United States Department of Agriculture / Forest Service

Rocky Mountain Research Station

Research Paper RMRS-RP-90

May 2012

Ecological Associations, Dispersal Ability, 

and Landscape Connectivity in the 

Northern Rocky Mountains

Samuel A. Cushman and Erin L. Landguth
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Cushman, Samuel A.; Landguth, Erin L. 2012. Ecological associations, dispersal 

ability, and landscape connectivity in the northern Rocky Mountains. Res. Pap. 

RMRS-RP-90. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, 

Rocky Mountain Research Station. 21 p.

Abstract

Population connectivity is a function of the dispersal ability of the species, 

influences of different landscape elements on its movement behavior, density and 

distribution of the population, and structure of the landscape. Often, researchers 

have not carefully considered each of these factors when evaluating connectivity 

and making conservation recommendations. We present a general method for 

efficient evaluation of functional connectivity for large numbers of native species 

across vast geographical areas. Connectivity was evaluated for 36 groups of species 

with different ecological associations; within each of these groups, three dispersal 

abilities were evaluated across the United States northern Rocky Mountains. We 

quantified the extent and fragmentation of predicted connected habitat for each of 

these 108 species and identify those for which the current landscape has the lowest 

area and the highest fragmentation of habitat. We then conducted a multivariate 

ordination and use landscape trajectory analysis to assess multivariate differences 

in the extent and fragmentation of connected habitat across taxa. We mapped 

habitat connectivity for each of the 108 species, quantified the extent and pattern 

of connected habitat for each species, identified which species have the most 

limited extent and most highly fragmented pattern of connected habitat, identified 

any groups of species with similar patterns of connected habitat across dispersal 

abilities, and quantified the sensitivity to landscape pattern of connected habitat to 

dispersal ability and different ecological associations. We found large differences 

among groups of species in terms of the extent and connectivity of habitat, and 

the sensitivity of connectivity to dispersal ability. Species with limited dispersal 

ability associated with low-elevation forest have the most limited and fragmented 

distribution of connected habitat. Species associated with high-elevation forest also 

appear highly vulnerable to habitat loss and fragmentation based on limited extents 

and connectivity of habitat.

Keywords: landscape connectivity, dispersal ability, resistant kernel, multi-taxa, 

Rocky Mountains

Authors

Samuel A. Cushman, U.S. Department of Agriculture, Forest Service, Rocky 

Mountain Research Station, Flagstaff, Arizona.

Erin L. Landguth, University of Montana, Division of Biological Sciences, Missoula, 

Montana.
Contents

Introduction...................................................................................................1

Methods.........................................................................................................1

Study Area ..............................................................................................1

Resistance Hypotheses............................................................................1

Resistant Kernel Modeling ......................................................................3

Analysis of Extent and Pattern of Connected Habitat ...............................4

Landscape Trajectory Analysis.................................................................4

Results............................................................................................................5

Landscape Connectivity Across Resistance Models and 

 Dispersal Abilities............................................................................5

Principal Components Analysis.............................................................10

Landscape Trajectory Analysis...............................................................13

Discussion....................................................................................................14

Habitat Connectivity, Dispersal Ability, and Ecological Associations.....14

Importance of Broad-Scope Multi-Taxa Assessment of 

 Landscape Connectivity.................................................................16

Species-Specific Connectivity ...............................................................17

Dispersal Ability and Habitat Connectivity............................................17

Scope and Limitations..................................................................................18

Uncertainty in Landscape Resistance....................................................18

Uncertainty in Dispersal Ability ............................................................18

Uncertainty in Species Distributions.....................................................18

Uncertainty in Critical Fragmentation Thresholds..................................18

Conclusion...................................................................................................19

References ...................................................................................................19
USDA Forest Service RMRS-RP-90. 2012. 1

Introduction

Habitat loss has consistently negative effects on biodiversity (Fahrig 2003), including reductions in species 

richness (Findaly and Houlahan 1997; Gurd and others 2001; 

Schmiegelow and Monkkonen 2002; Steffan-Dewenter and 

others 2002), population declines, and changes in distribution (Gibbs 1998; Sanchez-Zapata and Calvo 1999; Best 

and others 2001; Bascompte and others 2002; Donovan 

and Flather 2002). Habitat loss and fragmentation change 

the distribution of resources and can affect individual behavior and spatial activity patterns, changing the ability 

of the organism to acquire the resources needed to survive 

and reproduce (Mangel and Clark 1986; Wiens and others 

1993). Reduction in movement among habitat patches can 

have dire consequences for individuals and populations. 

Increased population isolation increases extinction risk by 

reducing demographic and genetic input from immigrants 

and reducing the chance of recolonization after extinction 

(Lande 1988; Schoener and Spiller 1992; Sjogren-Gulve 

1994). Subdivision and isolation of populations can lead 

to reduced dispersal success and patch colonization rates, 

which may reduce the persistence of the local populations 

and increase probability of regional extinction for the entire 

metapopulation (e.g., Lande 1987; With and King 1999).

One of the ultimate consequences of habitat loss and 

fragmentation is the disruption of movement patterns and 

the resulting isolation of individuals and local populations. 

The degree to which habitat loss or fragmentation is biologically relevant will vary among species depending on how 

each perceives and interacts with landscape patterns (Dale 

and others 1994; With and Crist 1995; Pearson and others 1996; With and others 1997). Less vagile species with 

restrictive habitat requirements and limited gap-crossing 

ability will likely be most sensitive to isolation effects (e.g., 

Marsh and Trenham 2001; Rothermel and Semlitsch 2002). 

In addition, the composition and structure of the intervening landscape mosaic may determine the permeability of the 

landscape to movements. Each habitat may differ in its “viscosity” or resistance to movement—facilitating movement 

through certain elements of the landscape and impeding it 

in others (e.g., Cushman 2006).

The functional connectivity of a landscape is a composite result of the simultaneous effects of several important 

processes. These include the dispersal ability of the species, the influences of different landscape elements on its 

movement behavior, the density and distribution of the 

population, and the structure of the landscape. Often, researchers do not carefully consider each of these factors 

when evaluating connectivity and making conservation 

recommendations (Cushman 2006), which may lead to erroneous conclusions. The goal of this paper is to present a 

general method for efficient evaluation of functional connectivity for large numbers of native species across vast 

geographical areas. The specific illustration focuses on 

functional landscape connectivity across the United States 

northern Rocky Mountains for a broad range of organisms 

expressing different sensitivity to landscape structure and 

different dispersal abilities. Specifically, we evaluate connectivity for 36 groups of species (totaling 108 species) 

with different ecological associations; within each of these 

groups, we evaluate three dispersal abilities.

We quantify the extent and fragmentation of predicted 

connected habitat for each of these 108 species and identify 

those for which the current landscape has the lowest area and 

the highest fragmentation of habitat. We then conduct a multivariate ordination and use landscape trajectory analysis to 

assess multivariate differences in the extent and fragmentation of connected habitat across taxa. The specific objectives 

are to: (1)map habitat connectivity for each of the 108 species, 

(2) quantify the extent and pattern of connected habitat for 

each species, (3) identify which species have the most limited extent and most highly fragmented pattern of connected 

habitat, (4) identify any groups of species with similar patterns of connected habitat across dispersal abilities, and 

(5) quantify the sensitivity to landscape pattern of connected habitat to dispersal ability and different ecological 

associations.

Methods

Study Area

The study area includes Montana and northern Idaho in 

the United States Rocky Mountains (Figure 1) and contains 

large areas of Federally managed forest land, including 

extensive Wilderness and roadless areas and private land, 

mainly in the large valleys between major mountain ranges. 

The human population in this study area is rapidly growing 

(up to 44% increases since 1980 in some counties; 2000 U.S. 

Census data), causing extensive changes in land-use practices on the landscape, and necessitating the evaluation of 

wildlife corridors. In addition, an extensive network of highways bisects the study area, potentially impeding species’ 

movement.

Resistance Hypotheses

Our analysis is based on quantification of landscape 

connectivity across a broad range of landscape resistance 

hypotheses. These resistance hypotheses express different 

patterns of movement cost across the study area as functions 

of landscape conditions, such as elevation, vegetation cover, land use, and roads. Each resistance hypothesis is in the 

form of a landscape resistance map (Spear and others 2005; 

Vignieri 2005; Cushman and others 2006).

We defined 36 resistance surfaces for analysis from 

the pool of 108 models evaluated in Cushman and others 

(2006). The selected landscape resistance models represented combinations of the effects of three landscape features of 

resistance to movement: elevation, forest cover, and roads 
2 USDA Forest Service RMRS-RP-90. 2012.

(Cushman and others 2006). Resistance of these features 

was modeled across four levels for elevation and three levels 

for roads and forest (Table 1). The four levels for elevation

(E) consisted of a null model (EN), in which there was no 

penalty for elevation in the resistance surface, and three inverse-Gaussian resistance models with minimum resistance 

of 1 at 500 (EL), 1000 (EM), and 1500 (EH) m elevation 

above sea level, respectively, 500 m standard deviation, and 

maximum resistance of 10. Similarly, three levels of forest 

were modeled. The first level was the null model (FN), in 

which forest cover had no effect in the resistance surface. 

The remaining two levels were models in which we posited 

that landscape resistance is minimum in closed canopy forest and linearly increases in non-forest cover types. In the 

forest high (FH) level, we stipulated high relative resistance 

for crossing non-forest cover types, representing a condition 

where an individual bear strongly favors movement through 

forest. In the forest low (FL) level, non-forest classes have 

lower landscape resistance (Table 2). Finally, three levels for 

roads (R) were used: a null model (RN) where there was 

no effect for resistance of roads, a model with relatively 

strong effect of roads on resistance (RH), and a model with 

Table 1. Description of factors and levels combined to create 36 landscape resistance hypotheses.

Factor Level Code Description

Landcover High selectivity FH Low resistance forest; high resistance non-forest

Low selectivity FL Low resistance forest; moderate resistance non-forest

Null FN No relationship with landcover classes

Roads High resistance RH High resistance due to roads

Low resistance RL Low resistance due to roads

Null RN No relationship with roads

Elevation High elevation EH Minimum resistance at high elevation

Middle elevation EM Minimum resistance at middle elevation

Low elevation EL Minimum resistance at low elevation

Null EN No relationship with elevation

Figure 1. Study area orientation map 

showing major roads and major 

land ownerships. BLM: Bureau 

of Land Management; FS: U.S. 

Forest Service; FWS: U.S. Fish and 

Wildlife Service; NPS: National 

Park Service.
USDA Forest Service RMRS-RP-90. 2012. 3

relatively weak effect of roads on resistance (RL; Cushman 

and others 2006). Isolation by Euclidean distance was included as a 36th model, represented by a raster layer with 

uniform resistance of 1 cost unit. The landscape resistance 

models corresponding to each feature and level were combined into the 36 landscape resistance models by addition as 

in Cushman and others (2006). To improve computational 

efficiency, the 36 resistance models were resampled to 270 m 

pixel size by bilinear interpolation. Cushman and Landguth 

(2010) showed that coarsening the pixels size in floating 

point resistance grids has little effect on the strength of landscape genetic relationships, which suggests that connectivity 

models are quite robust to coarsening of pixel grain.

Resistant Kernel Modeling

Pixel-level resistance to movement does not provide sufficient information to evaluate the strength and location of 

barriers and corridors. Cushman and others (2008) argued 

that while resistance maps are point specific, connectivity 

is route specific. The resistance model is the foundation for 

connectivity analyses, but it is explicit consideration of connectivity across the resistance surface that provides the key 

information for conservation and management. Specifically, 

functional landscape connectivity is a product of multiple 

factors acting simultaneously, including the dispersal ability of the species, its response to landscape conditions (the 

resistance map), and its distribution and density in the landscape. We utilize a resistant kernel connectivity modeling 

approach (Compton and others 2007) to explicitly incorporate these factors into our analysis.

Resistant kernel connectivity modeling has a number 

of advantages as a robust approach to assessing functional 

landscape connectivity for multiple wildlife species. First, 

unlike most corridor prediction approaches, it is spatially 

synoptic and provides prediction and mapping of expected 

migration rates for every pixel in the study area extent rather 

than only for a few selected “linkage zones” (Compton and 

others 2007). Second, scale dependency of dispersal ability 

can be directly included to assess how species of different 

vagilities will be affected by landscape change and fragmentation under a range of scenarios (e.g., Cushman and others 

2010a). Third, it is computationally efficient, enabling simulation and mapping across the entire vast geographical 

extents for a large combination of species (e.g., Cushman 

and others 2010b, 2011).

The resistant kernel approach to connectivity modeling 

is based on least-cost dispersal from a defined set of sources 

cumulatively across a resistant landscape. The sources in our 

case are all pixels in the study area with resistance of 1 (lowest resistance and highest quality dispersal habitat) in each 

of the 36 resistance models. The resistance surface is in the 

form of the cost of crossing each pixel. These costs are used 

as weights in the dispersal function such that the expected 

density in a pixel is down-weighted by the cumulative cost 

from the source, following the least-cost route (Compton 

and others 2007).

The initial expected density was set to 1 in each source 

cell. Using the model, we calculated the expected relative density of each species or species group in each pixel 

around the source given the dispersal ability of the species, 

the nature of the dispersal function, and the resistance of the 

landscape (Compton and others 2007; Cushman and others 

2010a). We wrote an ESRI ArcGrid (ESRI 2007) script to 

calculate the resistant kernel (Rk) density. The script uses 

the ArcGrid COSTDISTANCE function to produce a map of 

the movement cost from each source up to a specified dispersal threshold. These COSTDISTANCE grids are inverted 

and scaled such that the maximum value for each individual 

kernel is 1. Once the expected density around each source 

Table 2. Cover classes and resistance values used in landcover resistance modeling.

Cover class Resistance in FL Resistance in FH

Urban, Water 10 10

Water 10 10

Surface Mining 7 10

Shrub Flats 7 8

Rock 6 6

Agricultural, Snowfields or Ice 5 7

Snowfields or Ice 5 6

Mixed Barren Lands 4 6

Alpine Meadow, Shrub-dominated Riparian, Grass-dominated 3 6

Riparian, Wetlands, Mesic Upland Shrub, Xeric Upland 

Shrub Subalpine Meadow

Clearcut Conifer, Burned Forest 2 4

Forest-dominated Riparian, Aspen, Ponderosa Pine, 1 1

Lodgepole Pine, Western Red Cedar, Western Hemlock,

Mixed Conifer, Mixed Subalpine Forest, Mixed Whitebark Pine
4 USDA Forest Service RMRS-RP-90. 2012.

cell is calculated, the kernels surrounding all sources are 

summed to give the total expected density at each pixel. 

The results of the model are surfaces of expected density 

of dispersing organisms at any location in the landscape. To 

bracket the range of dispersal abilities of most animal species in the study area, we ran the models for each of the 35 

resistance maps across four levels of dispersal ability (D) 

corresponding to maxima of the COSTDISTANCE function 

of 5000, 10,000 and 20,000 cost units. These reflect dispersal abilities in optimal habitat that range from 5 to 20 km.

Analysis of Extent and Pattern of 

Connected Habitat

The resistant kernel modeling produces spatial predictions of the areas on the landscape that are connected by 

dispersal given the resistance model, distribution, and 

density of the population and the dispersal ability of the 

species. Our objectives were to quantify the differences in 

the extent and pattern of connected habitat across resistance 

models and dispersal abilities. To accomplish this, we calculated a suite of fragmentation metrics with FRAGSTATS 

(McGarigal and others 2002) metrics on each of the 108 

maps of predicted connected habitat. We selected eight 

landscape metrics (Table 3) that reflect several universally 

important gradients of landscape structure (Cushman and 

others 2008). Specifically, these metrics were chosen to robustly reflect two major gradients of landscape structure that 

are particularly important in driving population response 

to landscape structure (Cushman and others 2010b). These 

two gradients are (1) a gradient from high extent of connected habitat to low extent of connected habitat; and (2) a 

gradient from low edge density, small number of isolated 

patches, and high habitat aggregation to highly fragmented 

conditions characterized by high density of isolated habitat 

patches of small size and high total edge density.

Landscape Trajectory Analysis

Multivariate ordination has frequently been used to 

efficiently summarize differences in landscape structure 

among many landscapes, as measured by many landscape 

metrics (e.g., Riitters and others 1995; Cushman and others 

2008). In our case, we have a single study area landscape 

but 108 different maps of functional connectivity based 

on different ecological associations and dispersal abilities. 

In addition, we were interested in quantifying the differential effects of resistance map (ecological association) 

from dispersal ability. This was done by conducting landscape trajectory analysis within the ordination framework 

(Cushman and Wallin 2000; Cushman and McGarigal 

2006). Landscape trajectory analysis is a method to quantify multivariate change in landscape structure across 

a landscape, usually measured at multiple times (e.g., 

Cushman and Wallin 2000; Cushman and McGarigal 2006; 

Nonaka and Spies 2006). In such an application, the displacement of a landscape in the multivariate ordination 

space between dates indicates the amount of change in 

landscape structure over time (Cushman and McGarigal 

2006). Comparison between initial and final locations in 

ordination space quantifies the total degree of landscape 

change. Displacement along each ordination axis provides 

quantification of landscape change along independent gradients of landscape structure. The degree of divergence of 

different landscapes in the ordination over time quantifies 

the degree to which the landscapes become more different 

in terms of landscape structure.

In this analysis, instead of quantifying landscape trajectories through time, we quantified trajectories in the extent 

and pattern of connected habitat across the three levels of 

dispersal abilities. We used principal components analysis 

on the correlation matrix of all 108 connectivity maps. We 

plotted 36 trajectories, consisting of the three different dispersal abilities (5000 m, 10,000 m, and 20,000 m) for each 

of the resistance maps. We then clustered trajectories based 

on proximity in the ordination space (McGarigal and others 

2000), enabling us to identify the resistance maps that are 

most similar in terms of the extent and pattern of connected 

habitat across dispersal abilities. Next, we quantified the 

displacement of each trajectory relative to the first two ordination axes to measure the amount of change in landscape 

structure as a function of dispersal ability. Then, we quantified the divergence of all pairs of trajectories (resistance 

Table 3. Landscape metrics calculated for each of the 108 connectivity maps produced by resistant kernel modeling.

Metric name Acronym Description

Percentage of Landscape PLAND Percentage of the landscape occupied by connected habitat

Number of Patches NP Number of isolated habitat patches

Correlation Length GYRATE_AM Correlation length of connected habitat

Area-weighted Mean Patch Size AREA_AM Area weighted mean patch size of connected habitat

Landscape Shape Index LSI Aggregation of connected habitat patches

Total Edge TE Total length of edge between connected habitat patches and non-habitat

Largest Patch Index LPI Largest patch of connected habitat percentage of the landscape

Clumpy CLUMPY Composition adjusted aggregation of habitat
USDA Forest Service RMRS-RP-90. 2012.

5

maps) across dispersal abilities to identify which converge 

to similar final landscape structures and which retain different landscape patterns across all dispersal abilities.

Results

Landscape Connectivity Across 

Resistance Models and 

Dispersal Abilities

To visualize changes in landscape structure across the 

different resistance models, we produced three-dimension-

al colored cubes for each landscape metric (Figures 2 , 3, 

and S1-S4). The cubes are organized as in Cushman and 

others (2006) and reflect a factorial of the three landscape 

elements (elevation, roads, and forest) that constitute the 

36 resistance models. For example, Figure 2a shows differ-

ences in percentage of the landscape covered by connected 

habitat across the 36 models at a 5000 m dispersal ability. 

Figures 2b and 2c show changes in the percentage of the 

landscape in connected habitat at 10,000 m and 20,000 m 

dispersal abilities.

The figures show two main patterns. First, the percent-

age of the landscape covered by connected habitat increases 

substantially with increasing dispersal ability. Second, 

across dispersal abilities, the species with the largest extent 

of connected habitat are those that are not sensitive to el-

evation or forest cover or those that are associated with the 

lowest elevations with relatively weak preference for for-

est cover. Conversely, across dispersal abilities, the species 

with the most limited extent of connected habitat are those 

associated with the highest elevations or those strongly de-

pendent on forest cover for movement. At the 10,000 m 

dispersal threshold, on average across the 36 resistance 

models, 61.5% of the landscape is occupied by connected 

habitat patches. Eight resistance models show less than 

40% of the total study area occupied by connected habi-

tat at 10,000 m dispersal ability (Table 4). Six of the eight 

are models predicting strong ecological associations with 

high-elevation forest, with increasing resistance to move-

ment at lower elevations and non-forest cover types. The 

other two models with less than 40% coverage of connect-

ed habitat are for species strongly associated with forest 

cover at the lowest elevations. In contrast, six resistance 

models showed extent of connected habitat amounting to 

over 95% of the study area. These are species not associ-

ated with elevation or forest cover, or those associated with 

low elevations but not limited by the extent of forest cover 

(Table 4).

A somewhat different pattern was observed for the num-

ber of patches of isolated habitat across resistance models 

and dispersal abilities (Figure 3). Figure 3 shows differenc-

es in the number of isolated patches of habitat across the 

36 models at a 5000 m, 10,000 m, and 20,000 m dispersal 

Figure 2. Percentage of the landscape in connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the 

three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability.
6 USDA Forest Service RMRS-RP-90. 2012. Figure 3. Number of isolated patches of connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability. Figure S1. Correlation length of connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability.
USDA Forest Service RMRS-RP-90. 2012.

7

Figure S2. Landscape shape index of connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the 

three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability.

Figure S3. Total length of linear edge of connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the 

three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability.
8 USDA Forest Service RMRS-RP-90. 2012. Figure S4. Clumpy index of aggregation of connected habitat across 36 resistance models, at each of three dispersal abilities. Colored cubes represent a three-way factorial of the three factors (elevation, forest cover, and road resistance). There are 36 combinations across levels of the three factors. Each subcube represents a specific combination. The value of the landscape metric is represented by the color of the cube, scaled linearly from minimum to maximum. The maximum value is red and the minimum is blue. The transparency of the cubes also increases with decreasing relative value of the landscape metrics, such that the lowest value is fully transparent. (a) 5000 m dispersal ability, (b) 10,000 m dispersal ability, and (c) 20,000 m dispersal ability. a b c
USDA Forest Service RMRS-RP-90. 2012.

9

Table 4. Description of the 36 resistance models used in the analysis, their number, the landscape trajectory numbers associated with that model, the percent of the 

landscape covered by patches of connected habitat at 10,000 m dispersal ability, the number of isolated habitat patches at 10,000 m dispersal ability, and the clumpy aggregation index at 10,000 m dispersal ability.

Trajectory

Model Model numbers Numberacronym number (Figure 4) Model description Percent of patches ClumpyEH 1 1-3 Minimum resistance at high elevations (1500 m) 0.438 103 0.9791EHFH 2 4-6 Minimum resistance in forest (strong) at high elevations 0.382 148 0.972EHFL 3 7-9 Minimum resistance in forest (weak) at high elevations 0.393 121 0.9752EHRH 4 10-12 Minimum resistance at high elevations with high resistance of roads 0.431 102 0.9772EHRL 5 13-15 Minimum resistance at high elevations with weak resistance of roads 0.432 101 0.9783EL 6 16-18 Minimum resistance at low elevations (500m) 0.836 11 0.9636ELFH 7 19-21 Minimum resistance in forest (strong) at low elevations 0.405 627 0.9526ELFL 8 22-24 Minimum resistance in forest (weak) at low elevations 0.453 405 0.9569ELRH 9 25-27 Minimum resistance at low elevations with high resistance of roads 0.83 13 0.9626ELRL 10 28-30 Minimum resistance at low elevations with weak resistance of roads 0.831 13 0.9638EM 11 31-33 Minimum resistance at middle elevations (1000m) 0.857 20 0.9758EMFH 12 34-36 Minimum resistance in forest (strong) at middle elevations 0.535 319 0.9697EMFL 13 37-39 Minimum resistance in forest (weak) at middle elevations 0.566 223 0.9734EMRH 14 40-42 Minimum resistance at middle elevations with high resistance of roads 0.853 18 0.9718EMRL 15 43-45 Minimum resistance at middle elevations with weak resistance of roads 0.854 18 0.9744FH 16 46-48 Minimum resistance in forest (strong) 0.624 350 0.971FHEHRH 17 49-51 Minimum resistance in forest (strong) at high elevations with high resistance of roads 0.376 154 0.9701FHEHRL 18 52-54 Minimum resistance in forest (strong) at high elevations with weak resistance of roads 0.377 150 0.9712FHELRH 19 55-57 Minimum resistance in forest (strong) at low elevations with high resistance of roads 0.39 657 0.9489FHELRL 20 58-60 Minimum resistance in forest (strong) at low elevations with weak resistance of roads 0.393 649 0.951FHEMRH 21 61-63 Minimum resistance in forest (strong) at middle elevations with high resistance of roads 0.529 322 0.9671FHEMRL 22 64-66 Minimum resistance in forest (strong) at middle elevations with weak resistance of roads 0.53 318 0.9685FHRH 23 67-69 Minimum resistance in forest (strong) with high resistance of roads 0.615 360 0.969FHRL 24 70-72 Minimum resistance in forest (strong) with low resistance of roads 0.617 359 0.9704FL 25 73-75 Minimum resistance in forest (weak) 0.955 26 0.9169FLEHRH 26 76-78 Minimum resistance in forest (weak) at high elevations with high resistance of roads 0.386 125 0.9733FLEHRL 27 79-81 Minimum resistance in forest (weak) at high elevations with weak resistance of roads 0.387 121 0.9744FLELRH 28 82-84 Minimum resistance in forest (weak) at low elevations with high resistance of roads 0.436 438 0.9531FLELRL 29 85-87 Minimum resistance in forest (weak) at low elevations with weak resistance of roads 0.438 435 0.9554FLEMRH 30 88-90 Minimum resistance in forest (weak) at middle elevations with high resistance of roads 0.559 226 0.9706FLEMRL 31 91-93 Minimum resistance in forest (weak) at middle elevations with weak resistance of roads 0.56 223 0.9721FLRH 32 94-96 Minimum resistance in forest (weak) with high resistance of roads 0.95 29 0.9087FLRL 33 97-99 Minimum resistance in forest (weak) with low resistance of roads 0.951 29 0.9146RH 34 100 High resistance of roads 1 1 0RL 35 100 Weak resistance of roads 1 1 0Null 36 100 Uniform resistance 1 1 0
10 USDA Forest Service RMRS-RP-90. 2012.

abilities, respectively. Across dispersal abilities, species 

associated with forest cover at the lowest elevations had 

the largest number of isolated patches. Conversely, species that were not associated with elevation or forest cover 

existed in a single or a few large connected patches. At 

the 10,000 m dispersal threshold, there was an average of 

200 isolated patches of connected habitat across the 36 

resistance models. Eight resistance models had over 400 

patches of isolated habitat and three—FHELRH, FHELRL, 

and ELFH—had in excess of 600 isolated habitat patches, 

reflecting a high degree of habitat fragmentation (Table 4). 

In contrast, 6 resistance models had fewer than 15 patches 

of isolated habitat, including species that are not associated 

with elevation or forest cover (Null, RH, RL, 1 patch) and 

those that are associated with low elevation but are not limited by the extent of forest cover (EL, 11 patches; ELRH, 

13 patches; ELRL, 13 patches).

Principal Components Analysis

The principal components analysis effectively concentrated variance in landscape structure of the 108 

connectivity maps across the 8 landscape metrics onto two 

independent dimensions of landscape structure (Table 5). 

The first ordination axis accounted for approximately 

73% of the variance in landscape structure, and over 88% 

of the variance in landscape structure was accounted for 

by the first two ordination axes. The first axis is a gradient from high habitat area and low habitat fragmentation 

(right, Figure 4) to low area of connected habitat and high 

fragmentation into small, isolated patches with high edge 

density (left, Figure 4).

Inspection of the ordination trajectory biplot (Figure 4) 

shows seven distinct groups of resistance models that are 

similar with respect to location in the ordination space and 

trajectory of movement through the space as dispersal ability increases. The first group is in the upper left quadrant 

and includes trajectory numbers 7-8-9; 79-80-81; 76-77-

78; 4-5-6; 52-53-54; and 49-50-51 (Figure 4; Table 4). This 

group exclusively contains resistance models in which 

species movement is facilitated at high elevations and 

resisted at lower elevations. The second trajectory group 

consists of trajectory numbers 22-23-24; 85-86-87; 82-

83-84; 58-59-60; and 55-56-57 (Figure 4; Table 4). This 

group contains species associated with forest cover at the 

lowest elevations. The third trajectory group contains trajectory numbers 37-38-39; 91-92-93; 88-89-90; 34-35-36; 

64-65-66; and 61-62-63. These species are associated with 

middle-elevation forests that are sensitive to fragmentation 

by roads. The fourth trajectory group contains trajectory 

numbers 46-47-48; 67-68-69; and 70-71-72. These species 

are those strongly associated with forest cover that avoid 

moving through non-forest habitats but don’t have any association with elevation. The fifth trajectory group contains 

trajectory numbers 94-95-96; 97-98-99; and 73-74-75. 

These species are moderately associated with forest cover 

Table 5. Results of multi-temporal principal components 

analysis. Proportion of explained variance and axis 

loadings for the first three principal components.

Component

1 2 3

Proportional of variance 72.6% 15.4% 8.8%

Cumulative proportion 72.6% 88.0% 97.9%

Loadings

PLAND 0.402 -0.185 -0.474

NP -0.314 -0.544 -0.714

LPI 0.390 -0.281 -0.104

TE -0.342 -0.438 -0.199

LSI -0.371 -0.386 0.136

AREA_AM 0.389 -0.289 -0.134

GYRATE_AM 0.373 -0.298 -0.283

CLUMPY -0.205 0.278 -0.912

but are not associated with elevation. The sixth trajectory 

group includes trajectory numbers 40-42-32; 43-44-45; 

and 31-32-33. These species are associated with middleelevation forests but not with forest cover. The seventh 

trajectory group consists of trajectory numbers 28-29-30; 

25-26-27; and 16-17-18 and contains three species associated with low-elevation forests but not with forest cover. 

The eighth trajectory group consists of three models that 

were fixed at 100% cover of the study area at all dispersal 

abilities (Null, RH, and RL) and are given trajectory point 

100 in the principal components analysis (PCA) biplot.

There were significant differences between the mean 

PCA scores on axes 1 and 2 among trajectory groups at 

each dispersal ability (Table 6), indicating significant separation of the groups in PC space. Across dispersal abilities, 

over 80% of pairs of groups had significantly different average PC1 scores, and over 60% had significantly different 

PC2 scores (Table 7). On axis one, only groups 5, 6, and 

7 were not significantly different in average PC1 score at 

any dispersal ability (Table 7). On axis 2, only groups 4 

and 6 were not significantly different in average PC2 score 

at any dispersal ability (Table 7). On axis 1 at the 5000 m 

dispersal ability, Group 2 had by far the lowest average PC 

score, indicating that species depending on low-elevation 

forest and that have limited dispersal ability are probably 

most limited by the extent and fragmentation of habitat. In 

contrast, Groups 6 and 7 are approximately tied in average PC1 score at the 5000 m dispersal ability, indicating 

that species that are associated with low and middle elevations but are not dependent on forest cover have the most 

extensive and least fragmented distributions of connected 

habitat (Table 8). At 20,000 m dispersal threshold, there is 

a change in ranking of groups on PC1, with Group 1 having 

the lowest extent and highest fragmentation of connected 

habitat. This indicates that at higher dispersal abilities, species associated with low-elevation forest may be able to 
USDA Forest Service RMRS-RP-90. 2012. 11

Figure 4. Landscape trajectories PCA biplot. PLAND—percentage of landscape area occupied by connected habitat; 

LPI—percentage of the landscape occupied by the single largest patch of connected habitat; AREA_AM—area-weighted 

mean patch size of connected habitat; GYRATE_AM—correlation length of connected habitat; LSI—landscape shape index; 

TE—total length of connected habitat edge; and NP—number of patches of connected habitat.

Table 6. One-way analysis of variance difference between mean values on PCA 

axes 1 and 2 among PCA trajectory groups at 5000 m, 10,000 m, and 20,000 m 

dispersal ability.

PCA Dispersal Degrees Sum of Mean

axis ability of Freedom squares square F P

1 5000 m 7 229.1009 32.7287 240.41 <.0001

1 10,000 m 7 170.0089 24.28698 416.34 <.0001

1 20,000 m 7 96.7927 13.82753 316.62 <.0001

2 5000 m 7 45.73135 6.53305 64.07 <.0001

2 10,000 m 7 28.41451 4.059215 235.86 <.0001

2 20,000 m 7 21.78926 3.112751 898.45 <.0001

effectively integrate small and isolated patches, resulting 

in a large increase in the extent of connected habitat and 

decreases in fragmentation. Conversely, species in Group 

1 associated with high-elevation forests are less able to 

integrate isolated patches at higher dispersal abilities, and 

as a consequence, have the lowest PC1 average score at 

20,000 m dispersal ability. Groups 5, 6, and 7 retain the 

highest PC1 scores at 20,000 m dispersal ability (Table 8).
12 USDA Forest Service RMRS-RP-90. 2012.

Table 7. Tukey HSD test of significance of difference of mean value on the first two principal 

components analysis (PCA) axes between pairs of PC trajectory groups at 5000 m, 10,000 m, 

and 20,000 m dispersal distance. The mean differences between groups are shown in the right 

six columns. Pairs that are significantly different are in bold.

Pair Axis 1 Axis 1 Axis 1 Axis 2 Axis 1 Axis 2

comparison 5000 m 10,000 m 20,000 m 5000 m 10,000 m 20,000 m

1 – 2 1.5033 0.678 -0.24919 3.1938 2.0841 1.38908

1 – 3 -0.6349 -1.4535 -1.24251 1.8485 1.63018 0.98561

1 – 4 -1.6903 -1.6354 -1.45581 2.0274 1.77851 1.26326

1 – 5 -3.8912 -4.5178 -3.82893 2.9882 2.07917 1.70347

1 – 6 -4.4376 -4.0327 -3.28293 1.3266 1.53748 1.37907

1 – 7 -4.2878 -3.827 -3.18984 1.4911 1.90439 1.69534

2 – 1 -1.5033 -0.678 0.24919 -3.1938 -2.0841 -1.38908

2 – 3 -2.1382 -2.1314 -0.99332 -1.3453 -0.45392 -0.40348

2 – 4 -3.1936 -2.3134 -1.20662 -1.1664 -0.30558 -0.12582

2 – 5 -5.3945 -5.1958 -3.57975 -0.2056 -0.00493 0.31439

2 – 6 -5.9409 -4.7107 -3.03375 -1.8672 -0.54662 -0.01001

2 – 7 -5.7911 -4.5049 -2.94065 -1.7027 -0.17971 0.30626

3 – 1 0.6349 1.4535 1.24251 -1.8485 -1.63018 -0.98561

3 – 2 2.1382 2.1314 0.99332 1.3453 0.45392 0.40348

3 – 4 -1.0554 -0.1819 -0.2133 0.1789 0.14833 0.27766

3 – 5 -3.2563 -3.0643 -2.58642 1.1397 0.44899 0.71787

3 – 6 -3.8027 -2.5792 -2.04042 -0.5219 -0.0927 0.39346

3 – 7 -3.6529 -2.3735 -1.94733 -0.3574 0.27421 0.70974

4 – 1 1.6903 1.6354 1.45581 -2.0274 -1.77851 -1.26326

4 – 2 3.1936 2.3134 1.20662 1.1664 0.30558 0.12582

4 – 3 1.0554 0.1819 0.2133 -0.1789 -0.14833 -0.27766

4 – 5 -2.2009 -2.8824 -2.37313 0.9608 0.30066 0.44021

4 – 6 -2.7473 -2.3973 -1.82712 -0.7008 -0.24103 0.1158

4 – 7 -2.5975 -2.1915 -1.73403 -0.5363 0.12588 0.43208

5 – 1 3.8912 4.5178 3.82893 -2.9882 -2.07917 -1.70347

5 – 2 5.3945 5.1958 3.57975 0.2056 0.00493 -0.31439

5 – 3 3.2563 3.0643 2.58642 -1.1397 -0.44899 -0.71787

5 – 4 2.2009 2.8824 2.37313 -0.9608 -0.30066 -0.44021

5 – 6 -0.5464 0.4851 0.546 -1.6616 -0.54169 -0.32441

5 – 7 -0.3966 0.6908 0.63909 -1.4971 -0.17478 -0.00813

6 – 1 4.4376 4.0327 3.28293 -1.3266 -1.53748 -1.37907

6 – 2 5.9409 4.7107 3.03375 1.8672 0.54662 0.01001

6 – 3 3.8027 2.5792 2.04042 0.5219 0.0927 -0.39346

6 – 4 2.7473 2.3973 1.82712 0.7008 0.24103 -0.1158

6 – 5 0.5464 -0.4851 -0.546 1.6616 0.54169 0.32441

6 – 7 0.1498 0.2058 0.09309 0.1645 0.36691 0.31627

7 – 1 4.2878 3.827 3.18984 -1.4911 -1.90439 -1.69534

7 – 2 5.7911 4.5049 2.94065 1.7027 0.17971 -0.30626

7 – 3 3.6529 2.3735 1.94733 0.3574 -0.27421 -0.70974

7 – 4 2.5975 2.1915 1.73403 0.5363 -0.12588 -0.43208

7 – 5 0.3966 -0.6908 -0.63909 1.4971 0.17478 0.00813

7 – 6 -0.1498 -0.2058 -0.09309 -0.1645 -0.36691 -0.31627
USDA Forest Service RMRS-RP-90. 2012. 13

Table 8. Mean PC1 and PC2 scores for each group at each of 

the three dispersal abilities.

Group Axis 5000 m 10,000 m 20,000 m

1 1 -2.6972 -1.48777 -0.35429

2 0.737049 1.526015 1.491194

2 1 -4.50015 -2.33104 -0.14447

2 -2.36197 -0.19959 0.84885

3 1 -2.36197 -0.19959 0.84885

2 -1.02951 0.065395 0.671277

4 1 -1.30655 -0.01766 1.062149

2 -1.20842 -0.08294 0.393618

5 1 0.894339 2.864715 3.435274

2 -2.16921 -0.3836 -0.04659

6 1 1.440701 2.379656 2.889273

2 -0.50761 0.158093 0.277815

7 1 1.290927 2.173873 2.79618

2 -0.67215 -0.20881 -0.03846

Table 9. One-way analysis of variance of mean displacement 

between PC trajectory groups from 5000 m to 20,000 m dispersal 

on each of the first two PCA axes.

Degrees

Dependent of Sum of Mean

variable freedom squares square F P

Disp1 6 27.14947 4.524911 70.76 <.0001

Disp2 6 16.99167 2.831945 34.94 <.0001

Landscape Trajectory Analysis

One-way analysis of variance showed highly significant 

differences in mean displacement in PC space from 5000 m 

to 20,000 m dispersal ability among PC trajectory groups 

(Table 9). This indicates that the groups are substantially 

different in the degree to which landscape structure changes as functions of dispersal ability. Eighty-one percent of 

group pairs had significantly different axis 1 displacement, 

and 67% had significantly different axis 2 displacement 

(Table 9). Only groups 1, 4, and 5 and groups 6 and 7 were 

not significantly different from each other in the degree to 

which landscape structure changed from 5000 m to 20,000 

m dispersal ability (Table 10).

On both axes, Group 1 had, by far, the largest displacement, showing that species associated with low-elevation 

forest have the largest change in the extent and fragmentation of connected habitat across the three dispersal abilities 

(Table 11). In contrast, Groups 6 and 7 had the lowest displacement, indicating that species that are associated with 

low and middle elevations but are not dependent on forest 

cover have relatively little change in extent and pattern of 

connected habitat as dispersal ability increases.

Table 10. Tukey HSD test of significance of difference of 

displacement on the first two PCA axes between pairs 

of PC trajectory groups. The mean difference between 

groups are shown in the right two columns. Pairs that are 

significantly different are in bold.

Group Axis 1 mean Axis 2 mean

pair difference difference

1 – 2 -1.7524 -1.8047

1 – 3 -0.6076 -0.8629

1 – 4 0.2345 -0.7641

1 – 5 0.0623 -1.2847

1 – 6 1.1547 0.0525

1 – 7 1.098 0.2042

2 – 1 1.7524 1.8047

2 – 3 1.1449 0.9419

2 – 4 1.987 1.0406

2 – 5 1.8147 0.52

2 – 6 2.9071 1.8572

2 – 7 2.8504 2.009

3 – 1 0.6076 0.8629

3 – 2 -1.1449 -0.9419

3 – 4 0.8421 0.0988

3 – 5 0.6699 -0.4218

3 – 6 1.7622 0.9154

3 – 7 1.7056 1.0671

4 – 1 -0.2345 0.7641

4 – 2 -1.987 -1.0406

4 – 3 -0.8421 -0.0988

4 – 5 -0.1722 -0.5206

4 – 6 0.9201 0.8166

4 – 7 0.8634 0.9683

5 – 1 -0.0623 1.2847

5 – 2 -1.8147 -0.52

5 – 3 -0.6699 0.4218

5 – 4 0.1722 0.5206

5 – 6 1.0924 1.3372

5 – 7 1.0357 1.4889

6 – 1 -1.1547 -0.0525

6 – 2 -2.9071 -1.8572

6 – 3 -1.7622 -0.9154

6 – 4 -0.9201 -0.8166

6 – 5 -1.0924 -1.3372

6 – 7 -0.0567 0.1517

7 – 1 -1.098 -0.2042

7 – 2 -2.8504 -2.009

7 – 3 -1.7056 -1.0671

7 – 4 -0.8634 -0.9683

7 – 5 -1.0357 -1.4889

7 – 6 0.0567 -0.1517
14 USDA Forest Service RMRS-RP-90. 2012.

Table 11. Average displacement on PC1 and PC2 between 

5000 m and 20,000 m dispersal ability for each of the 

seven trajectory groups.

Group Axis Mean displacement

1 1 2.603232

2 0.837939

2 1 4.355678

2 2.642651

3 1 3.210817

2 1.700792

4 1 2.368699

2 1.602033

5 1 2.540935

2 2.12262

6 1 1.448572

2 0.785424

7 1 1.505253

2 0.63369

Table 12. Mean within-group divergence among pairs of 

models within each of the seven trajectory groups across 

dispersal abilities (5000 m, 10,000 m, and 20,000 m).

Trajectory 

group 5000 m 10,000 m 20,000 m

1 0.762487 0.385477 0.215961

2 1.292505 0.529829 0.490538

3 0.541026 0.287545 0.197921

4 0.393994 0.099931 0.037889

5 0.427155 0.083046 0.022481

6 0.350103 0.066114 0.023388

7 0.407022 0.159388 0.024642

The average divergence of the locations of the members 

of each group in PC space gives an indication of how similar 

the landscape patterns of connected habitat are across the 

members of each group at each of the three dispersal abilities 

(Table 12). Across all dispersal distances, Group 2 had the 

highest average distance in PC space between pairs of group 

members, while Group 7 had the lowest. This indicates that 

species associated with low-elevation forest express a relatively broad range of extent and pattern of connected habitat 

in response to the effects of factors such as sensitivity to 

roads and the strength of dependency on forest cover. All 

seven groups showed very large decreases of within-group 

divergence as dispersal ability increased. Groups 4, 5, 6, and 

7 had a decrease in average pair-wise separation in PC space 

of over 90%. Groups, 1, 2, and 3 had a decrease in average pair-wise separation of between 60 and 70%, indicating 

that landscape structure of connected habitat becomes much 

more similar within groups as dispersal ability increases.

Quantifying the average divergence between groups 

across the three dispersal abilities provides a measure of 

how the differences in landscape structure between groups 

change as dispersal ability increases (Table 13). As dispersal 

ability increases, the average landscape structure of connected habitat among groups becomes more similar. Specifically, 

at the 5000 m dispersal distance, the average distance between group centroids in PC1xPC2 space is 3.30 units. This 

decreases to 2.71 units at 10,000 m dispersal ability and 

drops to 2.04 units at 20,000 m dispersal ability. Across dispersal abilities, Groups 1 and 2 are most distant in PC space 

from Groups 5, 6, and 7 (Table 13). This indicates that there 

is substantial difference in the extent and pattern of connected habitat for species associated with both forest cover and 

either high or low elevation and for species associated with 

elevation but not with forest cover.

Discussion

Habitat Connectivity, Dispersal Ability, 

and Ecological Associations

Population connectivity is a function of three factors. 

First, connectivity is fundamentally mediated by the extent 

of the distribution and density of the population. A species with a broad distribution across a landscape and with 

relatively high density will express a very high degree of 

population connectivity given there are few gaps in distribution to be spanned by dispersal. Conversely, species 

that have limited distributions or are highly fragmented 

will probably have much less extensive connected habitat, 

given that there will be large extents of unoccupied habitat 

between core population patches. Second, dispersal ability critically determines connectivity. At any pattern of 

distribution and population density, the degree to which 

a population is connected across the broad landscape will 

increase with increasing dispersal ability. Species with 

very limited dispersal ability will not be able to disperse 

across even quite small gaps in the distribution, resulting 

in highly fragmented populations. In contrast, species with 

very high dispersal ability can cross even broad gaps in 

distribution, thus spatially integrating the population into a 

few or a single core patch. Third, connectivity is driven by 

the resistance of the landscape to dispersal. For example, 

consider a species that is highly dependent on forest cover 

at a particular elevation in a complex mountainous landscape such as the northern Rocky Mountains. Resistance to 

dispersal will be low in forest cover at the optimal elevation but will increase substantially in non-forest areas and 

at suboptimal elevations. This pattern of strongly heterogeneous resistance gradients across a complex landscape will 

result in fracture zones and barriers where there are breaks 

in connectivity because of cumulative movement costs that 

exceed the dispersal ability of the species. Conversely, a 

species whose movement costs are independent of forest 
USDA Forest Service RMRS-RP-90. 2012. 15

Table 13. Average divergence between mean trajectory groups across dispersal abilities (5000 m, 

10,000 m, and 20,000 m).

Trajectory 

group 1 2 3 4 5 6

5000 m 1

2 3.529886

3 1.954463 2.526213

4 2.639591 3.399948 1.070473

5 4.906195 5.398407 3.449992 2.401467

6 4.631628 6.227383 3.838317 2.835228 1.749125

7 4.539686 6.036204 3.670334 2.652257 1.548702 0.222499

10,000 m 1

2 2.191593

3 2.184059 2.179247

4 2.416133 2.333473 0.234735

5 4.973272 5.195756 3.097024 2.898015

6 4.315879 4.742303 2.58091 2.409404 0.727126

7 4.274607 4.508495 2.38925 2.195146 0.71261 0.420676

20,000 m 1

2 1.411255

3 1.585954 1.072139

4 1.92749 1.213163 0.35013

5 4.190771 3.593526 2.684199 2.413609

6 3.560826 3.033762 2.078012 1.83079 0.635104

7 3.612377 2.956557 2.072636 1.787052 0.639146 0.329691

cover, elevation, or roads would be able to integrate the 

landscape much more completely through dispersal. For 

example, many bird species are capable of flying over 

roads and other terrestrial barriers, and can traverse complex topography with ease.

The ultimate objective of this analysis was to predict 

the synergistic effects of multiple ecosystem stressors at 

broad geographical scales on habitat area, fragmentation, 

and connectivity. We present a general method to estimate 

habitat area, fragmentation, and corridor connectivity for 

multiple species across vast geographical areas. The resistant kernel approach to modeling landscape connectivity 

has a number of major advantages as a robust approach 

to assessing current and future landscape connectivity for 

multiple wildlife species under climate change scenarios. 

First, unlike most corridor prediction efforts, it is spatially 

synoptic and provides prediction and mapping of expected 

migration rates for every pixel in the study area extent, 

rather than only for a few selected “linkage zones” (e.g., 

Compton and others 2007). Second, it explicitly incorporates the influence of population distribution and density. 

Third, scale dependency of dispersal ability can be directly 

included to assess how species of different vagilities will 

be affected by landscape change and fragmentation under 

a range of scenarios (e.g., Cushman and others 2010a). 

Fourth, it ideally quantifies the effect of different patterns of 

landscape resistance on connectivity, given that the extent 

and shape of the least-cost dispersal kernels are fundamentally shaped and constrained by the cumulative movement 

cost across the resistance surface from the dispersal source.

The combination of the method’s sensitivity to distribution, dispersal ability, and differential landscape resistance 

enabled us to map species-specific, scale-dependent population core areas, fracture zones, and movement corridors 

across the United States northern Rocky Mountains. We 

produced 108 different connectivity maps for the combination of 36 resistance surfaces and 3 dispersal abilities. These 

connectivity surfaces provide spatially explicit prediction of 

core areas, fracture zones, and corridors for a broad range of 

native taxa, and could be extremely useful in guiding habitat 

protection, enhancement, and/or restoration efforts to maximally benefit particular species of concern.

The 108 connectivity maps represent a broad range of native species expressing different ecological associations and 

different dispersal abilities. Recent empirical research has 

enabled us to associate several of these hypothetical models 

with particular native species of conservation concern. For 

example, Cushman and others (2006) tested the same suite 

of resistance models in a study of the landscape controls on 

gene flow of American black bear (Ursus americanus). The 

authors identified the resistance model FHEMRH (model 

number 21, Table 4) as the most supported explanation of 

population connectivity for this species. More recently, 

Short Bull and others (2011) evaluated the same 36 resistance models for black bear population connectivity across 

a replicate sample of 12 different study areas distributed 

across the full extent of the U.S. northern Rocky Mountains 

and affirmed the conclusions of Cushman and others (2006) 

that black bear gene flow is facilitated by forest cover at 

middle elevations and is resisted by suboptimal elevations, 
16 USDA Forest Service RMRS-RP-90. 2012.

non-forest conditions, and roads. The predicted surface of 

population connectivity for the FHEMRH model at dispersal 

ability 20,000 m provides a spatially synoptic prediction of 

population connectivity for black bears across the northern 

Rocky Mountains. Cushman and others (2008) used a factorial implementation of least-cost paths to predict optimal 

movement routes of black bear from Yellowstone National 

Park to Canada based on the FHEMRH resistance layer. 

That prediction is useful to optimize the location of particular mitigation and restoration projects along the least-cost 

route of dispersal from Yellowstone to Canada but does not 

give a spatially complete picture of population core areas, 

barriers, fracture zones and corridors across the full extent 

of the northern Rocky Mountains, which is provided by the 

resistant kernel maps.

Recent work on the landscape genetics of wolverine 

(Gulo gulo; Schwartz and others 2009) identified high-elevation habitats as low resistance to dispersal of this species 

given its dependence on spring snow for denning and foraging habitat (Aubry and others 2007; Copeland and others 

2010). Our EH model (model number 1, Table 4) closely approximates this, and the EH model with a 20,000 m dispersal 

ability presents a spatially synoptic picture of population 

core areas, fracture zones, and corridors for this species of 

conservation concern. Schwartz and others (2009) used a 

factorial least-cost path approach to produce a network of 

predicted corridors across the northern Rocky Mountains. 

However, the factorial least-cost path approach did not 

include any dispersal thresholds. Thus, the network of predicted corridors includes many paths much greater in length 

than is reasonable for any terrestrial animal to disperse. The 

scale dependence of the resistant kernel approach produces 

predictions of functional landscape connectivity that incorporate the inherent spatial limits of dispersal and provide a 

more realistic picture of regional connectivity. In addition, 

the least-cost path approach emphasizes the lowest cost 

single routes between sources and destinations but ignores 

the fact that animals rarely utilize optimal dispersal paths 

and that dispersing animals are naïve to landscape structure, 

meaning this method may not accurately reflect the probability distribution of a species’ likely dispersal movements. 

The cumulative resistant kernel integrates all paths across 

the distribution of cumulative dispersal distances up to the 

dispersal threshold and thus provides a spatially complete 

and realistic picture of landscape connectivity.

A third species of conservation concern whose population 

connectivity has recently been studied in the northern Rocky 

Mountains is the American marten (Martes americana; 

Wasserman and others 2010, in press). Wasserman and others (2010) used landscape genetics to test several hundred 

alternative resistance models for gene flow of this species 

and identified elevation as the driver of population connectivity. Specifically, resistance to gene flow was lowest at 

1500 m elevation and increased as an inverse Gaussian function at elevations above and below 1500 m. This resistance 

model is identical to our EH model. Marten and wolverine 

have the same landscape resistance model, however, they 

differ greatly in vagility, such that predictions of population 

connectivity for marten would not accurately predict that 

of wolverine. In this case, the FH model at the 10,000 m 

dispersal threshold most accurately reflects the functional 

connectivity of American marten populations across the 

study area. The differences in predicted population connectivity for these two species illustrates the importance of 

explicit incorporation of dispersal ability. Even though they 

both have the same resistance model (EH), there are large 

differences in predicted population connectivity of these 

species based on dispersal ability. For example, the area of 

the landscape predicted to be connected by dispersal is 47% 

greater for the wolverine and the degree of habitat fragmentation is much lower. Specifically, the number of isolated 

patches of connected habitat is nearly seven-fold higher for 

marten than for wolverine, reflecting the effects of the wolverine’s greater dispersal ability on integrating across gaps 

that the marten cannot cross.

Importance of Broad-Scope 

Multi-Taxa Assessment of 

Landscape Connectivity

Most past evaluations of habitat connectivity and fragmentation in the U.S. northern Rocky Mountains have 

focused on large carnivores (Weaver and others 1996; Caroll 

and others 2001; Cushman and others 2008; Schwartz and 

others 2009). This is in part due to their large home range 

requirements and potential vulnerability to habitat fragmentation, as well as the fact that many large carnivore species 

are species of conservation concern. The long-term viability 

of large carnivores in the Rocky Mountains is believed to 

strongly depend on regional connectivity of habitat due to 

the low densities, large home range size, vulnerability to human disturbance, and low fecundity of these species (Noss 

1996; Weaver and others 1996; Caroll and others 2001). In 

addition, a number of researchers have proposed using large 

carnivores as umbrellas for habitat and connectivity protection plans (Noss 1996; Caroll and others 2001). Although 

large carnivores are appropriate focal species and flagships 

(Servheen and others 2001; Singleton and others 2002), 

other researchers have noted that they are generally highly 

mobile habitat generalists and thus likely will be inadequate 

umbrellas for other species (Beier and others 2009; Minor 

and Lookingbill 2010).

The purpose of this analysis was to produce connectivity 

mapping for a broad range of native taxa and to not assume 

that any particular taxa would serve as an umbrella species 

for many others. We found that several groups of species 

express similar patterns of landscape connectivity as a result of similar ecological associations. We identified seven 

species groups that have similar multivariate patterns of 

landscape structure and change in landscape structure of 

connected habitat as dispersal ability increases. Specifically, 

we found that species groups (in parentheses) are associated with (1) high-elevation forest, (2) low-elevation forest, 
USDA Forest Service RMRS-RP-90. 2012. 17

(3) middle-elevation forest, (4-5) forest cover but not elevation, and (6-7) particular elevations but not forest cover 

formed highly coherent groups in the principal components 

analysis of landscape structure trajectories. These groups 

were significantly different in the extent and pattern of connected habitat at each dispersal ability and the degree to 

which landscape connectivity changed with increasing dispersal ability. This emphasizes that connectivity predictions 

for one species or one species group are not likely to accurately reflect functional connectivity for other species with 

different ecological associations.

Species-Specific Connectivity

Our analysis identified several important patterns of 

functional landscape connectivity in relation to resistance 

model and dispersal ability. Across dispersal abilities, species strongly associated with forest cover and high-elevation 

or low-elevation habitats had the lowest extent and highest 

fragmentation of connected habitat. The vast majority of protected lands in the study area (Federal ownership, Figure 1) 

are at middle to higher elevations. The lower-elevation areas 

of the study area are mostly in private ownership and are 

experiencing rapid development. An extensive network of 

highways bisects the study area, with the majority of major 

highways located in lower elevation valleys. In addition, climate change will likely lead to an upward migration of lower 

tree lines in the northern Rocky Mountains (J. Littell, pers. 

comm.), further reducing the extent and increasing the fragmentation of lower elevation forest habitat. As a result of the 

combination of these factors, species with limited dispersal 

ability associated with lower elevation forest will probably 

be most vulnerable to habitat loss and fragmentation in the 

northern Rocky Mountains.

In contrast, among species with greater dispersal ability (20,000 m), the most limited extent of connected habitat 

across dispersal thresholds was for species associated with 

high forest cover at the highest elevations (FHEHRH). These 

species are likely less vulnerable to human development 

than those that rely on lower elevation habitats, given that 

much of the landscape these species occupy is protected by 

public ownership. However, there are numerous bottlenecks 

in the distribution of high-elevation habitat, and these usually coincide with mountain passes in which major highways 

have been built (e.g., Cushman and others 2008; Schwartz 

and others 2009; Shirk and others 2010). Thus, landscape 

connectivity of these species may also be highly impacted 

by transportation infrastructure. As climate warms, the ecological conditions these species depend on will shift upslope 

and become more limited in area and more fragmented.

Dispersal Ability and Habitat 

Connectivity

Our analysis showed important differences among species 

groups in terms of the sensitivity of landscape connectivity 

to dispersal ability. Species groups that are predicted to have 

high extent and low fragmentation of connected habitat 

showed relatively little change in connectivity with increasing dispersal ability. For example, groups 4, 5, 6, and 7, 

which are associated with forest cover but not elevation 

(4-5) or elevation and not forest cover (6-7) are predicted 

to have relatively high connectivity even at low dispersal 

abilities. As a result, as dispersal ability increases, there is 

relatively little change in connectivity for these species.

 In contrast, species groups 1 and 2, which are associated 

with high- and low-elevation forest habitats, respectively, 

have much higher sensitivity to change in dispersal ability. 

As dispersal ability increases, these species groups experience large increases in the extent of connected habitat and 

decreases in fragmentation. There is a large and important 

difference between these two groups. Models for group 2, 

the low-elevation forest associated species, predict a much 

greater increase in connectivity with increasing dispersal 

ability than for group 1. At low dispersal abilities, the lowelevation forest species have substantially lower area and 

higher fragmentation of connected habitat than any other 

group. However, at high dispersal abilities, it is the high-elevation forest species that are most limited by habitat extent 

and fragmentation. This follows from the differences in the 

patterns of landscape resistance in the two models. For lowelevation forest species, there is a large number of scattered 

and isolated patches of low resistance habitat, corresponding to low-elevation forest areas. At low dispersal abilities, 

these are mostly isolated as fragments. However, as dispersal ability increases, dispersing organisms are able to move 

between the fragments, resulting in coalescence of these 

isolated patches into large and contagious blocks of habitat 

that are connected by dispersal. Conversely, the high-elevation species are associated with relatively large but highly 

disjunct patches of low resistance habitat, corresponding to 

mountain peaks and ranges. As dispersal ability increases, 

individuals are increasingly able to move among neighboring mountains, but the average distance between such low 

resistance patches is much higher than for low-elevation forest and there is much less coalescence into large contiguous 

connected patches.

As dispersal ability increases, there is a marked convergence of habitat connectivity within species groups. At low 

dispersal abilities, the extent and fragmentation of habitat 

for species with similar ecological associations is modest but 

increases dramatically with increasing dispersal ability, such 

that by 20,000 m dispersal ability there is near complete 

overlap in the extent and pattern of connected habitat for 

species within each of the seven trajectory groups we identified. This suggests that multiple-taxa conservation efforts 

aimed at promoting population connectivity are likely to be 

more effective for highly mobile species than for species 

with limited dispersal ability. There is an analogous convergence of the extent and pattern of connected habitat among 

groups as well. The average separation of the seven species 

groups in the principal component space becomes significantly smaller as dispersal ability increases. This reflects that 
18 USDA Forest Service RMRS-RP-90. 2012.

as dispersal ability increases, the extent of connected habitat 

for each species increases, and thus, the degree of overlap 

among species and species groups also tends to increase.

Scope and Limitations

Uncertainty in Landscape Resistance

Most of the published studies using landscape resistance 

maps have utilized expert opinion to estimate resistance to 

movement due to landscape features given the lack of detailed information on animal movement or gene flow (e.g., 

Compton and others 2007). This is not surprising given the 

difficulty in gathering sufficient sample sizes of reliable data 

on relationships between animal movement and multiple 

landscape features at broad spatial scales (McGarigal and 

Cushman 2002; Cushman 2006). However, basing analyses 

on unvalidated expert opinions is not desirable (Seoane and 

others 2005) and has been a major weakness in past efforts. 

Landscapes are perceived by particular species in ways that 

may not correspond to our assumptions concerning connectivity and habitat quality (With and others 1997; Shirk and 

others 2010; Wasserman and others 2010).

We sought to mitigate this uncertainty by evaluating potential landscape resistance parameterizations that represent 

a broad range of species’ sensitivities to land use, forest 

cover, elevation, and roads. We repeated all analyses on 36 

different resistance maps that reflect different relative resistance of roads, human development, agriculture, and forest 

cover. The purpose was to explicitly evaluate the sensitivity 

of connectivity predictions to differences in ecological associations. We were also able to quantify uncertainty due to 

variability in functional landscape resistance among species 

and species groups.

Uncertainty in Dispersal Ability

What constitutes functional connectivity is highly dependent on the dispersal behavior of the particular species 

in question. For example, patches that are connected for 

one species may be isolated for another. Thus, habitat connectivity is affected by population distribution and habitat 

continuity, but the magnitude and nature of the effect depends on the dispersal ability of the particular species. The 

cumulative cost distances organisms are able to traverse, 

and the probability distributions of movements as function 

of cost distances between sources and potential destinations 

vary greatly among species. Generally, larger organisms 

can travel longer distances. Therefore, a 100 m wide agricultural field may be a complete barrier to dispersal for 

small organisms such as invertebrates (e.g., Usher and others 1993) or amphibians (Rothermel and Semlitsch 2002; 

Marsh and others 2004), yet may be quite permeable for 

larger and more vagile organisms such as birds. We sought 

to explicitly quantify this uncertainty by evaluating a range 

of potential dispersal abilities. Our goal was to evaluate a 

low end, middle, and high end estimate of dispersal ability to 

quantify the effects of differential mobility on predictions of 

the extent and connectivity of habitat in the northern Rocky 

Mountains. Our results indicate that predictions of the extent 

and pattern of core areas, and the degree to which they are 

linked by dispersal is extremely sensitive to dispersal ability.

Uncertainty in Species Distributions

 The methods we employ are based on predicting population cores, fractures, and corridors based on quantitative 

modeling of dispersal from a collection of source locations 

in the landscape. These sources reflect expected locations 

occupied by the species. Therefore, the analysis is highly dependent on accurate information on species distribution and 

density. Analysis based on incorrect species distribution information may be highly misleading. To mitigate uncertainty 

in the distribution of the focal species, we conducted a habitat-based species group analysis. Specifically, we modeled 

dispersal from all cells in the landscape that were predicted 

to have low resistance (and thus high suitability) for each 

of the 36 resistance maps. This analysis reflects connectivity of habitat but not any actual population, as we did not 

incorporate actual distribution and density information from 

real species. Given our goal of evaluating a broad range of 

ecological associations and dispersal abilities, it would have 

been impossible to obtain sufficiently accurate distribution 

and density information for real species reflecting each of 

our 108 combinations of resistance model and dispersal 

ability.

Uncertainty in Critical Fragmentation 

Thresholds

A critical threshold is an abrupt, nonlinear change that 

occurs in an organism response (e.g., dispersal success, 

productivity, and patch occupancy across a small range of 

habitat loss and/or fragmentation (With and King 1999). 

Both empirical data (Koopowitz and others 1994; Carlson 

and Stenberg 1995; Doncaster and others 1996; Jansson 

and Angelstam 1999) and theoretical models predict critical 

thresholds of habitat where ecological relationships change 

abruptly (O’Neil and others 1988; Turner and Gardner 1991; 

With and Crist 1995; Bascompte and Sole 1996; Flather 

and Bevers 2002). For example, neutral landscape models, 

derived from percolation theory as applied in the field of 

landscape ecology (Gardner and others 1987, 1989; Gardner 

and O’Neill 1991; Pearson and Gardner 1997; With 1997; 

With and King 1999), have been used to characterize habitat loss and fragmentation as a threshold phenomenon (With 

and King 1999). Above the so-called percolation threshold, 

habitat loss results in a simple additive loss of habitat. At the 

threshold, a qualitative change in landscape structure occurs. 

A small additional loss of habitat at this point produces a 

physically disconnected landscape in which the organism’s 
USDA Forest Service RMRS-RP-90. 2012. 19

habitat no longer maintains continuity across the landscape. 

Further habitat loss merely leads to greater discontinuity. 

The existence, nature, and severity of critical thresholds in 

the population response to fragmentation among wildlife 

species inhabiting the northern Rocky Mountains is largely 

unknown. Our analysis quantifies location, size, and connectivity of core patches, fracture zones, and corridors for a large 

range of ecological associations and dispersal abilities. The 

principal components analysis shows differences in connectivity among several species groups and the relative effects 

of changes in dispersal ability. However, full interpretation 

of the biological implications of these patterns would require 

knowledge of how incremental change in core areas, fracture 

zones, and corridors would affect demographic and genetic 

processes affecting viability. This would likely require modeling over a much larger number of increments in dispersal 

ability and a much finer gradation of resistance models—an 

area that deserves additional investment and research.

Conclusion

Population connectivity is a product of the dispersal 

ability of the species, the influences of different landscape 

elements on its movement behavior, the density and distribution of the population, and the structure of the landscape. 

Failure to explicitly consider each of these factors, however, may lead to incorrect conclusions. In this paper, we 

evaluated population connectivity across the United States 

northern Rocky Mountains for a broad range of organisms expressing different sensitivity to landscape structure 

and different dispersal abilities. Human land use and climate change alter the composition and configuration of 

landscapes, but the impact of these changes on loss and 

fragmentation of suitable habitat for a particular organism 

depends on the scale and nature of those changes in relation to how that organism perceives and interacts with 

landscape patterns (With and Crist 1995; Pearson and others 1996; With 1997; With and others 1997). For example, 

changes in the size and isolation of mature forest patches 

at a particular scale may have little or no detectable impact on species that perceive and respond to landscape 

patterns at a different scale, select habitat on the basis of 

other environmental variables (e.g., shrub cover and litter 

depth), or utilize a broad range of habitats (i.e., generalist 

or multi-habitat species). Our spatially synoptic predictions of population connectivity for all 108 species may be 

highly useful to guide species specific and multi-species 

conservation efforts. We found large differences among 

groups of species in terms of the extent and connectivity 

of habitat and the sensitivity of connectivity to dispersal 

ability. We found that species with limited dispersal ability and associated with low-elevation forest have the most 

limited and fragmented distribution of connected habitat. 

Species associated with high-elevation forest also appear 

highly vulnerable to habitat loss and fragmentation based 

on limited extent and connectivity of habitat.

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