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 have been developed to quantify categorical map patterns. An exhaustive review of all published metrics, therefore, is beyond the scope of this document. 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 -- 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:

    1. 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.

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

    3. 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.

    4. 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 -- 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:

    1. Patch area and edge -- 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.). Patch size is typically computed as the total area of the patch, regardless of its spatial character. However, patch size can also be characterized by its spatial extent; i.e., how far-reaching it is. This is known as the patch radius of gyration, which measures how far across the landscape a patch extends its reach on average, given by the mean distance between cells in a patch. 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 summarized for the class or landscape as a whole using an area-weighted mean, this metric is also known as correlation length and gives the distance that one might expect to traverse the map while staying in a particular patch, from a random starting point and moving in a random direction (Keitt et al. 1997). The boundaries between patches (or edges) represent another fundamental spatial attribute of a patch mosaic. The length of edge can be summarized at the patch level as the perimeter of the patch, and at the class and landscape levels as the total length of edge involving the focal class or across the entire mosaic, respectively.

    2. Patch shape complexity -- Shape complexity refers 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 or morphology. 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 measures emphasize particular aspects of patch shape, such as compaction/elongatedness (contiguity index, 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).

    3. Core Area -- Core area refers the interior area of patches after a user-specified edge buffer is eliminated. The edge buffer represents the distance at which the "core" or interior of a patch is unaffected by the edge 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 patch area (e.g., mean patch size and variability) can be formulated in terms of core area.

    4. Contrast -- Contrast refers to the relative difference among patch types. For example, mature forest next to young 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. Note, contrast is an attribute of the edge itself, whereas core area is an attribute of the patch interior after accounting for adverse edge effects that penetrate into patches (and thus have a corresponding depth-of-edge effect).

    5. Aggregation -- Aggregation refers to the degree of aggregation or clumping of patch types. This property is also often referred to as landscape texture. Aggregation is an umbrella term used to describe several closely related concepts: 1) dispersion, 2) interspersion, 3) subdivision, and 4) isolation. Each of these concepts relates to the broader concept of aggregation, but is distinct from the others in subtle but important ways. Aggregation metrics deal variously with the spatial properties of dispersion and interspersion. Dispersion refers to the spatial distribution of a patch type (i.e., how spread out or disperse it is) without explicit reference to any other patch types. Interspersion refers to the spatial intermixing of different patch types without explicit reference to the dispersion of any patch type. In the real world, however, these properties are often correlated. Not surprisingly, therefore, some aggregation metrics deal with dispersion solely, others deal with interspersion solely, and others deal with both, and thus there are a bewildering variety of metrics in this group. Many of the metrics in this group are derived from the cell adjacency matrix, in which the adjacency of patch types is first summarized in an adjacency or co-occurrence matrix, which shows the frequency with which different pairs of patch types (including like adjacencies between the same patch type) appear side-by-side on the map.

    6. Subdivision -- Subdivision refers to the degree to which the landscape 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. Note, subdivision and dispersion are closely related concepts. Both refer generally to the aggregation of the landscape, but subdivision deals explicitly with the degree to which the landscape is broken up into disjunct patches, whereas the concept and measurement of dispersion does not honor patches per se (since it is based on cell adjacencies). In the real world, these two aspects of landscape structure are often highly correlated. Subdivision can be measured quite simply by the number or density of patches. 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.

    7. Isolation -- Isolation refers to the tendency for patches to be relatively isolated in space (i.e., distant) from other patches of the same or ecologically similar class. Isolation is closely related to the concept of subdivision; both refer to the subdivision per se of patch types, but isolation deals explicitly with the degree to which patches are spatially isolated from each other, whereas subdivision doesn't address the distance between patches, only that they are disjunct. 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. Isolation can also 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, as in the similarity index (McGarigal et al. 2002). Importantly, in all of these measures of isolation, distance need not be defined as Euclidean (i.e., straight line) distance. Instead, the functional distance between patches might be based on some nonlinear function of Euclidean distance that reflects the probability of connection at a given distance, or a resistance-weighted distance function that reflects the cost distance between patches on a resistant (cost) surface.

    8. Connectivity -- Connectivity refers to the facilitation or impedance of ecological flows (e.g., organisms, materials, energy) across the landscape in space and/or time, and it is process-dependent; i.e., how the landscape pattern affects connectivity depends on the particular ecological flow under consideration. Connectivity is also a synoptic concept as it integrates multiple aspects of landscape pattern, including the aggregation, subdivision and isolation attributes of the landscape mosaic. As such, many of the  configuration metrics described above can affect landscape connectivity and could in their own right be considered connectivity metrics. However, each of the previous metric groups can be used to address pattern and process unrelated to landscape connectivity per se and thus have been separated out as separate groups. The group here considers metrics devoted specifically to landscape connectivity and currently includes only cell-level metrics; specifically, the Conductance metric based on resistant kernels.