Patches form the basis (or building blocks) for categorical maps (or patch mosaics). Depending on the method used to derive patches (and therefore the data available), they can be characterized compositionally in terms of variables measured within them. This may include the mean (or mode, median, or max) value and internal heterogeneity (variance, range). However, in most applications, once patches have been established, the within-patch heterogeneity is ignored and the patches are assigned a nominal class value to represent the composition of the patch. Landscape pattern metrics focus on the spatial character and distribution of patches in the neighborhood of each cell or across the landscape as a whole. While individual patches possess relatively few fundamental spatial characteristics (e.g., size, perimeter, and shape), collections of patches may have a variety of aggregate properties, depending on whether the aggregation is over a single class (patch type) or multiple classes, and whether the aggregation is within a specified subregion of a landscape (e.g., the neighborhood of each focal cell) or across the entire landscape. Consequently, landscape metrics can be defined at four levels corresponding to a logical hierarchical organization of spatial heterogeneity in patch mosaics.
- Cell-level metrics -- Cell metrics provide the finest spatial unit of resolution for characterizing spatial patterns in categorical maps (when defined as a raster image). They are defined for individual grid cells, and characterize the spatial context (i.e., ecological neighborhood) of cells without explicit regard to patch or class affiliation. In other words, cell metrics are not patch-centric, even though the ecological neighborhood (defined by the user) is characterized by the structure of the patch mosaic surrounding the cell. The result is a single value for each cell and the result is returned as a raster or grid. Importantly, cell metrics derive from the class of the focal cell in relation to its ecological neighborhood and, importantly, are agnostic to the particular patch it is in or the explicit patch structure of its neighborhood. In contrast, patch-based metrics characterize the patch itself as an independent spatial entity, or characterize the patch mosaic of a single class or the entire patch mosaic within a fixed ecological neighborhood or the full landscape.
- Patch-level metrics -- Patch metrics are defined for individual patches, and characterize the spatial character and context of patches. In most applications, patch metrics serve primarily as the computational basis for several of the landscape metrics, for example by averaging patch attributes across all patches in the class or landscape; the computed values for each individual patch may have little interpretive value. However, sometimes patch indices can be important and informative in landscape-level investigations. For example, many vertebrates require suitable habitat patches larger than some minimum size (e.g., Robbins et al. 1989), so it would be useful to know the size of each patch in the landscape. Similarly, some species are adversely affected by edges and are more closely associated with patch interiors (e.g., Temple 1986), so it would be useful to know the size of the core area for each patch in the landscape. The probability of occupancy and persistence of an organism in a patch may be related to patch insularity (sensu Kareiva 1990), so it would be useful to know the nearest neighbor of each patch and the degree of contrast between the patch and its neighborhood. The utility of the patch characteristic information will ultimately depend on the objectives of the investigation.
- Class-level metrics -- Class metrics are integrated over all the patches of a given type (class). These may be integrated by simple averaging, or through some sort of weighted-averaging scheme to bias the estimate to reflect the greater contribution of large patches to the overall index. There are additional aggregate properties at the class level that result from the unique configuration of patches across the landscape. In many applications, the primary interest is in the amount and distribution of a particular patch type. A good example is in the study of habitat fragmentation. Habitat fragmentation is a landscape-level process in which contiguous habitat is progressively sub-divided into smaller, geometrically more complex (initially, but not necessarily ultimately), and more isolated habitat fragments as a result of both natural processes and human land use activities (McGarigal and McComb 1999). This process involves changes in landscape composition, structure, and function and occurs on a backdrop of a natural patch mosaic created by changing landforms and natural disturbances. Habitat loss and fragmentation is the prevalent trajectory of landscape change in several human-dominated regions of the world, and is increasingly becoming recognized as a major cause of declining biodiversity (Burgess and Sharpe 1981, Whitcomb et al. 1981, Noss 1983, Harris 1984, Wilcox and Murphy 1985, Terborgh 1989, Noss and Cooperrider 1994). Class indices separately quantify the amount and spatial configuration of each patch type and thus provide a means to quantify the extent and fragmentation of each patch type in the landscape.
- Landscape-level metrics -- Landscape metrics are integrated over all patch types or classes over the full extent of the data (i.e., the entire landscape). Like class metrics, these may be integrated by a simple or weighted averaging, or may reflect aggregate properties of the patch mosaic. In many applications, the primary interest is in the pattern (i.e., composition and configuration) of the entire landscape mosaic. A good example is in the study of wildlife communities. Aldo Leopold (1933) noted that wildlife diversity was greater in more diverse and spatially heterogenous landscapes. Thus, the quantification of landscape diversity and heterogeneity has assumed a preeminent role in landscape ecology. Indeed, the major focus of landscape ecology is on quantifying the relationships between landscape pattern and ecological processes. Consequently, much emphasis has been placed on developing methods to quantify landscape pattern (e.g., O'Neill et al. 1988, Li 1990, Turner 1990, Turner and Gardner 1991) and a great variety of landscape-level metrics have been developed for this purpose.
It is important to note that while many metrics have counterparts at several levels, their interpretations may be somewhat different. Cell metrics represent the spatial context of local neighborhoods centered on each cell. Patch metrics represent the spatial character and context of individual patches. Class metrics represent the amount and spatial distribution of a single patch type and are interpreted as fragmentation indices.Landscape metrics represent the spatial pattern of the entire landscape mosaic and generally interpreted more broadly as landscape heterogeneity indices because they measure the overall landscape structure. Hence, it is important to interpret each metric in a manner appropriate to its level (cell, patch, class, or landscape).
In addition, it is important to note that while most metrics at higher levels are derived from patch-level attributes, not all metrics are defined at all levels. In particular, collections of patches at the class and landscape level have aggregate properties that are undefined (or trivial) at lower levels. The fact that most higher-level metrics are derived from the same patch-level attributes has the further implication that many of the metrics are correlated. Thus, they provide similar and perhaps redundant information (see below).
Lastly, class and landscape metrics are typically computed for the entire extent of the landscape; i.e., they quantify the structure of the individual class or the entire mosaic over the full extent of the data. This is referred to as global landscape structure, even though the focus may be on a single class within the landscape. However, both class and landscape metrics can also be computed for local windows (defined by the user) placed over each cell one at a time, via a moving window, where the value of the class or landscape metric in each window is returned to the focal cell. The result is new grid in which the cell value represents the local neighborhood structure. This is very similar to the cell metrics described above, since both focus on the structure of a local neighborhood around a focal cell; the main difference is that cell metrics employ unique algorithms that are defined only at the cell level, whereas here the metrics are literally the same as the class and landscape metrics only they are applied to local windows around each focal cell.