MODELING FUNCTIONAL LANDSCAPE CONNECTIVITY

Output

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).
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).
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.

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.
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.
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).

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.

Figure 7. Pinch-points in the Southern Rocky Mountains for lynx.

Discussion

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.

Acknowledgments

References

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