FRAGSTATS Metrics.--FRAGSTATS computes several isolation metrics based on nearest-neighbor distance at the patch, class, and landscape levels. Nearest-neighbor distance is defined as the distance from a patch to a neighboring patch of the same or different class, based on the nearest cell center-to-cell center. That is, the distance between the two closest cells from the respective patches, based on the distance between their cell centers. Note, this is a change from version 2.0 which based nearest neighbor distance on cell edge-to-edge distance. These metrics are all fundamentally patch-level metrics (i.e., measured for each patch) that can be summarized at the class or landscape levels.

FRAGSTATS computes two metrics that adopt an island biogeographic perspective on patch isolation: (1) Euclidean nearest neighbor distance and (2) proximity index. Euclidean nearest neighbor distance (ENN) is perhaps the simplest measure of patch context and has been used extensively to quantify patch isolation. Here, nearest neighbor distance is defined using simple Euclidean geometry as the shortest straight-line distance between the focal patch and its nearest neighbor of the same class. Even though nearest neighbor distance is often used to evaluate patch isolation, it is important to recognize that the single nearest patch may not fully represent the ecological neighborhood of the focal patch. For example, a neighboring patch 100 m away that is 1 ha is size may not be as important to the effective isolation of the focal patch as a neighboring patch 200 m away, but 1000 ha in size. To overcome this limitation, the proximity index (PROX) was developed by Gustafson and Parker (1992)[see also Gustafson and Parker 1994, Gustafson et al. 1994, Whitcomb et al. 1981]. This index considers the size and proximity of all patches whose edges are within a specified search radius of the focal patch. The index is computed as the sum, over all patches of the corresponding patch type whose edges are within the search radius of the focal patch, of each patch size divided by the square of its distance from the focal patch. Note that FRAGSTATS uses the distance between the focal patch and each of the other patches within the search radius, similar to the isolation index of Whitcomb et al. (1981), rather than the nearest-neighbor distance of each patch within the search radius (which could be to a patch other than the focal patch), as in Gustafson and Parker (1992). The proximity index quantifies the spatial context of a (habitat) patch in relation to its neighbors of the same class; specifically, the index distinguishes sparse distributions of small habitat patches from configurations where the habitat forms a complex cluster of larger patches. All other things being equal, a patch located in a neighborhood (defined by the search radius) containing more of the corresponding patch type than another patch will have a larger index value. Similarly, all other things being equal, a patch located in a neighborhood in which the corresponding patch type is distributed in larger, more contiguous, and/or closer patches than another patch will have a larger index value. Thus, the proximity index measures both the degree of patch isolation and the degree of fragmentation of the corresponding patch type within the specified neighborhood of the focal patch.

At the class and landscape levels, FRAGSTATS computes several distribution statistics associated with the Euclidean nearest neighbor distance and proximity index. At the class level, the mean proximity index measures the degree of isolation and fragmentation of the corresponding patch type and the performance of the index under various scenarios is described in detail by Gustafson and Parker (1994). FRAGSTATS also summarizes the proximity index at the landscape level by aggregating across all patches in the landscape, although the performance of this index as a measure of overall landscape pattern has not been evaluated quantitatively. Similarly, at the class and landscape levels, FRAGSTATS computes the mean and variability in Euclidean nearest neighbor distance. At the class level, mean nearest-neighbor distance can only be computed if there are at least 2 patches of the corresponding type. At the landscape level, mean nearest-neighbor distance considers only patches that have neighbors. Thus, there could be 10 patches in the landscape, but 8 of them might belong to separate patch types and therefore have no neighbor within the landscape. In this case, mean nearest-neighbor distance would be based on the distance between the 2 patches of the same type. These 2 patches could be close together or far apart. In either case, the mean nearest-neighbor distance for this landscape may not characterize the entire landscape very well. For this reason, these metrics should be interpreted carefully when landscapes contain rare patch types.

In addition to these first-order statistics, the variability in nearest-neighbor distance measures a key aspect of landscape heterogeneity. Specifically, the standard deviation (SD)in Euclidean nearest neighbor distance (ENN_SD) is a measure of patch dispersion; a small SD relative to the mean implies a fairly uniform or regular distribution of patches across landscapes, whereas a large SD relative to the mean implies a more irregular or uneven distribution of patches. The distribution of patches may reflect underlying natural processes or human-caused disturbance patterns. In absolute terms, the magnitude of nearest-neighbor SD is a function of the mean nearest-neighbor distance and variation in nearest-neighbor distance among patches. Thus, while SD does convey information about nearest neighbor variability, it is a difficult parameter to interpret without doing so in conjunction with the mean nearest-neighbor distance. For example, 2 landscapes may have the same nearest-neighbor SD, e.g., 100 m; yet 1 landscape may have a mean nearest-neighbor distance of 100 m, while the other may have a mean nearest-neighbor distance of 1,000 m. In this case, the interpretations of landscape pattern would be very different, even though the absolute variation is the same. Specifically, the former landscape has a more irregular but concentrated pattern of patches, while the latter has a more regular but dispersed pattern of patches. For these reasons, coefficient of variation (CV) often is preferable to SD for comparing variability among landscapes. Coefficient of variation measures relative variability about the mean (i.e., variability as a percentage of the mean), not absolute variability, and is akin to the familiar indices of dispersion in point patterns based on the variance to mean ratio in nearest neighbor distance (e.g., Clark and Evans 1954). Thus, it is not necessary to know the mean nearest-neighbor distance to interpret this metric. Even so, nearest-neighbor CV can be misleading with regards to landscape structure without also knowing the number of patches or patch density and other structural characteristics. For example, 2 landscapes may have the same nearest-neighbor CV, e.g., 100%; yet 1 landscape may have 100 patches with a mean nearest-neighbor distance of 100 m, while the other may have 10 patches with a mean nearest-neighbor distance of 1,000 m. In this case, the interpretations of overall landscape pattern could be very different, even though nearest-neighbor CV is the same; although the identical CV’s indicate that both landscapes have the same regularity or uniformity in patch distribution. Finally, both SD and CV assume a normal distribution about the mean. In a real landscape, nearest-neighbor distribution may be highly irregular. In this case, it may be more informative to inspect the actual distribution itself (e.g., plot a histogram of the nearest neighbor distances for the corresponding patches), rather than relying on summary statistics such as SD and CV that make assumptions about the distribution and therefore can be misleading.

FRAGSTATS computes two isolation metrics that adopt a landscape mosaic perspective on patch isolation: (1) functional nearest neighbor distance and (2) similarity index. Similarity index (SIMI) is a modification of the proximity index, the difference being that similarity considers the size and proximity of all patches, regardless of class, whose edges are within a specified search radius of the focal patch. The similarity index quantifies the spatial context of a (habitat) patch in relation to its neighbors of the same or similar class; specifically, the index distinguishes sparse distributions of small and insular habitat patches from configurations where the habitat forms a complex cluster of larger, hospitable (i.e., similar) patches. All other things being equal, a patch located in a neighborhood (defined by the search radius) deemed more similar (i.e., containing greater area in patches with high similarity) than another patch will have a larger index value. Similarly, all other things being equal, a patch located in a neighborhood in which the similar patches are distributed in larger, more contiguous, and/or closer patches than another patch will have a larger index value. Essentially, the similarity index performs much the same way as the proximity index, but instead of focusing on only a single patch type (i.e., island biogeographic perspective), it considers all patch types in the mosaic (i.e., landscape mosaic perspective). Thus, the similarity index is a more comprehensive measure of patch isolation than the proximity index for organisms and processes that perceive and respond to patch types differentially.

Similarly, functional nearest-neighbor distance (FNN) accounts for one of the major shortcomings of using Euclidean distance to assess ecological relationships; namely, that the shortest geographic distance may not be the shortest ecological distance as perceived by an organism or process. The character of the intervening landscape can significantly alter the rate of flow of the organism or process of interest. Therefore, it may be more meaningful to assess distance using a least cost path approach. Here, in effect, the distance across a cell is weighted by the degree of resistance it offers to the ecological flow of interest. Thus, the functional distance between two patches is increased proportionate the degree of resistance in the intervening landscape.