The common usage of the term “landscape metrics” refers exclusively to indices developed for categorical map patterns. Landscape metrics are algorithms that quantify specific spatial characteristics of patches, classes of patches, or entire landscape mosaics. A plethora of metrics has been developed to quantify categorical map patterns. An exhaustive review of all published metrics, therefore, is beyond the scope of this chapter. These metrics fall into two general categories: those that quantify the composition of the map without reference to spatial attributes, and those that quantify the spatial configuration of the map, requiring spatial information for their calculation (McGarigal and Marks 1995, Gustafson 1998).

Composition is easily quantified and refers to features associated with the variety and abundance of patch types within the landscape, but without considering the spatial character, placement, or location of patches within the mosaic. Because composition requires integration over all patch types, composition metrics are only applicable at the landscape-level. There are many quantitative measures of landscape composition, including the proportion of the landscape in each patch type, patch richness, patch evenness, and patch diversity. Indeed, because of the many ways in which diversity can be measured, there are literally hundreds of possible ways to quantify landscape composition. Unfortunately, because diversity indices are derived from the indices used to summarize species diversity in community ecology, they suffer the same interpretative drawbacks. It is incumbent upon the investigator or manager to choose the formulation that best represents their concerns. The principle measures of composition are:


    Proportional Abundance of each Class.–One of the simplest and perhaps most useful pieces of information that can be derived is the proportion of each class relative to the entire map.


    Richness.--Richness is simply the number of different patch types.


    Evenness.--Evenness is the relative abundance of different patch types, typically emphasizing either relative dominance or its compliment, equitability. There are many possible evenness (or dominance) measures corresponding to the many diversity measures. Evenness is usually reported as a function of the maximum diversity possible for a given richness. That is, evenness is given as 1 when the patch mosaic is perfectly diverse given the observed patch richness, and approaches 0 as evenness decreases. Evenness is sometimes reported as its complement, dominance, by subtracting the observed diversity from the maximum for a given richness. In this case, dominance approaches 0 for maximum equitability and increases >0 for higher dominance.


    Diversity.--Diversity is a composite measure of richness and evenness and can be computed in a variety of forms (e.g., Shannon and Weaver 1949, Simpson 1949), depending on the relative emphasis placed on these two components.

Spatial configuration is much more difficult to quantify and refers to the spatial character and arrangement, position, or orientation of patches within the class or landscape. Some aspects of configuration, such as patch isolation or patch contagion, are measures of the placement of patch types relative to other patches, other patch types, or other features of interest. Other aspects of configuration, such as shape and core area, are measures of the spatial character of the patches. There are many aspects of configuration and the literature is replete with methods and indices developed for representing them (see previous references).

Configuration can be quantified in terms of the landscape unit itself (i.e., the patch). The spatial pattern being represented is the spatial character of the individual patches, even though the aggregation is across patches at the class or landscape level. The location of patches relative to each other is not explicitly represented. Metrics quantified in terms of the individual patches (e.g., mean patch size and shape) are spatially explicit at the level of the individual patch, not the class or landscape. Such metrics represent a recognition that the ecological properties of a patch are influenced by the surrounding neighborhood (e.g., edge effects) and that the magnitude of these influences are affected by patch size and shape. These metrics simply quantify, for the class or landscape as a whole, some attribute of the statistical distribution (e.g., mean, max, variance) of the corresponding patch characteristic (e.g., size, shape). Indeed, any patch-level metric can be summarized in this manner at the class and landscape levels. Configuration also can be quantified in terms of the spatial relationship of patches and patch types (e.g., nearest neighbor, contagion). These metrics are spatially explicit at the class or landscape level because the relative location of individual patches within the patch mosaic is represented in some way. Such metrics represent a recognition that ecological processes and organisms are affected by the overall configuration of patches and patch types within the broader patch mosaic.

A number of configuration metrics can be formulated either in terms of the individual patches or in terms of the whole class or landscape, depending on the emphasis sought. For example, perimeter-area fractal dimension is a measure of shape complexity (Mandelbrot 1982, Burrough 1986, Milne 1991) that can be computed for each patch and then averaged for the class or landscape, or it can be computed from the class or landscape as a whole by regressing the logarithm of patch perimeter on the logarithm of patch area. Similarly, core area can be computed for each patch and then represented as mean patch core area for the class or landscape, or it can be computed simply as total core area in the class or landscape. Obviously, one form can be derived from the other if the number of patches is known and so they are largely redundant; the choice of formulations is dependent upon user preference or the emphasis (patch or class/landscape) sought. The same is true for a number of other common landscape metrics. Typically, these metrics are spatially explicit at the patch level, not at the class or landscape level.

The principle aspects of configuration and a sample of representative metrics are:


    Patch size distribution and density.–The simplest measure of configuration is patch size, which represents a fundamental attribute of the spatial character of a patch. Most landscape metrics either directly incorporate patch size information or are affected by patch size. Patch size distribution can be summarized at the class and landscape levels in a variety of ways (e.g., mean, median, max, variance, etc.), or, alternatively, represented as patch density, which is simply the number of patches per unit area.


    Patch shape complexity.--Shape complexity relates to the geometry of patches--whether they tend to be simple and compact, or irregular and convoluted. Shape is an extremely difficult spatial attribute to capture in a metric because of the infinite number of possible patch shapes. Hence, shape metrics generally index overall shape complexity rather than attempt to assign a value to each unique shape. The most common measures of shape complexity are based on the relative amount of perimeter per unit area, usually indexed in terms of a perimeter-to-area ratio, or as a fractal dimension, and often standardized to a simple Euclidean shape (e.g., circle or square). The interpretation varies among the various shape metrics, but in general, higher values mean greater shape complexity or greater departure from simple Euclidean geometry. Other methods have been proposed--radius of gyration (Pickover 1990), contiguity (LaGro 1991), linearity index (Gustafson and Parker 1992), and elongation and deformity indices (Baskent and Jordan 1995)–but these have not yet become widely used (Gustafson 1998).


    Core Area.--Core area represents the interior area of patches after a user-specified edge buffer is eliminated. The core area is the area unaffected by the edges of the patch. This “edge effect” distance is defined by the user to be relevant to the phenomenon under consideration and can either be treated as fixed or adjusted for each unique edge type. Core area integrates patch size, shape, and edge effect distance into a single measure. All other things equal, smaller patches with greater shape complexity have less core area Most of the metrics associated with size distribution (e.g., mean patch size and variability) can be formulated in terms of core area.


    Isolation/Proximity.--Isolation/proximity refers to the tendency for patches to be relatively isolated in space (i.e., distant) from other patches of the same or similar (ecologically friendly) class. Because the notion of “isolation” is vague, there are many possible measures depending on how distance is defined and how patches of the same class and those of other classes are treated. If dij is the nearest-neighbor distance from patch i to another patch j of the same type, then the average isolation of patches can be summarized simply as the mean nearest-neighbor distance over all patches. Alternatively, isolation can be formulated in terms of both the size and proximity of neighboring patches within a local neighborhood around each patch using the isolation index of Whitcomb et al. (1981) or proximity index of Gustafson and Parker (1992), where the neighborhood size is specified by the user and presumably scaled to the ecological process under consideration. The original proximity index was formulated to consider only patches of the same class within the specified neighborhood. This binary representation of the landscape reflects an island biogeographic perspective on landscape pattern. Alternatively, this metric can be formulated to consider the contributions of all patch types to the isolation of the focal patch, reflecting a landscape mosaic perspective on landscape patterns.


    Contrast.–Contrast refers to the relative difference among patch types. For example, mature forest next to younger forest might have a lower-contrast edge than mature forest adjacent to open field, depending on how the notion of contrast is defined. This can be computed as a contrast-weighted edge density, where each type of edge (i.e., between each pair of patch types) is assigned a contrast weight. Alternatively, this can be computed as a neighborhood contrast index, where the mean contrast between the focal patch and all patches within a user-specified neighborhood is computed based on assigned contrast weights. Relative to the focal patch, if patch types with high contrast lead to greater isolation of the focal patch, as is often the case, then contrast will be inversely related to isolation (at least for those isolation measures that consider all patch types).


    Dispersion.--Dispersion refers to the tendency for patches to be regularly or contagiously distributed (i.e., clumped) with respect to each other. There are many dispersion indices developed for the assessment of spatial point patterns, some of which have been applied to categorical maps. A common approach is based on nearest-neighbor distances between patches of the same type. Often this is computed in terms of the relative variability in nearest-neighbor distances among patches; for example, based on the ratio of the variance to mean nearest neighbor distance. Here, if the variance is greater than the mean, then the patches are more clumped in distribution than random, and if the variance is less than the mean, then the patches are more uniformly distributed. This index can be averaged over all patch types to yield an average index of dispersion for the landscape. Alternative indices of dispersion based on nearest neighbor distances can be computed, such as the familiar Clark and Evans (1954) index.


    Contagion & Interspersion.–Contagion refers to the tendency of patch types to be spatially aggregated; that is, to occur in large, aggregated or “contagious” distributions. Contagion ignores patches per se and measures the extent to which cells of similar class are aggregated. Interspersion, on the other hand, refers to the intermixing of patches of different types and is based entirely on patch (as opposed to cell) adjacencies. There are several different approaches for measuring contagion and interspersion. One popular index that subsumes both dispersion and interspersion is the contagion index based on the probability of finding a cell of type i next to a cell of type j (Li and Reynolds 1993). This index increases in value as a landscape is dominated by a few large (i.e., contiguous) patches and decreases in value with increasing subdivision and interspersion of patch types. This index summarizes the aggregation of all classes and thereby provides a measure of overall clumpiness of the landscape. McGarigal and Marks (1995) suggest a complementary interspersion/juxtaposition index that increases in value as patches tend to be more evenly interspersed in a "salt and pepper" mixture. These and other metrics are generated from the matrix of pairwise adjacencies between all patch types, where the elements of the matrix are the proportions of edges in each pairwise type. There are alternative methods for calculating class-specific contagion using fractal geometry (Gardner and O’Neill 1991). Lacunarity is an especially promising method borrowed from fractal geometry by which contagion can be characterized across a range of spatial scales (Plotnick et al. 1993 and 1996, Dale 2000). The technique involves using a moving window and is concerned with the frequency with which one encounters the focal class in a window of different sizes. A log-log plot of lacunarity against window size expresses the contagion of the map, or its tendency to aggregate into discrete patches, across a range of spatial scales.


    Subdivision.--Subdivision refers to the degree to which a patch type is broken up (i.e., subdivided) into separate patches (i.e., fragments), not the size (per se), shape, relative location, or spatial arrangement of those patches. Because these latter attributes are usually affected by subdivision, it is difficult to isolate subdivision as an independent component. Subdivision can be evaluated using a variety of metrics already discussed; for example, the number, density, and average size of patches and the degree of contagion all indirectly evaluate subdivision. However, a suite of metrics derived from the cumulative distribution of patch sizes provide alternative and more explicit measures of subdivision (Jaeger 2000). When applied at the class level, these metrics can be used to measure the degree of fragmentation of the focal patch type. Applied at the landscape level, these metrics connote the graininess of the landscape; i.e., the tendency of the landscape to exhibit a fine- versus coarse-grain texture. A fine-grain landscape is characterized by many small patches (highly subdivided); whereas, a coarse-grain landscape is characterized by fewer large patches.


    Connectivity.--Connectivity generally refers to the functional connections among patches. What constitutes a "functional connection" between patches clearly depends on the application or process of interest; patches that are connected for bird dispersal might not be connected for salamanders, seed dispersal, fire spread, or hydrologic flow. Connections might be based on strict adjacency (touching), some threshold distance, some decreasing function of distance that reflects the probability of connection at a given distance, or a resistance-weighted distance function. Then various indices of overall connectedness can be derived based on the pairwise connections between patches. For example, one such index, connectance, can be defined on the number of functional joinings, where each pair of patches is either connected or not. Alternatively, from percolation theory, connectedness can be inferred from patch density or be given as a binary response, indicating whether or not a spanning cluster or percolating cluster exists; i.e., a connection of patches of the same class that spans across the entire landscape (Gardner et al. 1987). Connectedness can also be defined in terms of correlation length for a raster map comprised of patches defined as clusters of connected cells. Correlation length is based on the average extensiveness of connected cells. A map's correlation length is interpreted as the average distance one might traverse the map, on average, from a random starting point and moving in a random direction, i.e., it is the expected traversibility of the map (Keitt et al. 1997).