Within each of these groups, metrics are further grouped into patch, class, and landscape metrics.
9.3
Distribution StatisticsPatch metrics can be summarized at the class and landscape levels using a variety of distribution statistics that provide first-and second-order statistical summaries of the patch metrics for the focal class or the entire landscape, such as: (1) mean, (2) area-weighted mean, (3) median, (4) range, (5) standard deviation, and (6) coefficient of variation. The difference between the mean and the area-weighted mean in this context is especially important as discussed below.Metrics applied to categorical patch mosaics (under the "landscape mosaic model" of landscape structure) fundamentally represent the structure of the landscape as defined by its patch structure. Clearly, patches are the basic building blocks of categorical patch mosaics and, as such, most metrics derive from the spatial character and distribution of the patches themselves. However, most patch-based metrics can be summarized at the class and landscape levels to reflect the character and distribution of individual patches over a broad extent. Indeed, in most applications, the objective involves characterizing the patch structure for a single focal class or for the entire patch mosaic across the full extent of the landscape, rather than focusing on individual patches. Despite the common objective of characterizing the class or landscape structure, metrics differ in whether they offer a "patch-based" or "landscape-based" perspective of landscape structure. This is perhaps best illustrated by the difference between class and/or landscape distribution metrics based on the simple arithmetic mean or the area-weighted mean.
9.4
Mean versus area-weighted meanMetrics based on the mean patch characteristic, such as mean patch size (AREA_MN) or mean patch shape index (SHAPE_MN), provide a measure of central tendency in the corresponding patch characteristic across the entire landscape, but nevertheless describe the patch structure of the landscape as that of the average patch characteristic. Thus, each patch regardless of its size is considered equally (i.e., given equal weight) in describing the landscape structure. Consequently, metrics based on the mean patch characteristic offer a fundamentally patch-based perspective of the landscape structure. They do not describe the conditions, for example, that an animal dropped at random on the landscape would experience, because that depends on the probability of landing in a particular patch, which is dependent on patch size.
9.5Conversely, metrics based on the area-weighted mean patch characteristic, such as the areaweighted mean patch size (AREA_AM) and area-weighted mean patch shape index (SHAPE_AM), while still derived from patch characteristics, provide a landscape-based perspective of landscape structure because they reflect the average conditions of a pixel chosen at random or the conditions that an animal dropped at random on the landscape would experience. This is in fact the basis ...