David M. Theobald, Ph.D.

A significant challenge for conservation science is to understand the needs of wide-ranging species during the design of nature reserves. Although numerous GIS methods exist to analyze patch composition and structure, few methods readily allow a user to incorporate species behavior and scaling. Here I describe a general approach that allows functional properties of organisms and processes to be modeled so that possible habitat fragmentation due to land use change (including housing development and roads) can be assessed. Results of this modeling approach are illustrated through landscape connectivity maps for lynx (Lynx canadensis).


Habitat loss and fragmentation are a main threat to conservation of biodiversity. Much of the discussion about landscape fragmentation has been framed by the patch-matrix-corridor conceptualization of a landscape (Forman and Godron 1986). However, it is limited because it does not incorporate functional responses of species or processes to landscape structure (Theobald and Hobbs 2001). Connectivity is species and landscape-specific (Tischendorf and Fahrig 2000). Four aspects of understanding landscape connectivity need to be considered. The first is related to how a patch is defined. The basis for most studies of landscapes is a land cover or vegetation map, produced from photo-interpretation of aerial photography or aggregation of adjacent (either 4 or 8) cells from a classified remotely-sensed image. These patches are not usually not defined consistently nor are they biologically-based (Paton 1994). Non-contiguous patches of vegetation can be functionally integrated if a species or process of interest operates at a scale that can span patches (With and Crist 1995). Thus, patches need to be defined in relation to a particular species or process.

A second problem is that the space between patches of habitat – the matrix – is typically considered to be biologically inert and isolation is computed as the Euclidean distance between patches (e.g., Doak et al. 1992). Yet, species movement or dispersal mechanisms are influenced not just by the inter-patch distance, but by the characteristics of the matrix such vegetation type, structure, and land use (Wiens et al. 1993). A third aspect is to recognize that patches, while often conceptualized as a point or "node" in reality have a spatial extent and are often irregular in shape. Much of the connectivity literature has ties to meta-population theory, which in most cases represents a patch as a single point -- usually a polygon centroid. Simplifying the geographic complexity of patches is generally done to provide adequate performance. (e.g., RAMAS GIS). When the inter-patch distance is very large relative to the variation in distances from patch centroid to patch edge, this assumption is reasonable (Moilanen and Nieminen 2002). However, edge-to-edge measures are preferred (e.g., Keitt et al. 1997), are straightforward to calculate in GIS, and are more robust to geographic complexity (Crooks 2002).

A fourth aspect is that the spatial configuration of patches is important. That is, some patches are more important than others, not because of size or habitat quality, but because of the position of a patch within the network. Critical connector patches are located at a nexus where the overall landscape connectivity is sensitive to inclusion or removal of these patches. A number of specific purpose GIS-based modeling efforts have begun to build landscape connectivity models. These have typically taken advantage of cost-distance methods in raster GIS. For example, Walker and Craighead (1997) used least-cost path modeling to identify grizzly bear corridors. Bunn et al. (2000) also used least-cost paths but used graph-theoretic metrics to better quantify how the configuration of patches related to landscape connectivity.

Building on this previous research, I describe a general modeling approach here that incorporates an organism-centric perspective to define landscape connectivity, especially to examine the consequences of landscape changes such as development and roads and their possible fragmenting effects. This approach has the following advantages:
1. Gradients in habitat quality can be recognized so that binary species- vegetation modeling can be improved to reflect species-specific use of the landscape. This also provides a way to include uncertainty in land cover data and can incorporate edge effects.
2. Patches are defined relative to a species' mobility. Generally, this is related to levels of organization, so patches refer to individual – population level, where foraging behavior and home range requirements can be used to estimate the minimum patch size.
3. Matrix quality (the intervening area between patches) is explicitly recognized by modeling the "resistance to movement" through different land cover types. For example, for a lynx, it may be relatively easy to move through sagebrush, because it provides some cover, while traveling through open grasslands is more risky, and traveling through human-occupied land (urban areas) is typically avoided.
4. The potential direct and indirect (adjacent) affects of land use on habitat are explicitly incorporated. Known effects of different land use types and roads can be incorporated. This addresses important questions such as: are we likely to have increased fragmentation because of new development?

Model description

Using the general approach described above, I created a general, GIS-based tool to model landscape connectivity. The tool is an ArcView v3.2 extension that allows users to model landscape connectivity based on user-defined input parameters. There are 3 basic steps to the model: defining habitat quality, defining matrix quality, and establishing clusters of habitat.

Habitat quality

First, a map of habitat quality needs to be prepared. This usually relies on species-affinities for certain land cover types, but other factors such as elevation gradients, distance from water, etc. can be incorporated. Then, habitat quality (values can range from 0 to 100, not just 0 or 1) is then "integrated" using the species scale of foraging (Addicott et al. 1987). Patches that are below a minimum size (e.g., related to minimum home range size) can be removed. This results in a map that represents functionally-defined patches of habitat.


1. Habitat (resource) value GRID (MH)
      a. Values ranges from 0? 100.
      b. Typically created by reclassing land cover data (e.g., GAP vegetation, USGS National Land Cover Data) to different quality values
      c. Can also incorporate environmental gradients that might modify quality (e.g., moisture, elevation, aspect, etc.)
2. In-situ habitat disturbed GRID (MD)
      a. Accounts for reduction of habitat quality due to, typically, human-associated land uses. Typical indicators are road density, housing density, developed areas, etc.
      b. Disturbed areas are reclassed (RD) to the degree of reduction of a cell's habitat quality. For example, urban 100%, exurban 50%, ski area 75%, etc.; or according to type of road: 100% paved, 50% gravel, etc.
3. Edge effects on patch habitat quality
      a. Usually this is used to model reduction in patch area due to reduction of quality, often due to micro-climatic changes (Chen et al. 1995), at patch edges for species that need undisturbed core areas.
      b. There are two ways this can be incorporated: a) RECLASS (RE) on habitat (MH) using distance from edge parameters (e.g., 0- 100 m: 0%; 100-200 m: 50%; 200-300 m: 75%; >300 m 100%); or b) resample MH to a larger cell size that reflects the edge effect distance (e.g., from 30 m to 300 m) so that each resulting cell is the average of the original cell values. Note that often resampling to coarser resolution is required for computational efficiency.
4. Habitat quality to habitat patches
      a. In order to convert the habitat quality map from a gradient map (continuous) reflecting habitat quality for each cell to patches of habitat, two parameters are required. First, a threshold (A) is used to identify a minimum patch size, which corresponds (roughly) to the concept of a home range. In addition, the percent of an area (t) within the local (foraging) scale that is habitat needs to be specified. That is, often minimum habitat patches can include small portions of low quality habitat, and t generally ranges from 25% to 75%.

Matrix quality

Matrix quality is also derived from a land cover map and reflects the ability of a species to move through various land cover types. The matrix quality map is the "cost GRID" input to the cost-distance function (the habitat patches map supplies the "seed" locations). The matrix quality map can be best thought of as a 3-D surface, where areas of high resistance are peaks and ridges, and areas of low resistance to movement are the valleys and low areas. The path of a species moving from one patch to another would avoid peaks and ridges and instead travel around "contouring" around an area, incurring the "least-cost" path, rather than necessarily the shortest Euclidean distance.

Although using cost-distance weights or resistances for different types of land cover instead of Euclidean distance makes reasonable sense to most biologists, a significant challenge is to estimate the resistance parameters. Commonly, cost-distances for different types are simply estimated through "expert opinion", by applying knowledge of a species' life history characteristics and habitat use. An innovative example of this was Boone and Hunter (1996) examination of grizzly bear movement assuming different sensitivity to land cover types. An empirically-based method is to generate cost-distance parameters directly through examining movement data. For example, Palomares et al. (2000) and Ferreras (2001) used movement data collected through radiocollars to relate the proportion of use of different habitat types (using Jacobs' index) to the "friction" or resistance. Ricketts (2001) used maximum likelihood to estimate the resistances of matrix types for butterfly movement.


5. Convert land cover to matrix quality
      a. The land cover map (MM), with roads (MR)burned in, is reclassed (RM) to reflect "resistance" or "impedance" values for the cost- distance function.
      b. Types that allow minimal resistance are given a value of 1, while other types offer greater resistance. Because the reclass function only creates integer GRIDs, enter the values in the reclass tables as percentages, ranging from (potentially) 0 to 100 (high quality habitat) to very large numbers. For example, if grassland is twice as resistant to movement, enter a value of 200.

Connected habitat (clusters)

If the distance between habitat patches is below a threshold related to movement (i.e. dispersal) ability, then the patches are considered "connected". Thus patches that are functionally connected to one another by the dispersal ability are considered a "cluster" of patches or a functioning network of patches.


6. Dispersal distance
      a. movement is specified by (D), measured in km


The user parameterizes the model through a series of interactive dialog boxes. For each dialog box, there is a brief description of the parameters requested, the units, and default values. The values are checked and if they are outside of a pre-defined range, the user will be asked for confirmation to proceed with that value(s).


1. Select the habitat map:
2. Select the ROADs map:
3. Select the DEVELOPMENT map(s): (e.g., for 1990, and 2050)
4. Select the MATRIX QUALITY map(s): (e.g., National Land Cover dataset)
5. Select sensitivity to development and roads (matrix quality): Note: the output values (those in field "impede") are multiplied by 100, so that a value of 100 is the minimum resistance value of 1, while a value of 150 is 1.5 times, while a value of 1000 is 10 times the minimum impedance value.
6. Specify minimum area required (in hectares) - default "10, 50, 100" for the first time, otherwise defaults to values that were run last time
7. Specify the edge threshold (0-100) - default "75"
8. Specify the dispersal distance(s) - default "10, 50, 100" for the first time, otherwise defaults to values that were run last time


The list of number of patches, and model parameters are written out to a tab-delimited text file that can be easily imported into Excel. The output GRIDs are added to a new view.

For each scenario run, a new view (named with a time-stamp) is created and GRID output files are placed inside the view. Grids that begin with "Patches …" provide output for patches of habitat that meet the minimum requirements specified. GRIDs that begin with "Clusters…" provide output for clusters of patches that are "connected" by dispersal ability and matrix quality assumptions. Use the "Unique Value" legend to display, so that same-colored patches are connected. Note that the GRIDs inside the output view are "temporary" GRIDs, in the ArcView sense, so that they physically located in the working directory. If you want to save these GRIDs, make these permanent or copy them over into another directory that will not get periodically cleaned.

Example of Lynx canadensis in the Southern Rocky Mountain Ecoregion

Note: the purpose of this example is to illustrate the modeling process in the Southern Rocky Mountain Ecoregion (central Colorado, south-central Wyoming, and north-central New Mexico), not to produce a definitive map of lynx connectivity. Four major steps in the process are described. The first step is to create the habitat map, and for the lynx in the Southern Rocky Mountains I converted National Land Cover data to create a habitat map (Figure 1). The 30 m resolution was aggregated to 300 m resolution using BLOCKSTATS (with sum) to produce a GRID with values ranging from 0 to 100, or the proportion of a cell that is habitat. Using a coarser GRID was needed to ensure that the cost-distance functions perform reasonably. Based on housing density values, the effective area of habitat in a cell was reduced (e.g., urban – 100% loss, suburban – 75% loss, exurban – 50% loss). Cells that had a highway run through them had a 100% loss of habitat (while smaller roads had no reduction). Land Cover Data
Figure 1. Creation of habitat map for Lynx in the Southern Rocky Mountain Ecoregion. The coniferous and mixed forest cover types were extracted from the USGS National Land Cover Dataset (30 m) represent, in a course way, critical habitat for Lynx.

The second step is to determine habitat patches that meet the minimum area requirement. Those patches that have an area smaller than A are removed (Figure 2). Land Cover Data
Figure 2. Removal of patches that are below the minimum area requirements. Different color patches represent separate habitat patches, and patches that are to be removed are shown in Red (Left) and subsequently removed (Right).

A third major step is to create the matrix quality map by reclassing the land cover map to reflect assumed resistance to movement (Figure 3). Resistance values are described in a reclass table (Table 1). Note that different assumptions about sensitivity of a species to movement through different types of land cover can be represented.

Table 1. Matrix resistance values.
Cover type Low Sensitivity High Sensitivity
Forest 1.0 1.0
Shrubland 1.5 1.5
Grasslands 2.0 2.0
Secondary roads 2.0 2.5
Ice-snow 5.0 5.0
Agriculture 5.0 5.0
Barren 8.0 8.0
Orchards-vineyards 8.0 8.0
Wetlands 8.0 8.0
Residential-Commercial 10.0 100.0
Highways 20.0 1000.0
Water 100.0 1000.0

Land Cover Data
Figure 3. Conversion of land cover types to matrix quality. A resistance value for each cell is created through RECLASSing the land cover data (left) that has roads "burned-in". Higher resistance values are shown using darker shades of red (right), so that urban areas such as Denver (far right, top) and highways stand out.

The fourth step is to identify "clusters" of patches – those that are within the prescribed dispersal distance (Figure 4). That is, a single path between patches is not assumed, rather, patches are found to be "connected" if any part of a patch can reach any part of another patch assuming a given dispersal distance (that reflects matrix quality). Using this methodology provides much improved computer performance, as compared to finding the least-cost path. Land Cover Data
Figure 4. Finding "clusters of habitat patches. Individual patches are shown in unique colors (left). Groups of patches that are within the dispersal distance are considered clusters. For example, cluster "A" is composed of patches: 1, 2, and 3; "B" is composed of 4, 5, and 14; etc.

This modeling approach supports two modes of use. The first is that if specific parameters are available for a given species, then those can be input and the model results interpreted. But, a more robust mode of use is to examine how connectivity changes over a range of parameter values (e.g., a sensitivity analysis). The model input is set to handle this, as each set of major parameters allows a list of parameter values. This enables a critical range or threshold to be identified. For example, given a range of sensitivities and dispersal ability, the output of a series of models can be grouped to illustrate critical scales that might result in markedly different connectivity regimes (Figure 5). The ability of a single species can be compared directly to this critical scale. Also, a broad range of species can be filtered to determine if they are likely to be sensitive to fragmentation. Land Cover Data
Figure 5. Identifying critical scales. A critical scale of dispersal ability occurs between 10 and 30 km.

Also, by examining the output maps directly, locations on the landscape that are critical to maintain connectivity can be identified (Figure 6). That is, the "pinch-points" or "bottle-necks" to landscape movement can be readily identified (Figure 7).
Land Cover Data
Figure 6. Dispersal ability ranging from 1 km to 10 km to 100 km. Different colored areas represent distinct clusters of patches, so that at short dispersal distances (Left), roads (grey lines) are seen to delimit patches and create a fragmented landscape. With greater dispersal ability, landscape connectivity increases, and important locations (I-70 west of Vail) become apparent (middle). At large distances, the landscape is fairly-well connected.
Land Cover Data
Figure 7. Pinch-points in the Southern Rocky Mountains for lynx.


Because land use and roads are explicitly incorporated in the model, and alternative scenarios can be easily generated, fragmentation can be assessed in a meaningful way by comparing natural vegetation patterns to a human-modified landscape. Often, landscape fragmentation is being caused by modifications in the intervening matrix that are occurring at a much faster rate changes directly to the habitat. Given these situations, models of landscape fragmentation must incorporate direct changes to matrix. Ideally, model- and field-based inquiry operate in tandem. This modeling approach was developed to provide improved biological realism into understanding landscape-level processes, but models are typically challenged – and rightly so -- on the basis of the empirical data that provide the foundation for the estimated input parameters. Modeling is valuable when field-based data are not available. An interesting finding of a model of black-bear dispersal near Banff, Canada (Clevenger et al. 2002) suggests that a model based on expert literature performed better, as assessed by comparison to an empirical model, than an expert opinion-based model. Also, models can be used to conduct a preliminary analysis to determine what field parameters are the most important to collect.

Landscape graphs

Most models have relied on the least-cost path to derive cost-distances between patches (e.g., Bunn et al. 2000; Singleton and Lehmkuhl 2000). Least-cost paths are presumed to better approximate the actual distance a species moves, as compared to Euclidean distance, but estimating these paths is demanding on computer resources (Bunn et al. 2000). Part of the demand is related to computing distances for all pairs of patches – though assumptions of uni-directional flow require only roughly half of the pairs -- O(n(n-1)/2).

A refinement to this standard methodology uses "landscape graphs" – work in progress -- that differ from traditional graphs (sensu Bunn et al. 2000; Urban and Keitt 2001; Wallis 2000) in two ways. First, the topology of landscape graphs is computed by establishing adjacencies through Thiessen polygons (computed either with Euclidean- or cost-allocation methods). Practically this reduces the number of edges (connections between nodes or patches) in a graph and hence computation complexity -- and an adjacency list stores only connected features (Theobald 2001). Second, instead of computing inter-patch distance using the least-cost path, I find the average distance of paths that travel through the shared boundary of the habitat patches allocation polygon. Though this has not been tested, this more reasonably approximates the approach of individual-based models that allow for a probabilistic interpretation of species moving across a landscape (e.g., Boone and Hunter 1996; Shippers et al. 1996). The connection between patches is represented, not as a straight-line edge between nodes, but as a polyline that begins at a patch edge, passes through the mid-point of the shared boundary of the Thiessen polygons, then ends at the adjacent patch edge. This allows a somewhat more realistic portrayal of the linkage between patches.


This work was completed with support from the David H. Smith Fellowship, The Nature Conservancy and the Colorado Department of Transportation. I thank Randy Boone for discussions about alternative approaches to least- cost path modeling.


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Author Information

David M. Theobald, Ph.D.
David H. Smith Conservation Fellow, The Nature Conservancy
Research Scientist, Natural Resource Ecology Lab
Assistant Professor, Department of Natural Resource Recreation & Tourism
Colorado State University
Fort Collins, CO 80523-1499