Patch-based metrics for categorical landscape mosaics (i.e., patch mosaics) are metrics computed for each individual patch, or for aggregations of patches by patch type (class), or for the entire landscape mosaic. These are the conventional landscape metrics. The model can be parameterized to compute patch-based metrics at any combination of patch, class, and landscape levels. Moreover, the model can be parameterized to compute these metrics for the full landscape or for sub-landscapes based on uniform tiles or user-supplied tiles, or for user-defined uniform windows around random sample locations, user-supplied sample locations. or for every cell in an exhaustive moving window approach. In all but the exhaustive moving window approach, the patch-level metrics return a unique value to each patch, the class-level metrics return a value to each class (patch type), and the landscape-level metrics return a single value for the landscape mosaic, and this tabular output may be for the full landscape, each sub-landscape tile, or each local window around sample locations.
Patch-based metrics have the following distinctive characteristics:
- As the name implies, patch-based metrics are mostly patch-centric; i.e., they are computed for each patch separately, returning a unique value for each patch, or they are computed for aggregations of patches of the same type (i.e., class) or for the entire patch mosaic, returning a unique value for each class or for the entire landscape mosaic, respectively.
- Most patch-based metrics are derived from characteristics of the individual patches, such as their size and shape, or their spatial distribution in relation to other patches. For example, mean patch size is simply a statistical summary of individual patch sizes for all patches of the same class (class level) or for all patches in the landscape (landscape level). Even if mean patch size is calculated within a local window around a focal cell, it is still a statistical summary of the patch size distribution within the window that is independent of the patch membership or patch type of the focal cell. This is in contrast to cell-based metrics in which the calculations are always relative to the patch type of the focal cell.
- Some patch-based metrics summarize the patch mosaic structure based on calculations derived from cell adjacency information. For example, edge density is derived from the frequency of cells abutting unlike cells (i.e., cells of different patch types), which represent edges. Similarly, several of the aggregation metrics, such as the aggregation index and clumpiness index, also derive from cell adjacency information, since the proportion of cell adjacencies that are “like adjacencies” (i.e., cells of the same patch type abutting each other) is a reflection of the aggregation of the patch mosaic. Despite using cellular information in the calculations, these metrics are nonetheless devised to summarize the patch mosaic structure of the landscape or local ecological neighborhood independent of the patch membership or patch type of the focal cell. Cell-based metrics, on the other hand, always summarize the ecological neighborhood in relation to the patch type of the focal cell.
- Patch-based metrics can be computed within local ecological neighborhoods around a sample of focal cells or around all cells in an exhaustive moving window approach. The local ecological neighborhood is represented by a use-specified standard kernel, in which the size of the kernel is adjusted to reflect the ecological process under consideration. Because of mathematical considerations with many of the patch-based class and landscape metrics, the kernel is always treated as a uniform kernel or unweighted kernel, in which each neighboring cell within the window is given equal weight in the calculations. Cell-based metrics, on the other hand, employ non-uniform standard kernels or resistant kernels to represent the local ecological neighborhood around focal cells (see Cell-based metrics for details).