FRAGSTATS Metrics.--FRAGSTATS computes several simple statistics representing area and perimeter (or edge) at the patch, class, and landscape levels. Area metrics quantify landscape composition, not landscape configuration. As noted above, the area (AREA) of each patch comprising a landscape mosaic is perhaps the single most important and useful piece of information contained in the landscape. However, the size of a patch may not be as important as the extensiveness of the patch for some organisms and processes. Radius of gyration (GYRATE) is a measure of patch extent; that is, how far across the landscape a patch extends its reach. All other things equal, the larger the patch, the larger the radius of gyration. Similarly, holding area constant, the more extensive the patch (i.e., elongated and less compact), the greater the radius of gyration. The radius of gyration can be considered a measure of the average distance an organism can move within a patch before encountering the patch boundary from a random starting point. When aggregated at the class or landscape level, radius of gyration provides a measure of landscape connectivity (known as correlation length) that represents the average traversability of the landscape for an organism that is confined to remain within a single patch.

Class area (CA) and percentage of landscape (PLAND) are measures of landscape composition; specifically, how much of the landscape is comprised of a particular patch type. This is an important characteristic in a number of ecological applications. For example, an important by-product of habitat fragmentation is habitat loss. In the study of forest fragmentation, therefore, it is important to know how much of the target patch type (habitat) exists within the landscape. In addition, although many vertebrate species that specialize on a particular habitat have minimum area requirements (e.g., Robbins et al. 1989), not all species require that suitable habitat to be present in a single contiguous patch. For example, northern spotted owls have minimum area requirements for late-seral forest that varies geographically; yet, individual spotted owls use late-seral forest that may be distributed among many patches (Forsman et al. 1984). For this species, late-seral forest area might be a good index of habitat suitability within landscapes the size of spotted owl home ranges (Lehmkuhl and Raphael 1993). In addition to its direct interpretive value, class area (in absolute or relative terms) is used in the computations for many of the class and landscape metrics.

FRAGSTATS computes several simple statistics representing the number or density of patches, the average size or radius of gyration of patches, and the variation in patch size or radius of gyration at the class and landscape levels. These metrics usually are best considered as representing landscape configuration, even though they are not spatially explicit measures. Number of patches (NP) or patch density (PD) of a particular habitat type may affect a variety of ecological processes, depending on the landscape context. For example, the number or density of patches may determine the number of subpopulations in a spatially-dispersed population, or metapopulation, for species exclusively associated with that habitat type. The number of subpopulations could influence the dynamics and persistence of the metapopulation (Gilpin and Hanski 1991). The number or density of patches also can alter the stability of species interactions and opportunities for coexistence in both predator-prey and competitive systems (Kareiva 1990). The number or density of patches in a landscape mosaic (pooled across patch types) can have the same ecological applicability, but more often serves as a general index of spatial heterogeneity of the entire landscape mosaic. A landscape with a greater number or density of patches has a finer grain; that is, the spatial heterogeneity occurs at a finer resolution. Although the number or density of patches in a class or in the landscape may be fundamentally important to a number of ecological processes, often it does not have any interpretive value by itself because it conveys no information about the area or distribution of patches. Number or density of patches is probably most valuable, however, as the basis for computing other, more interpretable, metrics.

In addition to these primary metrics, FRAGSTATS also summarizes the distribution of patch area and extent (radius of gyration) across all patches at the class and landscape levels. For example, the distribution of patch area (AREA) is summarized by its mean and variability. These summary measures provide a way to characterize the distribution of area among patches at the class or landscape level. For example, progressive reduction in the size of habitat fragments is a key component of habitat fragmentation. Thus, a landscape with a smaller mean patch size for the target patch type than another landscape might be considered more fragmented. Similarly, within a single landscape, a patch type with a smaller mean patch size than another patch type might be considered more fragmented. Thus, mean patch size can serve as a habitat fragmentation index, although the limitations discussed below may reduce its utility in this respect.

Mean patch size at the class level is a function of the number of patches in the class and total class area. In contrast, patch density is a function of total landscape area. Therefore, at the class level, these two indices represent slightly different aspects of class structure. For example, two landscapes could have the same number and size distribution of patches for a given class and thus have the same mean patch size; yet, if total landscape area differed, patch density could be very different between landscapes. Alternatively, two landscapes could have the same number of patches and total landscape area and thus have the same patch density; yet, if class area differed, mean patch size could be very different between landscapes. These differences should be kept in mind when selecting class metrics for a particular application. In addition, although mean patch size is derived from the number of patches, it does not convey any information about how many patches are present. A mean patch size of 10 ha could represent 1 or 100 patches and the difference could have profound ecological implications. Furthermore, mean patch size represents the average condition. Variation in patch size may convey more useful information. For example, a mean patch size of 10 ha could represent a class with 5 10-ha patches or a class with 2-, 3-, 5-, 10-, and 30-ha patches, and this difference could be important ecologically. For these reasons, mean patch size is probably best interpreted in conjunction with total class area, patch density (or number of patches), and patch size variability. At the landscape level, mean patch size and patch density are both a function of number of patches and total landscape area. In contrast to the class level, these indices are completely redundant (assuming there is no internal background). Although both indices may be useful for "describing" 1 or more landscapes, they would never be used simultaneously in a statistical analysis of landscape structure.

In many ecological applications, second-order statistics, such as the variation in patch size, may convey more useful information than first-order statistics, such as mean patch size. Variability in patch size measures a key aspect of landscape heterogeneity that is not captured by mean patch size and other first-order statistics. For example, consider 2 landscapes with the same patch density and mean patch size, but with very different levels of variation in patch size. Greater variability indicates less uniformity in pattern either at the class level or landscape level and may reflect differences in underlying processes affecting the landscapes. Variability is a difficult thing to summarize in a single metric. FRAGSTATS computes three of the simplest measures of variability–range, standard deviation, and coefficient of variation.

Patch size standard deviation (AREA_SD) is a measure of absolute variation; it is a function of the mean patch size and the difference in patch size among patches. Thus, although patch size standard deviation conveys information about patch size variability, it is a difficult parameter to interpret without doing so in conjunction with mean patch size because the absolute variation is dependent on mean patch size. For example, two landscapes may have the same patch size standard deviation, e.g., 10 ha; yet one landscape may have a mean patch size of 10 ha, while the other may have a mean patch size of 100 ha. In this case, the interpretations of landscape pattern would be very different, even though absolute variation is the same. Specifically, the former landscape has greatly varying and smaller patch sizes, while the latter has more uniformly-sized and larger patches. For this reason, patch size coefficient of variation (AREA_CV) is generally preferable to standard deviation for comparing variability among landscapes. Patch size coefficient of variation measures relative variability about the mean (i.e., variability as a percentage of the mean), not absolute variability. Thus, it is not necessary to know mean patch size to interpret the coefficient of variation. Nevertheless, patch size coefficient of variation also can be misleading with regards to landscape structure in the absence of information on the number of patches or patch density and other structural characteristics. For example, two landscapes may have the same patch size coefficient of variation, e.g., 100%; yet one landscape may have 100 patches with a mean patch size of 10 ha, while the other may have 10 patches with a mean patch size of 100 ha. In this case, the interpretations of landscape structure could be very different, even though the coefficient of variation is the same. Ultimately, the choice of standard deviation or coefficient of variation will depend on whether absolute or relative variation is more meaningful in a particular application. Because these measures are not wholly redundant, it may be meaningful to interpret both measures in some applications.

It is important to keep in mind that both standard deviation and coefficient of variation assume a normal distribution about the mean. In a real landscape, the distribution of patch sizes may be highly irregular. It may be more informative to inspect the actual distribution itself, rather than relying on summary statistics such as these that make assumptions about the distribution and therefore can be misleading. Also, note that patch size standard deviation and coefficient of variation can equal 0 under 2 different conditions: (1) when there is only 1 patch in the landscape; and (2) when there is more than 1 patch, but they are all the same size. In both cases, there is no variability in patch size, yet the ecological interpretations could be different.

FRAGSTATS computes several statistics representing the amount of perimeter (or edge) at the patch, class, and landscape levels. Edge metrics usually are best considered as representing landscape configuration, even though they are not spatially explicit at all. At the patch level, edge is a function of patch perimeter (PERIM). At the class and landscape levels, edge can be quantified in other ways. Total edge (TE) is an absolute measure of total edge length of a particular patch type (class level) or of all patch types (landscape level). In applications that involve comparing landscapes of varying size, this index may not be useful. Edge density (ED) standardizes edge to a per unit area basis that facilitates comparisons among landscapes of varying size. However, when comparing classes or landscapes of identical size, total edge and edge density are completely redundant. Alternatively, the amount of edge present in a class or landscape can be compared to that expected for a maximally compact class or landscape of the same size but with a simple geometric shape (square) and no internal edge, respectively. Landscape shape index (LSI) does this. This index measures the perimeter-to-area ratio for the landscape as a whole. This index is similar to the habitat diversity index proposed by Patton (1975), except that we apply the index at the class level as well. LSI is identical to the shape index at the patch level (SHAPE), except that it is based on class area and the associated class perimeter at the class level and the total landscape area and all edges at the landscape level. The minimum value of LSI is always equal to 1 when either the class is maximally compact (at the class level) or the landscape consists of a single patch (at the landscape level). However, the maximum value of LSI varies at the class level with class area. Hence, FRAGSTATS also computes a normalized landscape shape index (nLSI) in which the metric is rescaled by the minimum and maximum values.

Note, shape complexity and aggregation or contagion are closely related concepts. Holding area constant, as shape complexity increases (as measured by any of the perimeter-area ratio measures described above) the patch, class, or entire patch mosaic becomes increasingly disaggregated (i.e., less contagious). For this reason, many of the shape metrics described here are closely related, at least in concept, to the Contagion metrics described elsewhere.