and ecological 

variables; 

2. Home range selection function (HSF): correlation between home range data (generally based on telemetry of instrumented organisms) and ecological variables;

3. Matrix selection function (MSF): correlation between distance (genetic or individual occurrence locations) and ecological variables without assuming the actual 

movement paths between locations; and 

4. Path selection function (PathSF): correlation between ecological variables (or 

the final resistance surface) to observed paths from empirical movement data 

(Figure 3). 
22 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Figure 3—Examples of resource selection functions used to create resistance surfaces, 

from Zeller and others (2012, Figure 2). (Permission to reprint figure granted by Springer 

and by the authors.)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 23

See Zeller and others (2012) for a discussion of the pros and cons associated with 

these approaches. Of the 24 papers that used empirical data to quantify resistance, 14 

began with expert opinion and used empirical data for model selection, 9 conducted a 

single stage empirical analysis, and 1 paper used empirical data for both model creation 

and selection. Empirical PSF were most commonly used (14 papers), followed by MSF 

(6), HSF (3), and PathSF (1). 

Although empirically based resistance surfaces are more closely tied to measured 

organism behavior than those derived from expert opinion, using habitat quality as a 

proxy for resistance (the most common approach in the literature) makes the implicit 

assumption that habitat suitability is a valid approximation for permeability to movement (Hagerty and others 2011). The extent to which this assumption is valid depends 

on the organism and movement type. For example, for an organism with low vagility, 

the organism can only move through habitats in which it can live for extended periods 

of time, possibly generations. In this case, movement corridors need to be habitat to 

be effective, and using habitat measure as a proxy for movement resistance is likely 

reasonable. Examples include the spread of plants and movement of small mammals 

along powerlines. On the other extreme are high vagility organisms and associated rapid 

movements. For example, the seasonal movements of ungulates from high elevation 

summer habitats to low elevation winter ranges may occur in hours or, at most, days; 

the habitat quality along the movement path is less relevant than the presence of actual 

physical barriers to movement. 

This understanding underscores the need to think carefully about the functional 

biological underpinnings of animal movements and of the types of connectivity to be 

modeled. Of the four approaches that use empirical data to model resistance (above), only 

the path selection function transforms movement directly into resistance and therefore 

does not contain implicit assumptions concerning the relationship between landscape 

attributes and movement. However, although path selection functions clearly require 

fewer assumptions than do the other approaches, there is often a mismatch between 

measured movements and the movement type associated with the desired connectivity 

map. Within-home-range movement data are easiest to acquire, but are only directly 

pertinent to Daily Habitat movement analyses. Demographic movements, for example, 

occur between sub-populations and are generally rare in empirical datasets. Therefore, 

using path selection functions to inform resistance surfaces generally requires the assumption that the rules that guide within-home-range movements are identical to those 

that guide between-population movements. Because between-population movements by 

necessity require crossing areas not suitable for home range establishment, the validity 

of this assumption is tenuous.

In many cases, landscape resistance is assumed to be functionally related to a combination of multiple ecological variables. The transformation of any multivariate habitat 

model into a resistance surface will, for example, require combining variables. But the 

need to combine variables may occur in structural connectivity analyses as well. For 

example, a cell that contains a plowed field and a road may be considered to be more 

resistant to travel than a similar cell lacking a road. While the premise that combinations of factors can lead to differential resistance is reasonable, it leads to additional 

complexities and uncertainties. Specifically, decisions need to be made concerning how 

these elements should be combined, and whether they should be, in a relative sense, 

scaled (e. g., should roads and habitat quality be considered of equal importance). In 

essence, combining environmental variables to produce a resistance value requires the 

creation of a mathematical model in which resistance is the dependent variable, and 

environmental variables are associated through arithmetic operators (e. g., addition 

or multiplication) with each environmental variable multiplied by a scaling coefficient (in this context even the decision not to scale is an explicit scaling: all coefficients 
24 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

are set to 1.0). Because resistance controls putative movement and the operators used 

to combine variables control resistance values, these decisions translate directly into 

understandings of how multiple environmental factors affect organism movement. For 

example, summing the resistance values across variables reflects an assumption that 

variable effects are additive while using a product assumes that effects are cumulative; 

a geometric mean assumes additive effects with a log-scale transformation. 

In general, there is very little to guide the choice of these weighting parameters and 

arithmetic operators unless they can be empirically derived from movement data (see 

Parks and others 2012) or represent the direct application of an a priori model. Combination of variables and weighting schemes should therefore not be taken lightly and, 

if model fitting is not possible, uncertainty analyses should consider the sensitivity of 

results to the chosen approach. 

Step 2d. Validate the resistance surface. In connectivity modeling, there are two 

important validation steps. The first, discussed in detail in Chapter 4, is the validation 

of the final connectivity model. This is critical, as the entire process of connectivity 

modeling contains so many assumptions that resulting models and connectivity maps are 

best thought of as a hypotheses rather than predictions. Additionally, it is important to 

validate all intermediate steps to the extent possible, particularly the resistance-surface 

model. Six of the papers we reviewed conducted cross validation for their resistance 

values. We list these efforts under the “Uncertainty Analysis” column in Appendix 1, 

instead of under “Validation of Resistance Surface” because true validation requires 

independent data. Cross validation uses a subset of the model training data, not independent data, and therefore provides an assessment of the stability of the resistance model 

rather than its correctness. True validation of the resistance surface requires empirical 

movement data to assess how well a species moves through a given habitat type or barrier, and whether actual paths follow mapped corridors. Lacking this, various degrees of 

validation can be achieved through testing against independently collected proxy data. 

For example, assuming that the resistance surface was based on an expert-opinion-based 

habitat model, the model predictions could be checked using an independent data set 

of species occurrence data or to resource selection scores associated with independent 

studies. Even where habitat models are based directly on empirical studies, the habitat 

models generated by these studies generally use data types collected differently, at very 

different scales and in different times and locations. These models therefore have to 

be imperfectly crosswalked to available data, and this crosswalk needs to be validated. 

Similar to using rigorous methods to quantify expert opinion, validating a habitat model 

does not directly test the validity of a resistance surface. It does, however, avoid compounding errors associated with improper implementation of the habitat model. That 

is, whether a good habitat model serves as an adequate proxy for movement remains 

untested, but it is unlikely that a bad habitat model will serve this purpose.

A form of quasi-validation is model fitting, in which the resistance values and 

structure of the resistance surface is modified to maximize the fit to independent data. 

In the literature, this has most commonly been accomplished by correlating derived 

ecological distances with genetic distances. In this approach, resistance values are 

modified, connectivity models run, and the resulting ecological distances between 

location pairs compared to the genetic distances between organisms collected at those 

same locations. Historically, this has been done using Mantel tests and partial Mantel 

tests, but concerns have been raised about the validity of this approach given spatially 

autocorrelated data (Raufaste and Rousset 2001; Guillot and Rousset 2013). However, 

issues associated with the specifics of Mantel tests do not change the need to determine 

appropriate weightings for resistance surfaces. Without some form of fitting, there is no 

way to quantitatively determine appropriate weightings or to assert that one weighting 

scheme is superior to another. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 25

Of the papers we reviewed, six papers used independent occurrence data for validation, 

with one of those papers using actual movement data (Driezen and others 2007). Other 

papers used alternative semi-validation approaches, including correlating ecological distance with genetic distance with the assumption that resistance surfaces would correlate 

with genetic structuring (7 papers), or comparison to a null model (2 papers), or more 

simply conducting an assessment of similarity between multiple model outputs (1 paper). 

If validation is not possible, at a minimum sensitivity of the results to resistance values 

should be reported; 11 papers considered sensitivity of results to the contrast between 

resistance values, the resistance values themselves, or the habitat suitability models used 

to determine the resistance values. This left 24 (51%) of the papers with no discernible 

uncertainty analysis (excluding cross-validation) or validation of the resistance surface. 

A properly validated model is judged not by the robustness of its design and underlying data and assumptions, but rather by its proven efficacy. However, lacking formal 

validation, there exists a hierarchy of resistance surface quality, such that model inference is likely to be more robust as one moves from expert opinion only to increasing 

reliance on empirical data. Within models that are based on empirical data, reliability 

increases to the extent to which utilized data directly describes the desired movement 

type (Figure 4). Further validation of the resistance surface, by comparing multiple 

methods, correlating with genetic distance data, or field studies of dispersability for a 

released individual continues to reduce uncertainty.

Figure 4—Hierarchy of uncertainty associated with resistance surface 

creation.
26 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Step 3. Define What is Being Connected

This step is often listed as a first step, however we list this after creating the resistance surface because often linkage termini are derived from the resistance surface. 

For example, if a habitat model forms the basis for resistance, often linkage termini are 

limited to large, contiguous areas of high quality habitat. Additionally, the type of movement being modeled sets the context for choosing termini. For example, if modeling 

genetic connectivity, termini might be nesting or denning sites. This step, though often 

approached casually, is a critical step in the process—after definition of the resistance 

surface, likely the most critical because once linkage termini are selected, the range 

of potential corridors is largely defined (Laita and others 2011). Just as the resistance 

surface formally defines landscape connectivity, the selection of termini defines and 

limits the specific movements to be modeled (Figure 5). 

Figure 5—Placement of termini largely defines the modeled linkages: (a) Circuitscape run with 3 nodes on a forest / 

grassland ecosystem (white is grassland, purple is sage brush); (b-d) modeled linkages change when only two of three 

nodes are sampled.

(a)

(c)

(b)

(d)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 27

We use the term “termini” (sensu, Beier and others 2008) instead of “patches” because 

connectivity can be modeled between points or polygons (3-dimensional patches in a 

GIS). Aune and others (2011) and Beier and others (2008) review multiple approaches for 

identifying what should be connected. For structural connectivity models, termini often 

represent known protected areas, areas of high “naturalness” (low human modification), 

unique topological or geomorphological landscape elements, or locations chosen using 

expert opinion. For functional connectivity modeling, termini can be defined as habitat 

patches or empirically derived species occurrence points. Advances in computational 

power also allow modelers to avoid choosing unique termini, instead calculating linkages between all possible combinations of cells in a GIS, or at least numerous randomly 

selected cells. Some approaches to accumulating ecological distance (discussed in step 

4, below) avoid the identification of termini entirely. 

Of the papers we reviewed, 27 applied some statistical or subjective rule set to the 

resistance surface to identify termini. Examples include applying a threshold value to 

the resistance surface to form patches, while others calculated a minimum value from 

a moving window analysis (grouping contiguous cells with mean neighborhood resistance values below some threshold). One paper overlaid a threshold habitat suitability 

index with representation of landscape types and special landscape elements, similar to 

a Conservation Area Design approach (Beazley and others 2005). One interesting approach was to use cost distance to “grow” home ranges out from known breeding sites 

through the resistance surface and use derived home ranges as termini (Decout and others 

2012). Thatcher and others (2009) used an independent telemetry data set to determine 

the statistical distance between habitats in known home ranges versus modeled home 

range areas, and chose modeled home ranges with smaller statistical distances as termini. 

Twenty-three papers considered minimum size in determining patches containing termini, 

and required minimum sizes were often related to home range size. Avoiding patches 

all together, Cushman and Landguth (2012) used lowest resistance cells as termini, and 

Theobald and others (2012) iteratively and randomly selected cells with highest landscape integrity (in this case defined as an index of the amount of human activity in an 

area; see also McRae and others 2012; Figure 6a).

The other 21 papers identified termini through approaches not reliant on the resistance surface. Five papers used protected area boundaries to define linkage termini. One 

paper relied solely on expert opinion to define patches, while 11 papers used empirical 

occupancy data. Examples of empirical approaches included defining areas with some 

minimum probability of occurrence from empirical data (with data different than that 

used to develop resistance surface; 2 papers) or actual observed locations (2 papers). 

Three papers used the centroids of empirically determined population locations and 5 

papers created polygon patches around population locations. Carroll and others (2012) 

calculated centrality (discussed below) between all cells, which does not rely on the 

identification of unique termini.

When choosing termini, scale is critical. It is important that if patches are used as 

termini, they reflect the perceptual grain of the conservation target. Often, patches are 

defined using patterns evident to humans; but these may not be evident to other organisms. Even a seemingly discrete patch, like a pond boundary, becomes a continuous 

gradient as one zooms in to finer and finer scales. Chetkiewicz and others (2006) provide 

a useful framework for considering patch size and structure in relation to connectivity 

type, summarized in Table 1. 

A second caveat is that any “patch” is both spatially and temporally dynamic, and 

linkages modeled between fixed points may not persist into the future under changing 

climates, land uses, conservation policies, or species demographics. Modelers need to 

seek a balance between identifying structural landscape elements that are likely to persist and functionally defined patches that may be less spatially and temporally robust. 
28 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Figure 6—Examples of connectivity modeled between different termini: (a) iteratively, randomly selected cells of lowest resistance value (Figure 3 in Theobald and others 2012); (b) LaRue and Nielsen (2008) mapped Least cost paths from patch edges 

to confirmed cougar locations (Figure 3 in LaRue and Nielsen 2008); and (c) Cushman and others (2009) spaced termini along 

the northern and southern borders of Montana to model bear movement from Canada to the Greater Yellowstone Area (Figure 

1 in Cushman and others 2009). (Permission to reprint figures granted by Wiley (a, c), Elsevier (b), and by the authors.)

The internal structure of the patch should also be considered when modeling linkages 

between patches. In patch-based connectivity models, it is common to use the border of 

the patches as termini (Figure 6b). Locating termini in this manner implicitly assumes all 

movement within the patch is uniform such that organisms occur at all locations along 

the patch borders with equal likelihood. If termini are located in this manner, the least 

cost path algorithm will identify the shortest ecological distance between two patch 

boundaries, regardless of the structure of the landscape at that point along the patch 

perimeter. For example, ravines and riparian waterways may funnel species to a certain 

point along the patch edge, yet the modeled least-cost path may connect to another location along the patch edge where there is an impassable cliff band. Another approach is 

to place the termini at the centers of patches. While this has fewer ramifications than 

termini along the patch peripheries, it makes the equally unlikely assumption that all 

organisms originate their movements at the patch centroid. Where possible, we note 

whether a termini was represented as a patch edge, centroid, or otherwise in Appendix 1.

Of the papers in which we were able to determine whether linkage source was at 

the patch edge or centroid, 31 were from the patch edge, and only 1 paper used a patch 

centroid. Three other papers used other approaches, either systematically placing points 

within patches (Schwartz and others 2009; Wasserman and others 2012) or modeling 

linkages between all points at regular intervals along a patch edge (Cushman and others 

2009; Figure 6c). 

(a)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 29

(b)

(c)
30 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Perhaps the greatest effect of termini location, however, is associated with the decision 

to place a terminus at all. In most connectivity algorithms, paths are forced to connect 

all termini. For example, in the connectivity modeling software Circuitscape (McRae 

and Beier 2007), termini are designated as anodes or cathodes, and simulated electrons 

flow from the anode termini to the cathode termini. If a patch is designated to be a terminus, then electricity will flow from or to it, and flows will be concentrated around it. 

If a patch contains no termini, then electrons will only flow through it to the extent that 

it represents a low-resistance route between other patches that have been designated as 

having termini. In general, connectivity models obligately link one terminus to other 

termini, no matter how high the intervening landscape resistance. This attribute is largely 

due to the common assumption (found in all but two papers), that all paths are of equal 

value (e.g., in Circuitscape, that an equal quantity of electrons flow between each pair 

of termini) regardless of the landscape resistance between termini. Thus, these types of 

connectivity maps are better thought of as asking the question “if an organism were to 

travel from terminus A to terminus B, what path would it take?” rather than “how likely 

is an organism to travel between termini A and B?”.

Given the potential sensitivity of modeled results to selection of linkage termini, 

modelers must give careful consideration to this step in light of the connectivity model 

goals. Connectivity analyses should test the effects of different assumptions about how 

patches are calculated, identified, and the effects of different grains and extents of 

patches being considered. At a minimum, the effect of internal patch structure should 

be considered when modeling potential linkages. The majority of papers we reviewed 

did not test sensitivity of results to patch locations. However, Epps and others (2007) assessed three different approaches to identifying patches: expert-opinion-defined patches, 

minimum convex polygons around empirical sampling locations, and an occurrence 

model from telemetry locations. Since their goal was to optimize resistance values, not 

map linkages, their results were not overly sensitive to these choices. It is primarily in 

the mapping of linkages where decisions regarding termini location become critical.

Table 1—Wildlife movement type, patch spatial structure, and analysis spatial and temporal grain in relation to connectivity 

modeling intent, adapted from Chetkiewicz and others (2006). 

Connectivity type Movement type Spatial structure Spatial grain Temporal grain

•	 Daily habitat •	 Food items search •	 Food item distribution

•	 Food patch shape and size

•	 Small-scale obstructions

Resource 

patch

Daily

•	 Daily habitat •	 Patch searching

•	 Traplining

•	 Territory patrolling

•	 Food patch configuration

•	 Shelter

•	 Abiotic factors and topography

Habitat patch Weekly

•	 Demographic

•	 Genetic

•	 Dispersal •	 Patch distribution

•	 Landscape features

Patch mosaic Yearly or Decadal

•	 Genetic

•	 Seasonal migration

•	 Range shift

•	 Landscape pattern

•	 Migration •	 Large scale topography barriers Region Yearly or Decadal
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 31

Step 4. Calculate Ecological Distance

Connectivity models seek to calculate the ecological cost of movement through the 

landscape (ecological distance) by associating paths or flows with the mapped resistance 

values given specific termini. The presumed relationship between the resulting patterns 

and actual movements lies in the assumption that the likelihood of movement between 

two termini is proportional to the ecological distance between them. In practice, there 

are three common models applied for calculating ecological distance over a resistance 

surface between termini: cost distance, current flow, and network flow. The benefits, 

weaknesses, and assumptions for each modeling approach are summarized in Table 2. 

In general, cost distance and network flow are route optimization algorithms, whereas 

circuit theory is a flow algorithm.

Cost distance models first calculate a cost surface, which represents the lowest accumulative cost distance for each cell in a raster surface, to the nearest terminus based 

on the resistance surface. Then, it uses the values in this surface to compute the least cost 

paths (LCP) between any 2 termini. As applied to mapping linkages for wildlife, least 

cost distance models assume that organisms have perfect knowledge of the landscape 

and therefore will choose paths that minimize cumulative ecological cost across the entire path. Resistant kernel modeling approaches are built on the same algorithm of cost 

distance models, but add a dispersal function to model expected density of dispersing 

organisms from each terminus, which declines with greater accumulated cost. The kernel 

values radiating out from each terminus are then summed to create a resistant kernel map.

Current flow models are based on circuit theory, whereby the resistance surface is 

analogous to a conducting surface in which resistance to current flow is uneven (e.g., a 

metal sheet of unequal thickness). Flow is approximated by modeling the surface as a 

web of resistors, where each resistor represents the local resistance to current flow associated with its location on the surface. When these ideas and methods are applied to 

the question of landscape connectivity, a landscape is viewed as a large complex circuit 

composed of a web of resistors; generally each cell in a resistance surface is a resistor 

with “wires” connecting it to its neighbor cells. Standard rules for electrical resistance 

calculation apply (e.g., resistors in series produce additive resistance to flow). Current 

is added at source nodes (termini) and flows toward ground nodes through the circuit. 

As related to wildlife movement, current represents the probabilistic movement across 

all possible paths in the landscape, assuming that organisms have no prior knowledge 

of that landscape, but are driven to move from a source terminus to a ground terminus 

and move from cell to cell based on the resistance values they encounter. While high 

flow areas are generally consistent with paths produced by LCP algorithms (most of 

the electrons will find the path that minimizes overall resistance between the anode and 

cathode), circuit designs are sensitive to the width of low resistance areas because resistance decreases when resistors are parallel in a circuit (based on Ohm’s law) whereas 

LCP are not (see Step 5 for a more complete discussion of these differences). 

Network flow models visualize organismal movement as being similar to water flow 

through a connected network of pipes. Network flow resembles current flow, except 

that network flow algorithms seek to identify the optimum routing through the resistant surface that maximizes flow while minimizing accumulated ecological cost. The 

interpretation is therefore not probabilistic (it does not summarize the probability that 

a random walker will reach a termini) but, like cost paths, is an optimization problem. 

Network flow calculates the centrality of all termini in a network and therefore has the 

advantage of estimating the relative importance of each path to overall flow across the 

network. Thus, network analysis is particularly useful for problems that require prioritizing functional or structural linkages. 
32 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 Table 2 —Comparison of methods to calculate ecological distance over resistance surfaces. Portions of table adapted from Aune and others (2011), Carroll and others (2012), and McRae and others (2008). Method Advantages Disadvantages Assumptions Best modeling applications Cost distance •	 Modest data needs •	 Incorporates influence of matrix and individual species behavior •	 Computationally inexpensive •	 Can incorporate dispersal distance into analysis (as a threshold only) •	 Sensitive to termini locations •	 Sensitive to analysis grain •	 Cannot reflect differences in bi-direc- tional costs (ease of walking uphill vs. downhill cannot be incorporated) •	 Can only calculate least cost path be- tween one pair of termini at a time •	 Temptation to represent a linkage as a single, 1 cell wide, least cost path (do not succumb!) •	 Does not inherently incorporate disper- sal distance •	 Paths are computed between termini regardless of total cost •	 Organism has perfect knowledge of the entire landscape and moves with intent to minimize travel cost between two known locations •	 The organism is destina- tion driven and wants to move from one terminus to the next •	 Identify likely locations for further refinement and inves- tigation •	 Movement behavior for a single individual between re- source needs within a familiar territory Resistant kernel distance •	 Same as least cost distance •	 Inherently incorporates dispersal distance into analysis and can use any functional form (e.g., linear vs. exponential decline in likely dispersal with distance from terminus) •	 Can simulate population patterns by weighting termini where larger popu- lations exist •	 Can calculate least cost distances between multiple termini pairs •	 Same as least cost distance •	 Organism has perfect knowledge of landscape within dispersal distance from source and moves with intent to minimize travel cost; areas with low cost distance back to multiple termini are likely to represent areas with higher probability of movement or use •	 The organism is destina- tion driven and wants to move from one terminus to the next •	 Identification of resource patches most likely to be used (breeding sites or water use) in familiar territory •	 Movement between popula- tions or home ranges in famil- iar territory (continued)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 33 Table 2 (Continued) Method Advantages Disadvantages Assumptions Best modeling applications Current flow •	 Modest data needs •	 Precise relationship with directed random walks •	 Can simulate populations patterns by injecting more current into circuit where larger populations exist •	 Sensitive to termini locations •	 Sensitive to analysis grain •	 Cannot reflect differences in bi-direc- tional costs (ease of walking uphill vs. downhill cannot be incorporated) •	 More highly resistant circuits in paral- lel reduce overall resistance (e.g., a 5-mile long cliff has less resistance to movement than a 2-mile long cliff) •	 Does not inherently incorporate disper- sal distance •	 Computational limitations: a landscape with N cells is transformed into an NxN matrix. In practice this places severe constraints on the resolution of mod- eled landscapes •	 Current will flow between termini re- gardless of intervening resistance •	 Organism follows move- ment pattern of random walker with no previous knowledge of the land- scape; decisions are made at each step •	 The organism, while lo- cally ignorant, is destina- tion driven and wants to move from one terminus to the next •	 Identify bottlenecks within broader linkages •	 Movement behavior for migra- tion of a large population (e.g., many ungulates during a sea- sonal migration) •	 Flow of genes over time Network flow •	 Modest data needs •	 Can incorporate multiple, distinct criteria (such as habitat resistance and land purchase cost) into a single analysis •	 Can incorporate climate change scenarios •	 Computationally expensive •	 Does not inherently incorporate disper- sal distance •	 Linkages that maxi- mize the amount of flow across minimum distances reflect likely movement paths •	 Comparison of results against other methods to identify sen- sitivity to model chosen •	 Produces network metrics to prioritize important nodes and linkages
34 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

It is likely that most animal movement reflects neither perfect knowledge (as in cost 

distance models) nor complete local ignorance of the surrounding landscape coupled 

with the overwhelming drive to move from one location to another (as in current flow 

models) (McRae and others 2008; Carroll and others 2012). However, the difference in 

assumptions concerning an organism’s knowledge of the landscape associated with cost 

distance and current flow algorithms is often of low practical consequence, because, as 

in any circuit, all electrons will travel from the source to the ground and, probabilistically, most will travel along the same low cost paths that are identified by least-cost 

path algorithms. Both algorithms treat the termini as being of very special importance 

to the organisms, being both the only possible source and the ultimate obligate destination. As noted above, the generation of the resistance surface and decisions concerning 

valid termini to connect have far greater impacts on the understandings of landscape 

connectivity than the specific algorithm used to calculate ecological distance. 

Of the 47 papers we reviewed, 46 applied some form of algorithm to model connectivity and 41 of them used a cost distance algorithm. Least cost distances from multiple 

sources often represent only the distance to the nearest neighboring terminus. Three 

of the papers we reviewed applied the resistant kernel approach. Seven papers applied 

circuit theory in their connectivity model. One of the papers modeled connectivity on 

the basis of network flow.

Only one paper compared current and network flow and also cost distance. Carroll 

and others (2012) found that some resulting linkages for wolves overlapped, while others did not (Figure 7). Three papers compared results from cost distance and current 

flow. Van Strien and others (2012) found that the best correlation between ecological 

(or Euclidean) distance and genetic distance for a species of damselfly varied depending 

on the ecological variables used in creating the resistance surface. They created a new 

approach, termed least cost transect analysis, whereby land cover variables were quantified along a transect centered on the path with the single shortest cost distance. Least 

cost transects had significantly better correlation with genetic distance when compared 

to least cost distance or current flow. Hagerty and others (2011) also found differences 

in correlation strength between ecological distance measured with least cost distances or 

current flow when compared to genetic distance for a tortoise; cost distance was better 

able to parse out barrier effects whereas current flow identified Euclidean distance as the 

primary control on genetic differences. Schwartz and others (2009) also found that cost 

distance approaches better correlated likely habitat preferences of wolverine and genetic 

distance than current flow, which again only identified the importance of Euclidean 

distance. Koen and others (2012) also found that Euclidean distance performed better 

than current flow ecological distance for modeling marten gene flow. These examples 

support the recommendation of Carroll and others (2012) that multiple approaches 

should be compared in an uncertainty analysis, and that for genetic distance at least, 

the additional null model of Euclidean distance should be considered.

Step 5. Map Potential Linkages

Results from the previous step provide comprehensive values of ecological cost 

across the entire analysis extent, which can be several million pixels in size. Modelers 

can simply provide a gradient map of the probability for movement within, or the priority for conservation of a specific area. However, for implementation of connectivity 

projects, often a spatially explicit sub-set of highest quality potential linkages must be 

identified. Thus, in this step, one takes modeled ecological costs (cost distances, current 

flows, or network flows) and applies some rule-set to map spatially explicit linkages or 

corridors. This requires species-specific design criteria that considers width, length, and 

types of suitable human activities within the linkage, given the life history needs and 

connectivity intent of species of interest (Harrison 1992; Cushman and others 2009).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 35

Figure 7—Carroll and others (2012) compared cost distance, circuit flow, and network 

flow methods for calculating cost distance and subsequently mapping linkages. They 

found results varied depending on method (Figure 3 in Carroll and others 2012). (Permission to reprint figure granted by Wiley and by the authors.)

In the case of cost distance analyses, the single path with the lowest total sum between 

two termini is called the least cost path. These models are sometimes called shortest 

path models as opposed to least cost paths to avoid confusion with monetary costs. 

Unfortunately, often modelers have presented only this single-pixel-wide least cost path 

connecting two termini as the “solution” to a connectivity analysis (Figure 8a), which has 

fueled the continuation of the timeworn “corridor controversy” (reviewed in Anderson 

and Jenkins 2006). A single-pixel wide linkage is unlikely to represent the exact path 

taken by an organism, and the LCP is very sensitive to the location of termini, which 

also are not exact. Further, an LCP can be identified through an area of completely inhospitable landscape as the result for a single misclassified cell in the resistance surface 

(Kautz and others 2006). Thus, LCPs may be sensitive to small map irregularities and 

the grain at which the landscape is modeled (Theobald 2005). 
36 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Figure 8—Examples of mapped linkages or paths from the literature; (a) Larkin and others 

(2004) used simple least cost paths (LCP) to model cougar movement in Florida (Figure 

3 in Larkin and others 2004); (b) Schwartz and others (2009) placed termini on a grid and 

computed all pairwise LCP, buffering each path with an arbitrary kernel and adding kernel 

heights associated with each pixel; (c) Kindall and Van Manen (2007) calculated the cost 

surfaces and then mapped areas of connectivity by using thresholds based on relative 

cost (Figure 4 in Kindall and Van Manen 2007; upper 10% least cost paths displayed); 

d) Cushman and Landguth (2012) used resistant kernels centered at fixed map locations 

to generate cost surfaces (Figure 3c in Cushman and Landguth 2012); and (e) Hagerty 

and others (2011) used cumulative current flow between populations to model connectivity 

for desert tortoises in the Mojave Desert (Figure 3 in Hagerty and others 2011). (Permission to reprint figures granted by Wiley (a, c), Elsevier (d), Springer (e), and the authors.)

(a) (b)

(c)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 37

We believe that mapping techniques that display areas of very 

good connectivity have merit when compared to techniques that 

only map the very best connectivity routes. Ideally, connectivity 

maps should illustrate multiple potential linkages, reflecting the 

likelihood that wildlife experience the landscape as a shifting gradient of possible movement paths given their life history traits and 

movement needs (Cushman and others 2009). In the case of cost 

distance modeling, a least cost corridor can be designated by buffering the LCP to select a broader swath of landscape neighboring 

the LCP. However, buffering the LCP (Figure 8b) does not resolve 

the sensitivity of the LCP to resistance layer errors or uncertainty. 

Creating a least cost corridor by taking the top nth percentile of 

least cost paths better reflects the idea that, while an organism may 

not know the ideal route, it can find a route that is among the best 

(Figure 8c,d; Figure 9). 

Figure 9—Even a well-modeled LCP does not necessarily represent the 

actual path taken by a species. In this map, Pullinger and Johnson (2010, 

Figure 6) illustrate the inferred movement path for caribou from telemetry 

points versus the modeled LCP. Considering the top percentile least cost 

paths, out to some species-specific width around the LCP, may provide a 

more reasonable representation of a linkage modeled using cost distances. 

(Permission to reprint figure granted by Springer and the authors.)

(d) (e)

Figure 8—Continued.
38 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Because circuit theory maps current flows, and virtually all cells have some level of 

flow, the least cost corridor idea is also intrinsic to the mapping of multiple linkages 

in circuit theory. Connectivity areas can be identified through a cutoff in proportional 

current flow (e.g., cells in the top 20th percent of current flow; Figure 8e). A primary 

difference between using thresholds to map linkages or corridors with current flow as 

compared to cost distance methods is that circuit theory inherently places greater value 

on wide paths or alternative paths. When resistances are in series (such as when an organism travels down a narrow corridor made up of multiple resistance cells), resistances 

are additive. When resistances are parallel (such as would occur in a corridor wider 

than a single cell) resistance decreases with increasing numbers of parallel paths (the 

reciprocals of the resistance along each path are added). Thus, the circuit analogy will 

indicate that wide corridors are more favorable for travel than are narrow corridors and 

that termini connected by multiple corridors will be better connected than termini that 

only are connected by a single corridor. One of the distinct advantages of using current 

flow models is the ability to map a “pinch point,” which is a relatively restricted area 

representing a landscape feature through which dispersers must pass. It should be noted 

that while the idea that wider corridors are better has a long history and is biologically 

reasonable, the biological rationales for this idea have little to do with electron flow 

through parallel circuits. In a circuit, multiple paths or wider paths (e.g., thicker wires) 

allow more electron flow and hence lower resistance. However, connectivity is not 

generally limited by organisms queuing up at pinch points. Rather, the assumed lower 

resistance associated with wide corridors is due to corridor width being in and of itself 

a desirable property; it allows a corridor to function as habitat, provides protection 

from threats associated with the matrix, or perhaps is simply perceived as less hostile 

by the dispersing organism. The intrinsic quality of cells is conditioned by the quality 

of adjacent cells. These differences may be subtle, but they should not be dismissed; 

while equivalent electron flow can occur across a broad area of medium resistance or 

a narrow band of low resistance, these 2 landscapes may not be identical to the target 

organism. For a more complete discussion of current flow applications for connectivity 

modeling, see McRae and others (2008). 

Six of the papers that were reviewed categorically mapped cost distance (3), resistant 

kernel results (2), or current flow (2). Of the 30 papers that provided a map of potential linkage locations, 23 applied a cost distance approach (plus an additional 2 papers 

that used a resistant kernel and 3 papers that compared cost distance with current flow 

or another approach). Of those 24 papers, 6 used only the LCP, and only one of those 

conducted some form of validation on the potential LCP linkage. Two additional papers 

mapped the LCP, although the primary intent was to compare ecological distance to 

genetic distance or to use ecological distance to weight a graph (see step 8; Figure 9). 

One paper used buffered LCPs to identify likely highway crossing locations. Two 

papers used home range as a minimum width to buffer the LCP. This is likely over simplistic, but a better approach than the four papers that used arbitrary buffers surrounding the LCP. Three papers categorically mapped the nth top percentile least cost paths; 

however, it is difficult to find biologically relevant means for selecting the nth percentile 

cutoff threshold for LCP inclusion. Two papers used a parabolic kernel smoothing of 

the LCP, whereby likelihood of use of a linkage drops off with distance from the LCP, 

accounting for the surrounding habitat quality. Kautz and others (2006) used telemetry 

data, literature review, and the surrounding habitat quality to buffer the LCP by a width 

that was likely to support movement for panthers in Florida. 

In addition to identifying the spatial extent (width) of the potential linkage, it is often 

useful to prioritize the importance of each linkage. One prioritization approach is to 

map the redundancy of linkages as an estimate of likelihood of use. Schwartz and others 

(2009) mapped (parabolic kernel smoothed) LCP between all pairwise combinations of 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 39

wolverine locations, then categorized linkage potential by the number of times a given 

cell was part of a pairwise linkage; Li and others (2010) used a similar methodology. 

Similarly, the use of resistant kernel models overlays cost distances from multiple termini 

to help prioritize those areas with lowest cost distance to multiple termini. As mentioned 

above, network analysis allows linkage prioritization. To prioritize linkages, Theobald 

and others (2012) categorically mapped the betweenness centrality for every cell. Betweenness centrality accounts both for the ecological distance between two termini and 

the position of each terminus within the network of the termini. This approach could 

be applied to functional connectivity as well, using habitat quality in lieu of landscape 

naturalness, as was done by Carroll and others (2012). 

Prioritization of linkages, however, depends on the likelihood of use for any specific 

linkage. LCP and LCC compute the best possible paths between termini, but do not 

discriminate between short, easy routes and long difficult routes. The same is true of 

circuit theory. It is, however, not difficult to factor the ecological costs into the evaluation of linkage importance. The resistant kernel approach, for example, assumes that 

the ecological cost to move from one point to another represents the probability of 

organisms making that movement (e.g., Compton and others 2007). Epps and others 

(2007) eliminated paths based on a cost threshold based on the measured correlation 

between cost distance and genetic relatedness; paths with costs associated with genetic 

independence (and therefore no evidence of movement) were eliminated. Parks and others (2012) proposed a general framework for linking the movement types modeled to a 

linkage weighting scheme using the LCC approach. They note that for movement types 

where the total number of organisms moving is important (e.g., demographic connectivity), mapped linkages should strongly discount paths with large ecological costs as it is 

unlikely that many organisms will use them. However, for other movement types such 

as long term persistence (e.g., range shift connectivity), these longer paths are of critical 

conservation importance. Thus, the weighting scheme should be linked to the purpose 

of the connectivity that is being modeled. In all cases, it is probably a good idea to set a 

maximum allowable path cost representing an insurmountable barrier for the organism 

and to eliminate any paths with costs above this threshold. 

Lastly, it should be noted that many factors other than putative ecological costs affect the use of areas by wildlife for linkages. Lindenmayer and Fischer (2006) list 13 

factors that influence wildlife linkage use, including target species life history traits, 

gender, biotic interactions, edge effects, food availability, vegetation attributes in the 

linkage, linkage width and length, vegetation gaps, size of termini connected, linkage 

redundancy, matrix condition, and dispersal behavior of organism. 

Step 6. Validate Potential Linkages

Modeled wildlife linkages represent hypotheses about where habitat and open space 

should be protected or restored to provide functional connectivity. All hypotheses require 

testing. Unfortunately, many reviews of connectivity modeling approaches fail to discuss 

validation in depth. We detail options for validation in Chapter 4. In this section we review the papers in Appendix 1 in light of linkage validation efforts. We only considered 

a study as having validated potential linkages if the researchers directly compared modeled linkages to independent data describing wildlife movement paths. We considered 

all other efforts to be either sensitivity analyses or validations of the resistance surface. 

Two of the studies we reviewed had the stated intent of testing the validity of modeled 

linkages. Driezen and others (2007) used a path selection function and model selection 

to build a robust resistance surface and identify the LCP for hedgehog dispersal in Belgium. Subsequently, they compared the LCP to independent radio-tracked movement 

data for a single hedgehog. Although the hedgehog followed lower resistance cells, its 
40 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

movement path was substantially different from the LCP. The authors recognized the 

need to test with more independent hedgehog data, but noted that animals are searching 

for food and avoiding predators, illustrating the improbability of an organism following 

the optimum LCP. Pullinger and Johnson (2010) also found that the LCP was a poor 

predictor of the precise spatial location of movement paths for woodland caribou. They 

found no statistically significant improvement in modeling movement paths when comparing straight line paths between termini versus those indicated by LCP. 

Of the 29 papers that sought to map potential linkages for specific species, 23 attempted 

no validation. Of the studies that attempted validation, most were qualitative in nature 

and may have been more akin to uncertainty tests as opposed to true validation. Carroll 

and others (2012) used a weight-of-evidence approach to qualitatively compare potential 

linkages resulting from three separate modeling approaches. Chetkiewicz and Boyce 

(2009) compared LCP maps to known highway crossing locations for both bears and 

cougars in Canada (of the small number of telemetry monitored animals, none crossed 

at the modeled LCP location). Epps and others (2007) compared sheep populations 

putatively linked based on connectivity modeling to those with empirical evidence of 

linkage (telemetry, mark/recapture), and Meegan and Maehr (2002) visually compared 

telemetry data for panthers with a single modeled LCP. Rabinowitz and Zeller (2010) 

conducted field searches for signs of jaguar presence along modeled linkages (areas of 

high conductance). Walpole and others (2012) applied the most quantitative approach, 

statistically comparing known lynx movement paths with modeled conductance values. 

They found that lynx traveled through areas with higher modeled current flow. They 

did not map specific linkages, but categorically mapped conductance values. Thus this 

test indicated that the movement model was correlated with independent lynx movements, but represents a very different test from one that tests for use of a specific path 

or group of paths.

Step 7. Assess Climate Change Impacts (Optional)

For some applications, evaluating current connectivity is sufficient. However, many 

 applications involve high-cost one-time management actions. In these cases, it is 

important to assess not only the current landscape but likely future landscapes when 

prioritizing management activities. Protecting current functional linkages without an 

eye on the likely future landscape conditions greatly increases the odds of creating 

expensive “bridges to nowhere.” No papers sought to map connectivity for the purpose 

of assessing longer term persistence against climate change (i.e., range shift connectivity), although a well-connected landscape is likely to be important for climate induced 

range shifts (Heller and Zavaleta 2009; Hodgson and others 2009, but see Hodgson and 

others 2011). However, Wasserman and others (2012) considered the effects of climate 

change, assessing scenarios involving elevation shifts in suitable habitat on potential 

genetic connectivity for marten. Similarly McKelvey and others (2011) modeled expected 

changes in connectivity for wolverines based on modeled changes in spring snowpack. 

They used understandings derived from Schwartz and others (2009) where linkages 

were based on relating snow cover to genetic patterns. McKelvey and others (2011) 

looked at the change in location of the paths given climate change, and the changes in 

ecological cost associated with moving between termini.

Integrating climate change and connectivity is a relatively nascent area of research, 

but we expect a coming explosion of new tools. Analyses of wildlife connectivity under 

climate change are currently being conducted using landscape arrangement optimization 

algorithms (Carroll and others 2010; Faleiro and others 2013), and Nuñez and others 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 41

(2013) have developed approaches to create linkages between habitat patches that support continuity along projected climatic gradients over time. There are, however, many 

impediments to projecting connectivity over time. One is the availability of downscaled 

data for those variables that define the resistance surface and the reliability of those data 

if available. A second is the question of whether and how termini should change. If, for 

example, an organism was, in the future, extirpated from much of its current range, many 

of the current termini would be obsolete. Given the importance of both of these components in resulting connectivity maps, high levels of future uncertainty are problematic. 

However, even if formal landscape futuring and connectivity modeling is not possible, 

this issue should be given thoughtful consideration prior to management actions. 

Step 8. Quantify Connectivity (Optional)

Quantifying connectivity can provide a summary value to assist in prioritization of 

critical linkages or habitat patches for protection or to assess scenarios of landscape or 

climatic change on connectivity. There are many metrics for quantifying connectivity 

of landscape patches, and nearly as many papers reviewing the options (Calabrese and 

Fagan 2004; Fagan and Calabrese 2006; Kindlmann and Burel 2008; Rayfield and others 

2011). We will not review them again here, but instead will focus on common methods 

applied in the resistance-surface connectivity literature. Most frequently, graph theory 

is used as a means of quantifying connectivity (Urban and Keitt 2001; Garroway and 

others 2008). Graphs are mathematical structures made up of nodes and edges; for connectivity purposes, these are generally represented as termini and linkages, respectively 

(Bunn and others 2000). Graph theoretic connectivity metrics are especially helpful in 

assessing the effects of adding or deleting particular termini or linkages (see Table 3 for 

a brief summary of metrics). 

Table 3—A brief summary of graph theory connectivity metrics, adapted from Garroway and 

others (2008). 

Betweenness: the number of shortest paths that a particular node or edge lies on. Assuming 

that interactions take place through the shortest path, then betweenness is a measure of the 

importance of a node or edge in terms of the bottleneck it creates.

Centrality: a measure of the relative position of a node or an edge in terms of connectivity or 

facilitation of node interaction (e.g., betweenness, degree, eigenvector centrality).

Characteristic path length: the mean of all pairwise graph distances connecting nodes. It 

can be used as a ‘fitness’ measure describing the ease of node communication.

Clustering coefficient: a measure of the probability that two nodes connected to a particular 

other node are themselves connected.

Degree: the number of edges connected to a node. If the edges are weighted, then edge 

weights are summed and this measure is generally termed ‘strength’.

Degree distribution: the distribution of node degree values of a network. The degree distribution is a particularly important measure of network topology and together with other metrics 

is diagnostic of certain classes of networks and some general properties of network topology.

Graph distance: the sum of the shortest number of distinct edges (or edge weights) connecting a pair of nodes.
42 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Bunn and others (2000) and Ziółkowska and others (2012) illustrate the application 

of graphs to identify thresholds of change in connectivity given node and edge removal, 

and the sensitivity of connectivity given assumptions about maximum dispersal distances. 

O’Brien and others (2006) also assessed model sensitivity to dispersal distance assumptions using a measure of graph cluster size. Betweenness, a measure of the importance 

of each node given the number of linkages that pass through that node, is also a commonly applied metric to prioritize linkage or termini importance. This can be applied 

to patches (e.g., Goetz and others 2009), or to every cell in a resistance surface, thereby 

functioning less as a means of quantifying connectivity for a graph, but as a means of 

mapping potential linkages as part of Step 6 (e.g., Carroll and others 2012; Theobald 

and others 2012). The betweenness measure can also be weighted by the area or habitat 

quality of the termini, providing a useful means of incorporating both the ecological 

distance between, as well as the importance of the termini being connected. 

Other graph measures can be applied to summarize overall connectivity, although 

different metrics reflect different properties of connectivity, and modelers should be 

aware of these implications (see Laita and others 2011 for a review). Decout and others 

(2012) calculated the integral index of connectivity to calculate overall landscape connectivity for the common frog. Alternatively, non-graph based metrics can be calculated, 

such as the number of habitat patches connected in the landscape or the largest patch 

index of connected habitat patches (sensu McGarigal and others 2002), as was used 

by Wasserman and others (2012) to assess connectivity changes under various climate 

change scenarios.

We conclude by noting that very few extant connectivity analyses carefully followed 

these six-eight steps. We acknowledge that some, such as formal validation and modeling future landscapes, are difficult and may not be feasible for many analyses. However, 

if you follow these steps, we believe both that your connectivity analysis will be as 

conceptually solid and robust as is possible and that you will be fully aware of those 

areas where untested assumptions are being applied and the effects of these assumptions on derived connectivity linkages. Alternatively, failure to formalize the processes 

associated with developing resistance-surface-based connectivity models can, and has 

led to a series of conceptual omissions that not only render the ultimate reliability of 

an analysis speculative, but also preclude any clear statement concerning what is being 

modeled in the first place. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 43

Chapter 4. The Importance of Validating 

Wildlife Connectivity Models1

It is clear, from the logic presented in Chapter 3, that resistance-based connectivity 

modeling relies on many assumptions. The first assumption is that movement rules can be 

collapsed to pixel-level resistance factors based on precisely mapped landscape features. 

The second is that organisms are goal oriented—they are actively trying to move from 

the source to the destination. This is perhaps most obvious in electron-flow algorithms 

where current (dispersing organisms) is drawn from the origin to the destination. The third 

is that most models assume organisms are uniform in behavior (e.g., age and phenotype 

are irrelevant). Lastly, there are assumptions about the levels of organismal knowledge 

of the landscape. Least cost paths, for example, assume absolute knowledge. All steps 

taken are chosen to minimize the total cost of passage from the source to the destination; 

locally optimal, but globally sub-optimal paths are never taken. It is also clear, based 

on the literature review in Chapter 3, that these assumptions, while perhaps reasonable 

for some species and movement types, are almost entirely untested. 

Given the complexity of species habitat requirements during dispersal and movement, 

and the many untested assumptions associated with most connectivity models, much 

care is needed in translating models into local, regional, and national connectivity maps. 

Specifically, we suggest that broad-scale connectivity modeling used to inform management would be strengthened by (1) evaluating the robustness of the connectivity models 

and subsequent maps to resistance parameterization and patch definition, (2) evaluating 

the connectivity algorithm through a sensitivity analysis, and (3) validation using independent datasets, especially when connectivity models were initially derived from expert 

opinion. Here validation specifically is associated with the application of independent 

data to determine the degree to which a connectivity model accurately represents use 

patterns and movement trajectories of target organisms. In this review we discuss model 

validation and ways in which independent data can be used to provide confidence in 

connectivity modeling efforts.

Agencies and private conservation entities have proven willing to overhaul land management strategies to prioritize wildlife connectivity based on information derived from 

connectivity models (Schultz and others 2013) —information that inherently has some 

degree of uncertainty. Yet, given the fiscal costs and lost opportunities associated with 

imprecise corridor placement, it is important that we apply some validation approaches 

to existing models prior to using them to guide management plans on landscapes. 

Validation

Models can be validated many ways, but, in ecology, are most often validated with 

the use of independent data (Schlesinger and others 1979). For example, habitat use 

models (e.g., resource selection functions) are based on the probability of use or occurrence in focal areas and are statistically based on observed occurrence frequencies. 

These are typically internally validated using subsets of the total data (e.g., k-fold cross 

validation or withholding data from model development to use as test data) and may be 

1This chapter presents ideas associated with a forthcoming journal article on validation of resistance 

models. Contributors include Winsor H. Lowe, David Theobald, Kim T. Scribner, Leona K. Svancara, 

Meredith Rainey, Erin Landguth, Stephen Spear, Todd Cross, and John Pierce.
44 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

externally validated using fully independent data collected at a different time and place 

(Pearce and Ferrier 2000). Resistance-based connectivity models are not usually dataderived statistical models. Even if components of the model have been fit to data (e.g., 

LCP costs correlated with genetic relatedness), the overall model structure is likely to 

contain untested assumptions (e.g., that genetic relatedness captures the relevant movement types). In this, they have more in common with conceptual models—sometimes 

called process or mechanistic models—in which a logical framework is constructed 

to describe a process. Whereas statistical models are directly built from data, process 

models are built from concepts and then validated with data. Thus, until validated, process models are best thought of as elaborate hypotheses that may be partially or entirely 

incorrect. Recognizing connectivity models as a type of process model, we recommend 

a general validation framework that applies across many model types This framework 

acknowledges the many interdependent steps involved in model development, from 

formulating the problem, to developing a conceptual model, to building and verifying 

computer code to validating the outputs (Table 4). 

Table 4—Categories of data that can be used to validate connectivity models, specific data types within each category, descriptions 

of common uses, and examples of these types of data in the literature. Note that examples are not cases where these 

data have been used to validate connectivity models.

Categorical 

approach Data type for validation Description of common uses Examples

Inferential Genetic markers Often collected to estimate population 

structure, genotypic diversity, 

and inbreeding, or to evaluate 

biogeographic hypotheses. 

Keyghobadi and others 1999; 

Schwartz and others 2003; McRae 

and Beier 2007; Trumbo and others 

2013

Inferential Biogeochemical markers Using trace element concentrations 

or stable isotopes to infer geographic 

origins and movement patterns.

Marra and others 1998; Rubenstein 

and Hobson 2004; Brattström and 

others 2010; Muhlfeld and others 

2012

Occurrence 

based

Occurrence Collected at multiple scales, often 

presence / detection of a species. 

Sometimes absence data or associated 

probabilities of detection also available. 

Nichols and others 2007; Gil-tena 

and others 2009; Zanini and others 

2009; Russell and others 2012

Occurrence 

based

Radio / satellite telemetry Collected to describe habitat use or 

evaluate survival and reproduction. 

Can be used as paths if collected 

frequently enough, or devolved to point 

occurrence data.

Copeland and others 2007; Jonsen 

and others 2007; Squires and others 

2007; Vashon and others 2008; 

Klaassen and others 2010; Mate and 

others 2011

Occurrence 

based

Historical (museum) Historical specimens from museums 

can be useful for rare or difficult-todetect species. Must be spatially 

referenced. 

Marra and others 2009; Schofield 

2009

Occurrence 

based

Species distribution

(camera traps, casual 

observations, non-invasive 

genetic sampling, etc.)

Occurrence data is modeled to produce 

maps of species distribution.

Manel and others 1999; Guisan and 

Thuiller 2005; McKelvey and others 

2008; Varela and others 2009

Path Based Satellite telemetry Unlike telemetry occurrence data 

(above), here the path of animal 

movement is the unit of measurement. 

Horne and others 2007; Patterson 

and others 2008; Sawyer and others 

2009; Colchero and others 2011
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 45

We believe there are three validation techniques most appropriate for connectivity 

models: Event/Predictive Validity, Face Validity, and Comparison to Other Models 

(nomenclature from Sargent 2009, 2012;). Event Validity is the comparison of events 

predicted in the model to events that occur in the actual ecological system, whereas 

Predictive Validity tests models ability to forecast in space and time. For example, 

Event Validity can be assessed using the correlation between predicted movements and 

actual movements within the modeled landscape, whereas Predictive Validity might 

be assessed based on movements in an area outside of the modeled landscape. At least 

for broad, regionally based connectivity models, it is unlikely that independent data 

detailing actual movements will be available across the modeled landscape. Rather, 

these data are likely to be limited to particular places and times, and will only allow 

partial validation. However, because process models are not directly constructed from 

data, partial validation is, however, the norm and its utility should not be dismissed. 

We reiterate: process models contain assumptions that are not supported by data, and 

without validation, model reliability is largely unknown. Thus, any validation even if 

partial or anecdotal is important.

Face Validity is another term for expert opinion, where those knowledgeable about 

the system evaluate whether the model behavior seems reasonable. All models should 

have some level of Face Validity, but we suggest that this approach provides only weak 

or minimal validation, especially if expert opinion was used overtly (e.g., the model was 

formally based on expert opinion) or covertly (e.g., landscape variables associated with 

resistance scores were based on expert opinion) to construct the model. Comparisons to 

Other Models can be a useful approach when other independent models exist. A good 

example comes from short-term climate modeling, where multiple statistical and process 

models are used to produce consensus predictions (Murphy and others 2004). If independently built model results converge, this can be considered strong validation because 

convergence is unlikely to occur due to random chance (weather forecasters often frame 

their confidence in future weather based on the degree of model consensus). Validation 

through model comparison, however, suffers from the same weaknesses as does Face 

Validity; true independence between models is difficult to achieve. For example, comparing corridors that were created using circuit theory and cost path methods will tend 

to converge because both are constrained by the same resistance surfaces and termini. 

Validation of connectivity models is therefore not likely to be a binary, comprehensive 

process (e.g., the model was or was not validated). It is important to understand the degree 

to which the model has been validated and to provide clarity as to which approaches 

were used. It is equally important to assess the relative strengths and limitations of those 

approaches in the specific context of the modeled landscape and organism.

Data Types For Connectivity Model Validation

Wildlife and fisheries biologists collect many types of data suitable for validating 

connectivity models through event or predictive validation techniques (Table 4). These 

data can be grouped into three categories: inferential, occurrence, and path (Figure 10). 

These categories and their applications to model validation are described below.

Inferential Data

Inference-based data refers to either biological or biogeochemical markers used 

to make indirect evaluations of movement (Rubenstein and Hobson 2004). Biological 

markers are morphological, behavioral, or genetic markers used to track individual movement, or groups of individuals of similar type, across large landscapes. For instance, 
46 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

biogeochemical markers use trace element concentrations or stable isotope signatures 

associated with particular areas and diets (Rubenstein and Hobson 2004; Muhlfeld 

and others 2012). These markers have been especially useful for assessing movement in species producing large numbers of propagules that cannot be individually 

marked (Thorrold and others 2001) and in species that disperse especially long 

distances (Groves and others 2002; Sepulveda and others 2009).

Landscape genetic data are the most common form of inferential data used to validate 

connectivity models (Manel and others 2003; McRae and others 2008). Here an index 

of relatedness (or its inverse, genetic distance) can be calculated between individuals 

across a landscape. Genetic distance is inversely related to gene flow and gene flow occurs when organisms successfully disperse and breed; high rates of successful dispersal 

are assumed to reflect low movement costs. Thus, high levels pairwise genetic distance 

between samples or populations serve as proxies for low rates of movement and are 

assumed to represent high landscape resistance. Pairwise genetic distances between 

samples can therefore be correlated with putative cost distances between sample locations, and resistance models having higher correlations are considered better supported 

(Cushman and others 2006). For example, Short Bull and others (2011) examined 36 

different resistance hypotheses on how black bears moved through a Rocky Mountain 

landscape and found gene flow, as estimated by molecular genetic data, was best explained by elevation, forest cover, and roads. 

There are many advantages to using genetics to validate connectivity models. Gene 

flow is mediated by the movement and subsequent successful breeding of an organism. Because the movement of an organism across the landscape is limited by passable 

landscape features, so too is the resultant gene flow. Therefore, genetic samples 

and molecular markers have been used to validate connectivity models by calculating connectivity/isolation metrics at a population and individual level from a single 

sampling occasion. Data can be obtained relatively easily and at low cost; sampling 

can be systematic (e.g., non-invasive genetic sampling grid) and/or opportunistic (e.g., 

sportsman-contributed samples); samples are useful so long as spatial coordinates are 

Figure 10—A conceptual framework for model validation adapted from Sargent 

(2009, 2012).
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 47

collected at a resolution appropriate to the connectivity question (Galpern and others 

2012). Additionally, genotyping data are precise; genotyping error rates are low and 

quantifiable, species-level misidentification is virtually non-existent, and major modeling assumptions (e.g., marker neutrality) are testable. 

Several additional approaches can be taken to infer movements from genetic data. At 

a fine scale, one can establish multi-generational parent-offspring relationships to document the movement, breeding, and subsequent gene flow resulting from demographic 

connectivity (Peery and others 2006; Araki and others 2007; Hudy and others 2010). This 

approach has several advantages, perhaps the most important is that the temporal frame 

is well defined. When using inferential data, it is important to remember that movement 

is, by definition, inferred rather than measured and genetic distance does not change 

instantaneously with changes in the landscape; there is a lag time. For example, several 

generations must pass before a new landscape obstruction is detected through genetic 

analyses (Landguth and others 2010). Additionally, inferential data may be insensitive to 

certain types of movements that direct movement data would detect. Seasonal migrations 

or habitat patch utilization may be entirely absent from relatedness patterns revealed by 

genetic data (Spear and others 2010).

Occurrence Data

There are many potential sources of occurrence data for connectivity model validation, 

including satellite and radio telemetry data, ground and aerial observation, noninvasive 

sampling, museum specimens with associated spatial locations, and remotely triggered 

wildlife cameras (Table 4). Occurrence data can be invaluable for validation of connectivity models because they provide a direct means of assessing whether a species and, 

in some cases, an individual moves across a landscape as predicted, by noting when an 

observation is within a corridor or area of likely movement. 

Telemetry data: We distinguish telemetry data from other forms of occurrence data 

because the ability to collect multiple point locations for a specific individual at regular 

intervals is particularly useful in this context. Telemetry data are uniquely able to capture 

critical movements of individuals, including long-distance migration and dispersal, if 

collected on an appropriate temporal scale. However, we note that telemetry data are 

generally not used to infer paths (see below) but instead are seen as a series of detections or occurrences. 

While telemetry would appear to be an excellent choice to validate connectivity 

models, there are few examples in the literature. Most studies utilizing telemetry for 

model validation have done so opportunistically, making post hoc comparisons of 

model predictions with available data. As such, results tend to be more anecdotal than 

confirmatory. In an exploration of landscape restoration opportunities for the Florida 

panther, Meegan and Maehr (2002) noted that their predicted least cost path crossed a 

river within a 4-km reach known to have been crossed by three radio-collared individuals. Similarly, Chetkiewicz and Boyce (2009) noted the frequency of least cost paths 

that fell near known grizzly bear and cougar highway crossing sites. 

While the straightforward use of telemetry data is for Event Validity, it can also be used 

in a Model Comparison framework. For example, Cushman and Lewis (2010) compared 

landscape resistance surfaces estimated from genetic data with black bear occurrence 

based on telemetry. They found that both telemetry and landscape genetic data predicted 

that bear movement was sensitive to forest cover, development and roads, and elevation 

(Cushman and others 2006; Cushman and Lewis 2010). Pullinger and Johnson (2010) 

used two alternative resistance maps to compare least cost paths to caribou migration 

movements from GPS data. Observed and predicted paths were compared for path 

sinuosity and a path deviation index, which gives the average distance between paths.
48 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Critical to validation with telemetry data is the degree to which these data capture 

within versus between home-range movements. Habitats that animals use to move within 

a home range can be vastly different from habitats that they chose to move between 

home ranges. Further, we must also acknowledge that not all movement outside home 

ranges is beneficial. Often, exploratory movements are taken by inexperienced subadults or other individuals that are socially excluded from suitable habitat (e.g., Roznik 

and others 2009). In these cases, choice of dispersal habitat may not provide short-term 

fitness advantages or long-term demographic benefits; using telemetry data from these 

individuals to validate a connectivity model may prove misleading. Inferential genetic 

data are stronger for separating beneficial movements; gene movement only occurs when 

dispersals are successful. This is one reason that using genetic and telemetry data in a 

Model Comparison framework is potentially so powerful; Telemetry detects movements 

missed by genetic indices and results are relevant to the current landscape, but fails to 

differentiate between harmful and beneficial movements. Genetic indices ignore all 

movements except for those movements with the known benefit of producing viable 

offspring but contain a multi-generation time lag. Thus, these two approaches provide 

contrasting windows into organism movement patterns. Relating this to the movement 

types defined in Chapter 2, telemetry is ideal for assessing Daily Movement and Seasonal Migration, whereas genetic patterns are optimal for Demographic, Genetic, and 

Range Shift movement types.

Understandings from telemetry data are not, however, instantaneous. Time is required 

to generate use patterns. A statement such as “the organism uses areas within the corridor preferentially” requires a sufficient number of relocations to support this statement 

statistically. Using location data in this manner to validate corridor use represents a type 

of resource selection function (RSF; Manley and others 1993). In RSFs, importance 

is inferred through frequency of use. When based on regularly or randomly collected 

occurrence data, frequency is a measure of time spent in an area, which may or may 

not be a pertinent metric to describe movements. Just as it is critical to think carefully 

about the types of movements and nature of linkage use when building a connectivity 

model, these same understandings will inform the utility of various data for the purpose 

of model validation. 

Non-telemetry occurrence data: Occurrence data can come from multiple sources. 

For example, organisms may be identified during formal survey activities, accidentally 

or intentionally killed and subsequently recorded, captured on remote camera sets, or 

seen by casual observers. One important source of occurrence data is museum specimens 

(Graham and others 2004; Jackson and others 2012). In the last decades, museums have 

become repositories of spatially referenced tissue samples that can be analyzed genetically to verify species identification. Other repositories of occurrence data are Natural 

Heritage databases, where state-level species occurrence data is often collated, proving a 

wealth of opportunities for validating connectivity models. However, many movements 

will be poorly represented by non-telemetry occurrence data. For example, if an animal 

moves quickly through a corridor, the likelihood of casually detecting it while in the 

corridor may be low. Similarly, non-telemetry occurrence data are often limited spatially 

(e.g., adjacent to roads) and are therefore frequently non-representative; presence or 

absence of occurrences within corridors could be functions of sampling intensity rather 

than landscape condition. In general, casually collected occurrence data will therefore 

provide weak anecdotal validation. These data, however, should not be ignored. Often 

they are freely available and therefore can provide quick and inexpensive checks on 

model expectations. For example, if occurrence data showed no relationship to putative 

linkages, this could indicate a serious error in one or more of the model assumptions. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 49

Path Data

Most conventional telemetry data devolve into point or occurrence data largely 

because the time between detections was large and telemetry error great, preventing 

inferences about the actual path taken. However, with newer GPS-based telemetry devices, both of these issues can be resolved allowing inferences to be made of the actual 

path used by an organism (Brown and others 2012). These paths will provide strong 

validation for connectivity models. Unlike occurrence data, which are scalar, path data 

are composed of movement vectors, having properties such as velocity and direction. 

Paths are the movement data themselves and, therefore, do not require the steadystate assumptions needed when transforming telemetry data to movement data (see 

Moorcroft and others 2006; Patterson and others 2008). Because paths approximate 

actual movements, movement rules can be tested directly by comparing expectations to 

path structures (Chetkiewicz and others 2006). For example, if certain landscape features 

are considered to have high resistance (e.g., major highways), then, when faced with 

alternatives, organisms should choose to avoid crossing these areas (e.g., Whittington 

and others 2005). 

Path data can also be used to track rapid movements through areas for which, because cumulatively little time is spent there, occurrence data will be sparse. However, 

unless the instrumented organisms represent the population adequately, path data will 

be anecdotal in nature. 

Path data are not commonly used to validate connectivity models; however, we expect this to change with the development of new state-space models, which are a class 

of time-series model that predict a system’s future state based on a probabilistically 

derived process model (Horne and others 2007; Patterson and others 2008). Statespace models estimate the probabilities of a particular state (e.g., location) and model 

variables (mean speed and turn-angles) and subsequently incorporate these parameters 

into a flexible future forecasting model. The combination of these models with finescale satellite telemetry data is rapidly improving our understanding of animal dispersal 

and movement (Horne and others 2007). For example, Vergara and others (2013) used 

state-space models and translocation experiments with austral thrushes to show that the 

use of riparian strips for connecting between habitat patches is highly influenced by the 

surrounding landscape. We believe that state-spaced models will provide one of the best 

ways to validate connectivity.

The Case for Monitoring

Connectivity modeling is popular today due to perceived threats to natural linkages 

due to urbanization, land conversion, and climate change. Areas where conservation 

decisions are urgent may not be areas with large quantities of extant data on a specific 

target species. Thus, it is likely that connectivity models used to inform decisions will 

be largely or wholly unvalidated. However, there is no reason that this situation should 

be permanent. Targeted monitoring (Nichols and Williams 2006) provides an efficient 

and coherent approach to collect pertinent data, especially in a model-testing framework. 

Monitoring underpass and overpass structures in Banff provides a straightforward example. 

In Banff National Park, Alberta, Canada, an extensive system of underpasses, overpasses, and wildlife fences were constructed to prevent vehicle collisions with wildlife 

and to provide connectivity across Canada 1, the major east-west highway in the country. 

However, at the time of construction, the efficacy of these structures was unknown. The 

simplest indication of efficacy is the presence of occurrences in the corridors. To this 

end, a series of track beds and cameras were monitored; across the first 10 years, track 
50 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

beds indicated more than 84,000 occurrences within the structures (Clevenger 2007). 

Thus, this monitoring indicated that corridors were being used. Importantly, however, 

use increased over time as animals learned how to take advantage of the structures 

(Clevenger 2007). More recently, genetic monitoring has begun in the areas adjacent 

to Canada 1. A recent study indicated that, for bears (Ursus spp.), genetic connectivity 

across the road appeared adequate (Sawaya and others 2014). Note that elapsed time 

was required for both of these evaluations; occurrence was conditioned by learning, 

and genetic patterns require several generations to reflect barrier removal (Landguth 

and others 2010). 

Conclusions

Connectivity is a critical requirement for conserving native biological diversity. 

With the high probability of directional climate change in the near future, connectivity 

has emerged as perhaps the primary conservation need, supplanting the conservation 

of specific habitats. A number of high profile connectivity modeling exercises are in 

progress (e.g., WGA 2009), with the anticipation that results will drive policy at state 

and regional levels, and in both agencies and private conservation organizations. Given 

the importance of maintaining connectivity for conservation biology, and the potential 

high costs associated with implementing these models, robust validation of connectivity 

models is essential.

Ultimately, we believe that testing connectivity models with a combination of genetic 

and path-based methods will provide the best opportunities for model validation. Path 

approaches will reveal movements within home ranges and dispersal events; genetic data 

will provide information on the outcomes of important movements, such as effects on 

fitness and population growth. A combination of these approaches will be most powerful. 

We also note that the direct evaluation of linkages is likely to involve the long-term collection of specific data. However, given the preponderance of non-validated connectivity 

models, even weak validation using any available data would represent a step forward. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 51

Model Validation Framework

A useful conceptual framework for model validation is that of Sargent (1982, 2009, 2012). Figure 11 is 

adapted from Sargent (2009, 2012), where the first stage is to establish a “Problem Entity,” which is the system, idea, situation, policy, or phenomena to be explored with models (e.g., enhanced landscape connectivity 

for a particular threatened species). Subsequently, a “Conceptual Model” is built that provides the logical or 

mathematical construct of the problem entity. In developing conceptual models, decisions are made concerning the intrinsic nature of the problem, which will dictate which mathematical paradigm it approximates and, 

given this, acceptable levels of simplification and abstraction (e.g., parameterizing resistance surfaces). The 

step of collapsing a complex phenomenon (evaluating species connectivity) into a conceptual model requires 

simplification and abstraction and occurs in an “analysis and modeling phase” (e.g., choosing a connectivity 

algorithm to use in a GIS environment and statistical metrics to evaluate its output). It is during this phase that 

the model is subject to verification, the process of ensuring that algorithms within the computer model are 

performing as intended. Verification identifies coding errors, numerical instabilities, and errors in translation 

between the conceptual model and the computerized model (Schmolke and others 2010). 

Once verified, the model then produces inference about the initial problem entity through computer experiments and tests (e.g., connectivity maps). Validation also occurs in this last phase, when external data are used 

to assess whether the model accurately reflects the system under study. While coding and code verification 

need to be correctly executed, it isn’t until the validation step that the extent to which the decisions made in the 

conceptual model are assessed. The process of model creation, presented above as a linear progression from 

problem to validated model, is an iterative process (Figure 11).

Overall, a model is created to represent a specific reality and for a specific purpose, and is validated with 

respect to its intended accomplishments (Sargent 2009). There are multiple approaches to test the validity of 

a model. The most common is to have the development team make the decisions based on internal tests conducted during model development. This approach has been criticized for a lack of independence and excessive 

reliance on expert opinion (Tropsha and others 2003). A second approach is to have the model users validate 

the model independent of the model developers; independence is also an issue here. A third approach, which 

substantially increases model credibility, is to involve an external peer group to independently validate the 

model using independent data.

Figure 11—Graphic depicting the three data types that can be used for validating connectivity models. The pink shapes are source and destination nodes, 

while the color map is predicted corridors from resistance modeling efforts. In 

all cases, validation is through the degree of correlation between the putative 

corridor and applied data. (Adapted from Sargent 2009, 2012.)
52 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 53

Chapter 5. Practitioner Efforts 

In this chapter, we review 31 resistance-surface-based connectivity projects in the 

United States (Appendix 2). All of these projects have a primary purpose of mapping 

potential wildlife linkages to guide conservation efforts. Most of the projects are published 

as agency or organizational reports, although several are also published in the conservation planning literature. Although not an exhaustive review, our summary represents 

the majority of relatively broad extent, resistance-surface connectivity planning efforts 

since 1998. The primary organizations conducting these projects were state agencies (8 

projects), non-governmental organizations (NGO, 8), or Federal agencies (6). Nine of the 

projects were conducted by a consortium of organizations, primarily state (6) or Federal 

agencies (4) in collaboration with NGO (6) and/or academic institutions (7). Seven of 

the projects are in the early phases of development, and some methodological details are 

unknown (marked with a question mark in Appendix 2). We review practitioner efforts 

following the eight steps outlined in Chapter 3. 

There are a number of additional efforts inside the United States that apply alternative 

methods, such as using actual path data, like the Wildlife Conservation Society’s Path 

of the Pronghorn project, http://www.wcsnorthamerica.org/WildPlaces/YellowstoneandNorthernRockies/PronghornFieldProgram.aspx, or the State of Colorado’s efforts to 

map lynx roadway crossings (Crooks and others 2008). Simulated annealing models are 

also applied ( see From Adirondacks to Arcadia http://www.twp.org/sites/default/files/

Adirondacks_to_Acadia_08Mar07.pdf, or the Heart of the West Plan http://wildutahproject.org/programs/heartofthewest) while other projects use expert-opinion-delineated 

linkages (for example, see Connecting Alaska Landscapes Into the Future http://www.

snap.uaf.edu/resource_page.php?resourceid=5). The Western Governors Association 

(WGA) is currently funding a western state-wide Crucial Habitat Assessment Tool 

(CHAT) program, with an expected completion in 2013 http://www.westgov.org/initiatives/wildlife/380-chat/#CHAT_states. CHAT will provide internet-accessible information 

on crucial habitats and linkages. Much of the current CHAT connectivity work applies 

maximum entropy models or expert opinion. Additionally, across the United States, 

numerous projects are underway or have been completed to map wildlife road-crossing 

corridors, including efforts in Alaska, Arizona, Colorado, Florida, Idaho, Maine, New 

Hampshire, New Mexico, Oregon, Utah, Vermont, Virginia, and Wyoming. Many of 

these efforts are summarized by Feinberg (2007). There is also an active effort to map 

linkages for wildlife conservation abroad, and we provide some examples in Table 5. 

Worboys and others (2010) also provide a useful summary of a number of international 

connectivity modeling efforts. 
54 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 Table 5—Examples of international connectivity modeling projects. Project Title Lead organization Organization type Author, year Map extent Species Resistance layer type Variables used for resistance surface Resistance score basis Calculate ecological distance and map potential linkages Sensitivity analysis or validation? Website Canada Inland Temperate Rainforest Conservation Area Design Yellowstone to Yukon NGO Craighead et. al. , 2004 Canada inland temperate rainforest Multiple focal species Focal species habitat Suitability Human modification land cover types + topographic features Expert opinion Least cost corridor No http://www.y2y.net/ Taku River Area Conservation Design Round River Conservation Studies NGO Heinemeyer et. al. , 2003 Taku River watershed, northwestern British Columbia Multiple focal species Habitat suitability models Vegetation type + forest age + topography + human impact Scientific expert opinion, traditional ecological knowledge, telemetry data Least cost path Validated habitat model http://www.roundriver. org/index.php/taku-river Forest Habitat Networks Scotland Forestry Commission Scotland Federal Moseley et. al. , 2008 Scotland Generic focal species Habitat suitability models for generic focal species Forest cover type + quality, based on expert opinion Expert opinion Least cost path Sensitivity of results to resistance values http://www.forestry.gov. uk/fr/INFD-69PF6U Connecting priority conservation areas in the main island of Puerto Rico The Nature Conservancy NGO Leidner, 2004 Puerto Rico NA: linking natural landscapes and protected areas Landscape integrity Forest Cover type + human impact Expert opinion Least cost path No http://www. conservationgateway. org/Files/Pages/ connecting-priority- conse.aspx Establishing Connectivity in the Southwest Amazon World Wildlife Federation NGO WWF , 2002 Southwest Amazon NA: linking protected areas Landscape integrity Forest Cover type + human impact Expert opinion Least cost path No http://science. natureconservancy. ca/centralinterior/ docs/ERAtoolbox/11/ Standard11_casestudy_ SWAmazonConnectivity. pdf Snow Leopard Connectivity Snow Leopard Conservancy NGO Jackson et. al. , 2011 Snow Leopard Range, Mongolia Snow Leopard (Panthera uncia) Focal species habitat suitability Elevation + topography Expert opinion Least cost corridor, circuit theory Planned http://www.arcgis.com/ home/item.html?id=f005 22011f144a49ab1f5c84b 6c05b71 Canada Inland Temperate Rainforest Conservation Area Design* Craighead Institute NGO Craighead et. al. , 2004 Inland temperate rainforest, Canada Multiple focal species Focal species habitat suitability Human population density + road density + land cover + slope + elevation + Expert opinion Least cost distance No www. savethecedarleague. org/docs/Inland%20 Rainforest%20CAD.pdf
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 55

Resistance-Surface Connectivity Modeling Steps

Below we go through the eight steps in resistance-surface connectivity modeling and 

relate each of these to the identified practitioner’s connectivity modeling.

Step 1. Define Type of Connectivity to Be Modeled

The majority of practitioner connectivity efforts (Appendix 2) modeled structural 

connectivity (11 projects), with one of these assuming that landscape connectivity would 

also provide for long-term persistence, given climate change (Range Shift Connectivity). Although these projects developed resistance surfaces from measures of landscape 

integrity, several discussed their intent to represent “dispersal” or “functional” connectivity. The California Essential Habitat project (Spencer and others 2010) is a good 

example of a project with the goal of modeling functional connectivity, but that begins 

the process with broad extent landscape pattern connectivity with planned additional 

phases to model species specific linkages at finer scales. One project sought to model 

“dispersal” and genetic connectivity, but did so without reference to any specific species, using landscape integrity to quantify the resistance surface instead. The remaining 

papers all used focal species (generally a suite of species) to model undefined “dispersal” 

(four) or functional (two) connectivity, dispersal and daily habitat (one), or dispersal and 

genetic (one) connectivity. One project conducted a conservation area design (CAD), 

and three projects sought to represent all forms of connectivity in the mapped linkages 

(Washington Connected Landscapes Project [WHCWG 2010], with a focus on genetic 

and range shift connectivity; Staying Connected Initiative [SCI Ongoing]; Montana 

Connectivity Project [Herbert and others 2011]). Two projects looked at connectivity as 

a range shift against climate change. One project did not define the type of connectivity to be modeled and four were too early in development to infer connectivity intent.

As is often the case, efforts to model functional connectivity types relied mostly on 

structural landscape measures, but sought to include process-based understanding for 

species-specific modeling. For example, two projects led by Beier and others (2007; 

SCW 2008) included numerous focal species (20-100) to represent a broad-spectrum 

of potential connectivity types. Focal species were chosen to be taxonomically diverse, 

sensitive to habitat fragmentation, represent diverse ecological interactions, and to 

include both corridor dwellers and passage species (ability to move through a linkage 

within a day). 

Step 2. Create the Resistance Layer

Step 2a. Resistance layer scale. Of the projects where analysis extent was set by a 

state or other political boundary, we assessed whether the extent had been buffered beyond the arbitrary boundary to avoid mapping errors. Buffered extents were used in nine 

projects and un-buffered in seven projects. The majority of projects did not consider the 

analysis grain from a species’ point of view; 30-100 m cell resolutions were most often 

applied. There were six projects that did explicitly discuss scale issues. The Southern 

Rockies Wildlands Network Project (Miller and others 2003) reviews issues with scale 

in the introduction, and both the Washington (WHCWG 2010) and Montana (Herbert 

and others 2011) connectivity projects do an excellent job of discussing how scale affects 

analysis results and interpretability. Both reports further discuss how, for some species, lack of data limit the ability to model certain functional types of connectivity. The 

Washington (WHCWG 2010), Montana (Herbert and others 2011), Linking Colorado’s 

Landscapes (Kintsch and others 2005), and California Essential Habitat Connectivity 

(Spencer and others 2010) projects all provide examples of a hierarchical scale approach, 
56 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

where modeling began with a coarse scale analysis intended to be followed by further 

analysis at finer scales. The Arizona Missing Linkages (Beier and others 2007) project 

is an example of a secondary analysis using finer-scaled data. 

Step 2b. Determine ecological variables. As in the literature review (Chapter 3), most 

of the applied projects relied on land cover (24) and a measure of distance to roads or 

road density (15). While human population density or urban development was also 

included in 7 projects, a measure of topography was more common for practitioner 

projects (15 projects). Ten projects only used a combination of these four variables, and 

3 additional projects only used a variable (or variables) representing land cover. Other 

commonly used variables included hydrology (6) and conservation or protection status 

(6). Only one report (Great Northern Landscape Connectivity (GNLCC Ongoing)) 

considered the sensitivity or modeling results to the quality of the ecological data, and 

two projects (South Coast Missing Linkages [SCW 2008]), and Linkage Network for 

California Deserts [Penrod and others 2012]) ground-truthed land cover data.

Step 2c. Assign resistance values. Of the 31 projects reviewed, 5 were too early in 

development to determine the method of assigning resistance values, and 23 used expert 

opinion to model resistance surfaces on the basis of either landscape integrity (13, see 

Figure 12 for example) or habitat suitability (8). Two modeled both. These projects used 

various approaches to combine multiple ecological variables into the resistance surface, 

including taking the sum, product, geometric mean, or maximum of the variable values. 

Five projects applied empirical methods to modeling resistance. The Washington Connected Landscapes Project (WHCWG 2010) used expert opinion to develop a suite of 

models and compared circuit-theory-generated distances to genetic data for model selection for one focal species (mountain goat). The other four projects used occurrence data. 

Both the Montana Connectivity Project (Herbert and others 2011) and Mapping Habitat 

Figure 12—Fields and others (2010) used human modification to create a resistance surface for a 

structural connectivity analysis. Construction of this surface is fully described in Theobald and others 

(2011); figure is a reprint of Figure 1 in Theobald and others (2011). (Permission to reprint figure granted 

by Springer, Wildlands Network, and the authors.)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 57

Connectivity Around Military Installations (Moody and others 2011) used the maximum 

entropy program MaxEnt (Phillips and others 2006) to predict realized ecological niches 

from presence only data and, in turn, inverted the resulting habitat suitability model to 

create the resistance layer. The California Landscape Connectivity (CLCC Ongoing) 

project is currently conducting occupancy modeling with species presence data, and the 

Pathways project in the Hudson Valley (Howard and Schlesinger 2012) used occurrence 

points and randomly generated pseudo absences to conduct random forest (Liaw and 

Wiener 2002) bioclimatic niche modeling. 

Step 2d. Validate resistance surface. Of the projects using expert opinion to create a 

resistance surface, one project conducted semi-validation of the resistance surface. The 

Northeastern Resilience Network (Anderson and others 2012) calibrated the expertopinion-derived resistance surface to known movement paths. The Washington Connected 

Landscape Project (WHCWG 2010) plans to validate expert-opinion-derived resistance 

values for sage-grouse with genetic data. For empirically based efforts, the Mapping 

Habitat Connectivity Around Military Installations (Moody and others 2011) project 

conducted field experiments testing target species’ movement behavior in different habitat 

types and across habitat boundaries to validate their resistance surface values (Figure 13), 

and the California Landscape Connectivity project (CLCC Ongoing) plans to validate 

their occupancy modeling with genetic distance data. Seven other projects conducted 

uncertainty analysis on the resistance surface, including testing various resistance valFigure 13—Moody and others (2011) evaluated resistance surfaces by comparing independent species dispersal data against cost-distance models. Here (Figure 11 in Moody and others 2011), a longdistance dispersing juvenile red-cockaded woodpecker is compared to the 25% least-cost corridor. 

(Permission to reprint figure granted by the authors.)
58 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

ues (5 projects, 2 of which used a factorial design to test multiple resistance values) or 

conducting cross-validation of the resistance surface (1 project). One project, Mapping 

Habitat Connectivity on and Around Military Installations (Moody and others 2011), 

assessed uncertainty related to resistance variables and values, as well as the functional 

form of the relationship between habitat suitability and resistance. The Pathways project 

(Howard and Schlesinger 2012) provides a good example of conveying uncertainty, 

providing a ranking of relative confidence of model fit for each species.

Step 3. Define What Is Being Connected

Most projects applied rules to the resistance layer to delineate patches used as linkage termini. Approaches included simulated annealing or expert opinion to create 

patches that clustered areas with high levels of focal species habitat suitability (from 

resistance surface), species representation, and special elements (CAD, 2 projects) or 

moving window analyses over the resistance surface to group high quality habitat into 

patches (which then served as termini) for 4 projects. Of the moving window analyses, 

two projects (Arizona Missing Linkages (Beier and others 2007) and Linking Colorado 

Landscapes (Kintsch and others 2005) used different sized windows to represent focal 

species’ perceptual grain. Arizona Missing Linkages was further notable in that the 

researchers lowered the resistance values in some of the patches so as to encourage 

“stepping stone” behavior whereby species movement would follow paths of smaller 

patches linking larger patches. Three projects applied threshold values to the resistance 

surface and grouped contiguous cells above the threshold (high habitat suitability or 

landscape integrity); one of these projects (Montana Connectivity Project [Herbert and 

others 2011]) defined “contiguous” dependent on whether cells were within a speciesspecific “perception distance.” They also grouped several species with similar patch 

characteristic and movement behaviors into guilds to reduce the number of models 

computed. Three projects applied the resistant kernel approach, with lowest resistance 

cells serving as termini in two cases, and in one project, resistant kernels were run from 

all cells out to a limited distance to ensure computational feasibility. Wild Life Lines 

(Fields and others 2010) iteratively identified lowest resistance cells to serve as termini 

in modeling multiple pair-wise linkages.

For projects that identified termini independent of the resistance layer, several papers 

used protected areas or natural areas, not directly derived from resistance layer but often 

using similar variables. One paper identified patches using habitat quality models for 

vegetation types (forests, grasslands, wetlands; Minnesota Terrestrial Habitat Connectivity [Richardson 2010]). Two projects used occurrence data points as centroids for at 

least some species (Great Plains Landscape Connectivity [Cushman and others 2010], 

Mapping Habitat Connectivity Around Military Installations [Moody and others 2011]). 

The Washington Connected Landscape Project (WHCWG 2010) applied three different 

approaches to delineating termini: known centers of distribution for well-documented 

species, moving window analysis to identify patches of relatively low resistance surface 

values for less well defined populations, and contiguous cells of relative natural land 

cover for landscape pattern connectivity.

Overall, of the projects where methods were identifiable, 17 connected patches from 

their edge, and 8 projects used a patch centroid, occurrence data point, or cell as linkage termini. One project accounted for resistance patterns internal to a patch by using 

a point 1 mile within a patch on either side of a road to identify road crossing locations 

(Locating Potential Cougar Corridors in New Mexico [Menke 2008]). Thirteen projects 

applied a minimum size threshold to patches. Two projects conducted some form of 

uncertainty analysis regarding termini identification. The Montana Connectivity Project 

(Herbert and others 2011) tested multiple patch delineation methods for some species, 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 59

all of which were reviewed and selected by experts prior to the final model runs. Linking Colorado’s Landscapes (Kintsch and others 2005) project tested various moving 

window analysis sizes and minimum patch sizes.

Step 4. Calculate Ecological Distance

We were unable to determine the method of calculating ecological distance for 5 

nascent projects. For the remainder, 20 projects used cost distance, 2 applied resistant 

kernels (Figure 14), 1 project used circuit theory, and 3 projects used a combination 

of these approaches. Two of the projects that applied a resistant kernel approach tested 

the sensitivity to the assumed maximum dispersal distance for species of interest; one 

project is still ongoing, and the other found high sensitivity (Cushman and others 2010). 

The Pathways project in the Hudson River Valley (Howard and Schlesinger 2012) 

used a unique method of converting the resistance surface into a triangulated irregular 

network (TIN), calculating the least cost paths between neighboring patches, and then 

calculating cost distance between all pairs along the TIN to increase computational efficiency. The Montana Connectivity Project (Herbert and others 2011) also extended 

the traditional cost distance approach by calculating pairwise cost distances between 

all pairs of patches and then combining those; we assume additively, but the method 

is unstated. The researchers for the project also tested circuit and graph theory-based 

approaches, and used the software program CorridorDesigner (www.corridordesign.

Figure 14—Example of a resistant kernel spreading out to a maximum constrained distance (bottom image) given the underlying resistant layer (top image; here, land use) (Figure 3.6 in Anderson and Sheldon 2012). (Pemission 

to reprint figure provided by The Nature Conservancy and the authors.)
60 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

org) early in the project, but found none suited their modeling purposes. The authors of 

Mapping Habitat Connectivity Around Military Installations (Moody and others 2011) 

also found that current flow approaches, when compared to cost distance and individual 

based movement models, did not work for their purposes, because they failed to suitably 

represent species with low dispersability. 

Step 5. Map Potential Linkages

Only three projects mapped least cost paths directly. The Pathways project (Howard 

and Schlesinger 2012) also included maps of the LCP; however, the emphasis was on 

prioritizing importance of land parcels for multi-species linkages. The use of tax parcels 

to map the number of intersecting linkages provided a mapping unit more useful for planning; however, the use of the LCP fails to recognize the possibility of multiple potential 

linkages. Five projects buffered the LCP with a minimum width that was not justified 

in external documents. South Coast Missing Linkages and Arizona Missing Linkages 

projects (Beier and others 2007; SCW 2008) mapped the union of all focal species’ LCP 

and then buffered by a minimum width (Arizona used an arbitrary 500 m; South Coast 

tailored buffer width to surrounding habitat type and species dispersability, Figure 15).

Figure 15—South Coast Missing Linkages mapped linkages by adding a variable buffer around the LCP based on surrounding habitat quality and species-specific needs (page 18 in SCW 2008). (Permission to reprint figure provided by 

Science & Collaboration for Connected Wildlands.)
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 61

Eleven projects categorically mapped cost distance results, with two projects mapping resistant kernel modeling results (path density), one categorically mapping cost 

distance, two categorically mapping the nth lowest percentile distances, and one categorically mapping the redundancy of LCP between areas of high naturalness (network 

centrality). The California Essential Habitat project (Spencer and others 2010) only 

calculated least cost distances within a 5-km buffer around natural landscape blocks, 

and then mapped the lowest 5% of cost distances within the buffers. The Montana Connectivity Project (Herbert and others 2011) first combined the cost distance maps from 

all pairwise patch combinations and then categorically mapped the nth percentile lowest 

distance paths. The Montana project also identified stepping stone patches within identified linkages that could provide stop-over habitat for species with lower vagility. The 

Mapping Habitat Connectivity Around Military Installations project (Moody and others 

2011) categorically mapped cost distance outputs, and then combined all cost distance 

surfaces using a weighted zonation approach to prioritize linkages across multiple focal 

species (Figure 16). The Washington Connected Landscape Project (WHCWG 2010) 

Figure 16—Moody and others (2011) combined calculated least cost distances 

for all focal species using a weighted zonation approach (Figure 45 in Moody 

and others 2011); red areas are higher, blue are lower conservation priorities, 

respectively. (Permission to reprint figure granted by the authors.)
62 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

mapped cost distances from four different hypothesized resistance surfaces for species, 

and then normalized each potential linkage by the least cost path between each pair of 

natural area patches, categorically mapping linkages by normalized cost distance below 

a maximum dispersal distance threshold.

Step 6. Validate Potential Linkages

Of the 27 reports reviewed where we could determine validation efforts, 19 did not 

attempt to validate modeled linkages. However, Fields and others (2010) discuss the 

potential of the Wild Life Lines project to serve for comparison against other broad 

extent connectivity models (such as Yellowstone to Yukon). Two connectivity efforts 

had plans to conduct validation, and 6 remaining studies conducted some form of 

Model Comparison validation, 5 of which were primarily visual comparisons between 

potential linkages that were modeled using different approaches. The Washington 

Connected Landscape Project (WHCWG 2010) compared mapped linkages between 

focal species and landscape integrity approaches, and they also inspected sensitivity of 

mapped linkages to underlying assumptions about landscape resistance (Figure 17). Three 

other projects visually compared linkages to other modeled outputs. Although neither 

Herbert and others (Montana Connectivity Project; 2011) nor Howard and Schlesinger 

(Pathways project; 2012) conducted validation per se, both efforts provide exemplary 

uncertainty reporting, detailing confidence in modeled linkages for each focal species. 

The Mapping Habitat Connectivity Around Military Installations project (Moody 

and others 2011) conducted the most substantial validation. They considered multiple 

modeling approaches (IBM, current flow, and cost distance) and compared them all 

to field observation data about species movements. They found current flow was not 

as robust as other approaches for their organisms of interest. The report also provided 

excellent graphics mapping both priority areas for connectivity conservation, as well 

as uncertainty associated with those areas (Figure 18).

Step 7. Assess Climate Change Impacts (Optional)

Of the 3 projects with intent to measure connectivity as a range shift for species 

persistence under a changing climate, 2 have not yet completed the planned climate 

change analyses. The third, the Pathways Project (Howard and Schlesinger 2012), used 

a random forest (Liaw and Wiener 2002) analysis to correlate occurrence point with 

climatically static (geology, soils, elevation, etc.) and dynamic variables (temperature, 

precipitation, snow depth). Based on this climate model, habitat suitability was then 

projected using model-based climate change scenarios. The project provides maps of 

land parcels that intersect either a suitable habitat patch or a linkage between patches for 

current and future time periods and demonstrates a clear northward/upward shift in high 

priority parcels. A few project reports recommend the application of climate analyses for 

future, finer-scale connectivity modeling efforts. Great Plains and North Pacific Forest 

Landscape Connectivity projects are currently conducting climate analysis [NPLCC 

Ongoing; Cushman and others 2010]) and are modeling habitat conditions under three 

different emissions scenarios and mapping connectivity for each. The Linkage Network 

for California Deserts (Penrod and others 2012) project uses the Land Facet approach 

(Brost and Beier 2012), identifying connectivity within areas of relatively similar topographic position, solar insulation, steepness, and elevation, assuming contiguity through 

these areas represents continued connectivity under a changing climate.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 63

Figure 17—The Washington Connected Landscapes Project compared modeled potential linkage 

sensitivity to underlying assumptions about species sensitivity to landscape resistance (Figure 

3.69 in WHCWG 2010). (Permission to reprint figure granted by the Washington Wildlife Habitat 

Connectivity Working Group.)
64 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

Figure 18—Moody and others (2011, Figure 48) provided excellent graphics mapping both priority 

areas for connectivity conservation, as well as uncertainty associated with those areas. (Permission to reprint figure granted by the authors.)

Step 8. Quantify Connectivity (Optional)

Both the Delaware Ecological Network and Maryland Green Infrastructure projects 

(Weber and others 2006; Weber 2007a) prioritized natural areas and linkages by summarizing a number of ecological variables for each, including rare species habitat, unfragmented forest area, and distance to roads. Three projects weighted the edges in a 

graph network using cost distance. The Linking Colorado’s Landscape projects (Kintsch 

and others 2005) calculated patch connectedness and link importance, weighting edges 

by 10th percentile cost distance. The Pathways project (Howard and Schlesinger 2012) 

measured betweenness centrality for each patch, and then mapped that back to the tax 

parcels to provide a more management-relevant mapping unit. Mapping Habitat Connectivity Around Military Installations (Moody and others 2011) assessed changes in 

graph connectivity given assumptions about maximum dispersal distances.

We preface our conclusions by noting that many of these practitioner efforts were still 

in process at the time we compiled these lists. As with the published scientific literature, 

we note that very few extant connectivity analyses have followed all of these eight steps. 

However, in general we would argue that these efforts were more aware of the problems 

and limitations associated with the applied data and methodologies and in many cases 

applied thoughtful approaches to at least evaluate the associated uncertainties. We think 

that most of these projects would have benefited from a formal evaluation against a 

checklist such as our eight steps provide. Even if, ultimately, one decides that a step 

either is not relevant or cannot be assessed given data limitations, comparison with an 

a priori list of criteria ensures that these decisions are made explicitly; it makes sure 

that the right questions have been asked. In Chapter 6 we provide specific approaches 

to guide this process.
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 65

Chapter 6. Guiding Questions for 

Practitioners 

Each connectivity modeling project has unique conservation goals. No set of guidelines will ensure success for all connectivity modeling efforts; we urge modelers to 

review available “best practices” lists in addition to this report (Beier and others 2008, 

in particular, 2011; Sawyer and others 2011; Rudnick and others 2012). However, we 

believe that the eight steps we have identified, if closely followed, will ensure that all 

important aspects of model development and validation have been addressed. Here, we 

provide a set of guiding questions and suggestions to assist practitioners in modeling 

robust wildlife linkages with resistance-surface methods. Think of these questions as a 

kind of check-list. You may answer the question with “I don’t know” or “We didn’t do 

that,” but it is important to make these knowledge gaps and process omissions explicit. 

Once explicit, one can begin to ask ancillary questions such as: “Can we find out?” and 

“Can we and should we do that?” 

Step 1. Define Type of Connectivity to Be Modeled

 1. What is the conservation problem? How important is connectivity?

 2. What is (are) the species of concern?

 3. What type of movement(s) will best respond to the conservation problem for the 

given organism(s)? See chapter 2 for a complete discussion of the type of organism 

movement and hence connectivity being modeled. Specifically state the type(s) 

of connectivity to be modeled.

 4. Specifically, how will retaining or enhancing this type of movement improve the 

organism’s fitness or resilience?

 5. How will this movement change the probability of persistence of the organism 

in a patch?

 6. What is the state of the knowledge about the given organism’s habitat preferences, 

life history, genetic, and demographic needs, and associated movement behaviors?

 7. What biological requirements are associated with the modeled movement?

 8. What data are available, empirical or qualitative, about the organism’s movement behaviors? What data are available that could be used as proxies for these 

behaviors, and do they represent appropriate proxies?

 9. Will one model be adequate to represent all types of movement or are different 

movement types sufficiently diverse to require different modeling approaches?

 10. Draw a conceptual model linking conservation problem, organism’s fitness needs, 

type of connectivity, resistance layer development, and linkage modeling. What 

are the assumptions at each step?

Step 2. Create the Resistance Layer

Step 2a. Resistance layer scale

 1. Is a hierarchical modeling approach, starting with coarse scale models, qualitative 

data, and general assumptions and refined with finer scale models an appropriate 

paradigm? If so, how does this affect the generation of a resistance layer? Where 

is this particular modeling effort intended to fit into the hierarchy?

2. What modeling extent is appropriate for the type of movement modeled? What 

modeling extent is sufficient to maximize the number of potential links identified 

to avoid mapping artifacts? Are data beyond the target area available?
66 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

3. What is the organism’s perceptual grain? How does it see the world, given the 

type of connectivity being modeled? What cell size, in a GIS, best represents 

this perceptual grain? What other methods could be considered to represent the 

organism’s perceptual grain? 

Step 2b. Determine ecological variables

4. What, specifically, are resistance-surface values intended to represent? Travel 

time? Fitness costs (e.g., mortality risks)? Search time? Difficulty in travel (e.g., 

physical barriers)? Habitat suitability?

5. List all of the biotic and abiotic influences on movement behavior. What variables 

would best serve as proxies for these influential effects?

6. What data are available that relate to the identified proxy measures? Are these 

data available at an appropriate scale and resolution? 

7. How does the scale (temporal and spatial) of the data relate to the organism’s 

perceptual grain and extent? How can mismatches between spatial and temporal 

scales be minimized?

8. How good are the data? How do classification and other errors in the available 

data affect model performance and inference? How sensitive are the data to scaling decisions?

Step 2c. Assign resistance values

9. What are the best available data and how can they best be applied to minimize 

uncertainty in the relationship between resistance-surface values and hypothesized 

movement behavior (see Figures 3 and 4)?

10. Are empirical data available for developing resistance values in either a one-step 

(model development) or two-step (model selection) framework? 

11. If no empirical data are available, how can expert opinion be obtained and quantified to incorporate and minimize uncertainty?

12. How certain is the relationship between modeled resistance values and movement 

behavior? 

13. How certain are you regarding the contrast between different resistance values?

14. How do multiple ecological influences combine to affect likely resistance to organism movement? How should ecological variables be combined to best represent 

these relationships? Do they need to be combined, or can empirical data be used 

in a matrix regression to evaluate data?

15. See Zeller and others (2012) for additional decision support.

Step 2d. Validate resistance surface

16. How sensitive are results to the analysis grain? (Select a reasonable grain on the 

basis of organism size, dispersability, movement type, etc., and conduct sensitivity 

test against finer and coarser grains.) 

17. How sensitive are results to the quality of ecological variable data?

18. How sensitive are results to the incorporation of different ecological variables 

used in creating the resistance surface?

19. How sensitive are results to the resistance values assigned and the contrast between different values?

20. How sensitive are results to the method used to combine multiple ecological 

variables into a single resistance surface?
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 67

21. What empirical data are available to test stability (cross-validation) of resistancesurface model? 

22. Are independent empirical data available for validation of the resistance surface? 

Are the available data directly related to the type of movement being modeled 

(e.g., genetic data may not be appropriate for daily life history movement)? What 

are the potential mismatches between the resistance surface intent and the available validation data?

Step 3. Define What is Being Connected

1. What type of habitat or landscape element requires connectivity to address the 

conservation problem?

2. How does the organism perceive these habitats or landscape elements? How can 

termini be represented to reflect the organism’s perception (both temporal and 

spatial; see Table 1)?

3. If the termini represent some form of patch (polygon), how will modeling account 

for movement dynamics internal to the patch? How much of the landscape lies 

within patches?

4. Are there empirical or qualitative data to support the termini choice (e.g., do 

occurrence data suggest these termini are used by the organism)? Similarly, are 

there empirical or qualitative data to support the decision not to place termini in 

specific areas (e.g., evidence that the organism does not exist in certain areas)?

5. How does the distance between termini reflect the movement behavior of the 

organism? Are the distances appropriate for the type of movement?

6. How sensitive are results to the placement of termini? Size of termini? Number 

of termini? How sensitive are results to using the centroid of the termini versus 

the edge?

7. How temporally and spatially robust are the termini? How are they likely to shift 

or change over time, and how does this affect modeled linkages?

Step 4. Calculate Ecological Distance

1. What ecological distance method best corresponds to the organism and movement 

type (see Table 2)? How well do the methods reflect an organism’s knowledge 

and perception of the landscape?

2. Test two or more methods. How sensitive are results to the chosen methods?

3. Is one method best for one aspect of movement? Should results combine ecological distances from multiple approaches, or does one method appear better for the 

modeling purposes?

4. Is the goal to locate the least cost path, a pinch-point, or to evaluate general connectivity across a broad area?

Step 5. Map Potential Linkages

1. How will map of connectivity be used in conservation planning? Is categorical 

mapping of ecological distance sufficient for intended map purposes? Are spatially 

explicit linkages necessary? How will the map be perceived by policy makers, 

funders, and the public? Are there legal ramifications associated with corridor 

mapping?

2. Is there any scenario under which a single LCP is a suitable representation for 

potential linkages? If so, how sensitive is the resulting path to likely errors in the 

underlying data used to build the resistance surface? 
68 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

3. How do the mapped linkages incorporate the surrounding landscape and account 

for habitat quality, organism’s life history needs during movement, and potential 

for multiple linkages (e.g., corridor dwellers, use of stepping stones, edge effects 

from neighboring land uses)?

4. What is the width of a mapped linkage and how does that affect its potential for 

use as a movement path? 

5. What is the length of a mapped linkage and how does that affect its potential use? 

Does the resulting linkage map reflect the vagility of the organism?

6. How sensitive are the results to assumed functional relationship between ecological distance and likelihood of linkage use for wildlife movement? 

7. How should linkages be prioritized?

Step 6. Validate Potential Linkages

1. Are there independent occurrence, inferential, or path data (Chapter 4) available 

for validating models? 

2. If empirical data are available are they independent of the data used to build the 

initial map?

3. Are validation data collected at (or relevant to) the same temporal and spatial 

scale of the map to be validated?

4. What are the biases associated with the collected data (e.g., occurrence data only 

on public land)?

5. If validation is not possible, how should sensitivity be tested? What key variables 

should be allowed to vary for sensitivity testing?

Step 7. Assess Climate Change Impacts (Optional)

1. Do downscaled climate data exist at scales relevant to the connectivity modeling 

effort? 

2. What is the projected magnitude and rate of climatic change for the study area?

3. Will potential linkages remain robust under shifting temperature and precipitation 

regimes?

4. Are there landscape elements or ecological variables that should be included in 

the resistance surface to account for climate change? Can modeling be conducted 

with multiple scenarios of projected climate change?

Step 8. Quantify Connectedness (Optional)

1. What are the assumptions underlying the chosen measure of connectedness? How 

does the measure relate to the organism’s perception of a connected landscape?

2. How sensitive is model inference to the measure of connectedness?
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 69

Chapter 7. Conclusions and Synthesis 

Connectivity is important for the long-term persistence of many organisms. Maintaining or enhancing connectivity has become a common conservation goal to offset 

increasingly fragmented habitat throughout the world. Furthermore, connectivity is 

essential for organisms to respond to changes in climate, large scale disturbances, and 

ecological changes due to factors such as the invasion of exotic species. If we experience 

rapid directional climate change during the next several centuries, large spatial shifts 

in optimum climatic niches are anticipated for many—probably most—organisms; if 

species are to keep pace with shifting habitats, dispersal through well connected habitats 

will be essential (e.g., Iverson and Prasad 1998). 

Ecologists have long understood that connectivity is critical for species persistence 

(Levins 1969b, 1970), but the study of connectivity has been fraught with controversy. 

Much of the debate surrounding landscape connectivity concerns whether linkages are 

likely to be effective (both financially and ecologically) given the uncertainties concerning 

organism movement behavior. The advent of cost-path modeling, geographic information systems, and nationally available ecological resource datasets has revolutionized the 

field of connectivity modeling, providing numerous approaches for evaluating landscape 

permeability. Thus, connectivity modeling has become common. The resulting graphics 

are attractive and detailed, and the maps provide precise locations for presumed linkages, 

potentially facilitating directed conservation activities. 

The emerging field of landscape genetics (Manel and others 2003) has also provided 

impetus for renewed interest in connectivity modeling. The movement of genes is closely 

linked to the movement of organisms and, in many cases connectivity maps have been 

generated based on correlations with genetic patterns.

In this manuscript, we have given overviews of the various methodologies and a 

framework within which to organize connectivity modeling, implementation, and validation. Additionally, we have provided extensive references both to published journal 

articles and on-the-ground applications of these methods. However, we have provided 

relatively little information concerning the efficacy of these methods; the relationship 

between these maps and actual animal movement patterns remains largely unknown. 

Basing connectivity on genetic patterns or other movement-based data (e.g., the 

output from state-space models) is clearly desirable; using these types of data provides 

some rationale for considering one connectivity map to be better than another. It does 

not, however, indicate in any absolute sense the quality or sufficiency of the modeled 

corridors. While recent work has questioned the model selection process (e.g., Guillot 

and Rousset 2011; Cushman and others 2013), many more fundamental issues surround 

the use of resistance surfaces to evaluate connectivity. Critically, these models do not 

incorporate important, but likely ephemeral biological exigencies: the need to locate 

food, avoid predators, or invade a dominant competitor’s territory. Population dynamics, which strongly drive both dispersal dynamics and desirable destination locations, 

are also not generally considered.

All resistance-surface-based connectivity algorithms assume a directional force that 

drives movements; organisms are dedicated to moving from one terminus to another and 

in some cases know the perfect route to follow. This very specific drive, when applied 

to a resistance surface and given a finite and fixed group of specified termini, channels 

movement into tightly defined linkages, reinforcing the idea that these structures have 

both reality and merit. However, this is not necessarily the case. If we relax these assumptions then both movement patterns and our general perception of them become 

very different. If, for example, movements across areas lacking suitable habitat were 
70 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015

largely random, there would be no formal corridors. Similarly the locations of source 

and destination termini may be highly artificial. Organisms disperse, seeking better 

habitat, and settle based on a local evaluation of habitat quality—locations that may or 

may not be identified as containing a pre-defined terminal patch. 

None of this is to say that connectivity modeling using resistance surfaces is not a 

useful and appropriate activity, especially when combined with efforts to validate these 

surfaces. Quite the contrary; it is a much better approach than previous strategies, such 

as drawing lines on maps based solely on consensus opinion. Among other things, it 

requires formalization of connectivity assumptions and their quantification, and is both 

understandable and repeatable. 

However, any connectivity map based on the approaches examined here must, lacking strong external validation, be considered to be a largely untested hypothesis rather 

than a tested solution to a problem. As we have noted, validation of connectivity maps 

is virtually non-existent. In part, this may be due to the relative nascence of wildlife 

connectivity modeling. While efficient algorithms for least cost paths have been around 

since the 1980s (Fredman and Tarjan 1987) with current approaches based on accumulated 

cost surfaces dating to the mid 1990s (Douglas 1994), the utilization of these methods to 

identify connectivity patterns for wildlife is quite recent (Walker and Craighead 1997). 

As such, it is only recently that land management agencies have broadly embraced this 

approach and begun to apply it to actual land management problems. 

Perhaps a simpler explanation for the lack of connectivity validation is that it is difficult. Movement data, and particularly between-population movement data, has been 

notoriously hard to collect. New technologies to sample (forensic and environmental 

DNA, digital infrared cameras) and locate (reliable, energy efficient GPS) organisms 

coupled with advances in population and landscape genetics now allow us to better 

estimate movements and evaluate the efficacy of putative linkages. However, these 

new technologies do not remove the need for long-term targeted monitoring of putative 

linkages to determine how well they actually are working. 

From our review of connectivity modeling, we can now provide some broad advice to 

those thinking of embarking on a connectivity modeling exercise for their region. First, 

is the recognition that not all connectivity modeling efforts are equal. Nearly anyone can 

download a raster coverage, reclassify the pixels to create a resistance surface, identify 

termini, and produce a seemingly meaningful connectivity map. However, efforts that 

are spent articulating objectives, understanding data limitations, and considering how 

the focal species may view the landscape (if that is, indeed, the objective) produce far 

better products that are more justifiable than efforts that fail to complete these steps. Due 

to this recognition, we delineated the eight connectivity steps detailed previously and 

listed guiding questions for each step. If followed, these provide a logical framework 

for conducting connectivity modeling. Following this process ensures that appropriate 

measures to improve model quality have not been overlooked. For example, in reviewing 

extant connectivity modeling, it is surprising the degree to which basic ideas such as the 

type of movement and even the target species have not been well defined. Clearly, the 

formal clarification of model objectives will improve both model quality and facilitate 

model validation. 

In closing, our advice is to take advantage of the strengths of resistance-surface 

connectivity analyses; these methods provide valuable tools to avoid resource conflicts 

and provide clear rationales for management prioritization. However, it is essential to 

remain aware of their weaknesses, assumptions, and methodological quirks. Lastly, we 

believe that wildlife movement monitoring is required prior to making any declarations 

or assumptions concerning actual linkage efficacy. 
USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 71

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82 USDA Forest Service Gen. Tech. Rep. RMRS-GTR-333. 2015 Appendix 1—Resistance-surface connectivity modeling literature reviewed in this report. Papers highlighted in grey did not have the primary intent of mapping linkages, but we include them because they offer something novel in their approach to general resistance- surface-based connectivity assessment. For details on individual columns, refer to the discussion in the text for the appropriate related modeling step.
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