Background.--This group of metrics represents a loose collection of metrics that deal with the size of patches and the amount of edge created by these patches. Although these metrics could easily be subdivided into separate groups or assigned to other already recognized groups, there is enough similarity in the basic patterns assessed by these metrics to include them under one umbrella.

The area of each patch comprising a landscape mosaic is perhaps the single most important and useful piece of information contained in the landscape. Not only is this information the basis for many of the patch, class, and landscape indices, but patch area has a great deal of ecological utility in its own right. For example, there is considerable evidence that bird species richness and the occurrence and abundance of some species are strongly correlated with patch size (e.g., Robbins et al. 1989). Most species have minimum area requirements: the minimum area needed to meet all life history requirements. Some of these species require that their minimum area requirements be fulfilled in contiguous habitat patches; in other words, the individual habitat patch must be larger than the species minimum area requirement for them to occupy the patch. These species are sometimes referred to as "area-sensitive" species. Thus, patch size information alone could be used to model species richness, patch occupancy, and species distribution patterns in a landscape given the appropriate empirical relationships derived from field studies.

Although patch area per se may be extremely important ecologically, the extent of patch (or patches collectively) may be even more important. Connectivity is considered a "vital element of landscape structure" (Taylor et al., 1993), but it has eluded precise definition and has been difficult to quantify and implement in practice. In part, this is due to differences between the continuity or "structural connectedness" of patch types (or habitat) and the connectivity or "functional connectedness" of the landscape as perceived by an organism or ecological process. Continuity refers to the physical continuity of a patch type (or a habitat) across the landscape. Contiguous habitat is physically connected, but once subdivided, for example, as a result of habitat fragmentation, it becomes physically disconnected. Continuity can be evaluated by a measure of habitat extensiveness; i.e., the extent of the reach of a contiguous patch or collection of patches on average. The notion of continuity adopts an island biogeographic perspective because the focus is on the physical continuity of a single patch type. What constitutes connectivity or "functional connectedness" between patches, on the other hand, clearly depends on the organism or process of interest; patches that are connected for bird dispersal might not be connected for salamanders, seed dispersal, fire spread, or hydrologic flow. As With (1999) notes, "what ultimately influences the connectivity of the landscape from the organism's perspective is the scale and pattern of movement (scale at which the organism perceives the landscape) relative to the scale and pattern of patchiness (structure of the landscape); ...i.e., a species' gap-crossing or dispersal ability relative to the gap-size distribution on the landscape"(Dale et al. 1994, With and Crist 1995, Pearson et al. 1996, With et al. 1997). Functional connectedness, therefore, relates to the interaction of ecological flows (including organisms) with landscape pattern.

The amount of edge in a landscape is important to many ecological phenomena. In particular, a great deal of attention has been given to wildlife-edge relationships (Thomas et al. 1978 and 1979, Strelke and Dickson 1980, Morgan and Gates 1982, Logan et al. 1985). In landscape ecological investigations, much of the presumed importance of spatial pattern is related to edge effects. The forest edge effect, for example, results primarily from differences in wind and light intensity and quality reaching a forest patch that alter microclimate and disturbance rates (e.g., Gratkowski 1956, Ranney et al. 1981, Chen and Franklin 1990). These changes, in combination with changes in seed dispersal and herbivory, can influence vegetation composition and structure (Ranney et al. 1981). The proportion of a forest patch that is affected in this manner is dependent, therefore, upon patch shape and orientation, and by adjacent land cover. A large but convoluted patch, for example, could be entirely edge habitat. It is now widely accepted that edge effects must be viewed from an organism-centered perspective because edge effects influence organisms differently; some species have an affinity for edges, some are unaffected, and others are adversely affected.

Indeed, one of the most dramatic and well-studied consequences of habitat fragmentation is an increase in the proportional abundance of edge-influenced habitat. Early wildlife management efforts were focused on maximizing edge habitat because it was believed that most species favored habitat conditions created by edges and that the juxtaposition of different habitats would increase species diversity (Leopold 1933). Indeed this concept of edge as a positive influence guided land management practices for most of the twentieth century. Recent studies, however, have suggested that changes in microclimate, vegetation, invertebrate populations, predation, brood parasitism, and competition along forest edges (i.e., edge effects) has resulted in the population declines of several vertebrate species dependent upon forest interior conditions (e.g., Strelke and Dickson 1980, Whitcomb et al. 1981, Kroodsma 1982, Brittingham and Temple 1983, Wilcove 1985, Temple 1986, Noss 1988, Yahner and Scott 1988, Robbins et al. 1989). In fact, many of the adverse effects of forest fragmentation on organisms seem to be directly or indirectly related to these so-called edge effects. Forest interior species, therefore, may be sensitive to patch shape because for a given patch size, the more complex the shape, the larger the edge-to-interior ratio. Total class edge in a landscape, therefore, often is the most critical piece of information in the study of fragmentation, and many of the class indices directly or indirectly reflect the amount of class edge. Similarly, the total amount of edge in a landscape is directly related to the degree of spatial heterogeneity in that landscape. Note, edges have myriad ecological effects, as noted above, and may be addressed by simply quantifying the total length of edge (as in the edge metrics included here), or by quantifying the core area remaining after accounting for adverse penetrating edge effects (see core area metrics), or by quantifying the magnitude of contrast along edges due to differences between adjoining patch types (see contrast metrics).

Overall, the size and extent of patches and the edges associated with patch boundaries comprising a class or the entire landscape mosaic is one of the most basic aspects of landscape pattern that can affect myriad processes. For example, although there are myriad effects of habitat fragmentation on individual behavior, habitat use patterns, and intra- and inter-specific interactions, many of these effects are caused by a reduction in habitat area and continuity and an increase in the proportion of edge-influenced habitat. Briefly, as a species' habitat is lost from the landscape (without being fragmented), at some point there will be insufficient area of habitat to support a viable population, and with continued loss eventually there will be insufficient area of habitat to support even a single individual and the species will be extirpated from the landscape. This area relationship is expected to vary among species depending on their minimum area requirements. Moreover, the area threshold for occupancy may occur when total habitat area is still much greater than the individual's minimum area requirement. For example, an individual may not occupy available habitat unless there are other individuals of the same species occupying the same or nearby patches of habitat, or an individual's occupancy may be influenced by what other species are occupying the patch. Similarly, as habitat is lost and simultaneously fragmented into smaller and less extensive patches, at some point there will be insufficient contiguous area of suitable habitat within a home range size area to support an individual. Or the habitat may become too discontinuous, resulting in too much resistance to movement through nonhabitat to accumulate enough suitable habitat. This is the ultimate consequence of habitat loss and fragmentation - insufficient habitat quantity, quality and connectivity to support individuals and viable populations.

FRAGSTATS Metrics.--FRAGSTATS computes several simple statistics representing area, extent 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.

Class area (CA) and Percentage of landscape (PLAND) are fundamental 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.

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 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. When aggregated at the class or landscape level, the Area-weighted mean patch radius of gyration (GYRATE_AM) provides a measure of landscape continuity (also known as correlation length) that represents the average traversability of the landscape for an organism that is confined to remain within a single patch; specifically, it gives the average distance one can move from an random starting point and traveling in a random direction without leaving the patch.

Mean patch size (AREA_MN) at the class level is a function of the number of patches in the class and total class area. Importantly, 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, 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 landscapes of identical size, total edge and edge density are completely redundant. Alternatively, the amount of edge present in a landscape can be compared to that expected for a landscape of the same size but with a simple geometric shape (square) and no internal edge. This is the basis for the Landscape shape index (LSI) and its normalized version (nLSI) that are described in Aggregation metrics section.

Limitations.--Area metrics have limitations imposed by the scale of investigation. Minimum patch size and landscape extent set the lower and upper limits of these area metrics, respectively. These are critical limits to recognize because they establish the lower and upper limits of resolution for the analysis of landscape composition and configuration. Otherwise, area metrics have few limitations. All edge indices are affected by the resolution of the image. Generally, the finer the resolution (i.e., the greater the detail with which edges are delineated), the greater the edge length. At coarse resolutions, edges may appear as relatively straight lines; whereas, at finer resolutions, edges may appear as highly convoluted lines. Thus, values calculated for edge metrics should not be compared among images with different resolutions. In addition, patch perimeter and the length of edges will be biased upward in raster images because of the stair-step patch outline, and this will affect all edge indices. The magnitude of this bias will vary in relation to the grain or resolution of the image, and the consequences of this bias with regards to the use and interpretation of these indices must be weighed relative to the phenomenon under investigation.

Number Metric (acronym)
Patch Metrics
P1 Patch Area (AREA)
P2 Patch Perimeter (PERIM)
P3 Radius of Gyration (GYRATE)
Class Metrics
C1 Total (Class) Area (CA)
C2 Percentage of Landscape (PLAND)
C3 Largest Patch Index (LPI)
C4 Total Edge (TE)
C5 Edge Density (ED)
C6-C11 Patch Area Distribution (AREA_MN, _AM, _MD, _RA, _SD, _CV)
C12-C17 Radius of Gyration Distribution (GYRATE_MN, _AM, _MD, _RA, _SD, _CV)
Landscape Metrics
L1 Total Area (TA)
L2 Largest Patch Index (LPI)
L3 Total Edge (TE)
L4 Edge Density (ED)
L5-L10 Patch Area Distribution (AREA_MN, _AM, _MD, _RA, _SD, _CV)
L11-L16 Radius of Gyration Distribution (GYRATE_MN, _AM, _MD, _RA, _SD, _CV)