FRAGSTATS Metrics.–Although connectivity can be evaluated using a wide variety of FRAGSTATS metrics that indirectly say something about either the structural or functional connectedness of the landscape, FRAGSTATS computes a few metrics whose sole purpose is to measure connectivity. Patch cohesion (COHESION) was proposed by Schumaker (1996) to quantify the connectivity of habitat as perceived by organisms dispersing in binary landscapes. Patch cohesion is computed from the information contained in patch area and perimeter. Briefly, it is proportional to the area-weighted mean perimeter-area ratio divided by the area-weighted mean patch shape index (i.e., standardized perimeter-area ratio). It is well known that, on random binary maps, patches gradually coalesce as the proportion of habitat cells increases, forming a large, highly connected patch (termed a percolating cluster) that spans that lattice at a critical proportion (p_c) that varies with the neighbor rule used to delineate patches (Staufer 1985, Gardner et al. 1987). Patch cohesion has the interesting property of increasing monotonically until an asymptote is reached near the critical proportion. Another index, connectance (CONNECT), can be defined on the number of functional joinings, where each pair of patches is either connected or not based on some criterion. FRAGSTATS computes connectance using a threshold distance specified by the user and reports it as a percentage of the maximum possible connectance given the number of patches. The threshold distance can be based on either Euclidean distance or functional distance, as described elsewhere (see Isolation/Proximity Metrics). 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, and is computed as the area-weighted mean radius of gyration across all patches in the class or landscape. Correlation length is not included with the connectivity metrics in the FRAGSTATS graphical user interface because it is already included as a distribution metric for patch radius of gyration (GYRATE_AM) under the Area/Density/Edge metrics. 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 traversability of the map (Keitt et al. 1997).

Finally, FRAGSTATS also computes a traversability index (TRAVERSE) based on the idea of ecological resistance. A hypothetical organism in a highly traversable neighborhood cell can reach a large area with minimal crossing of “hostile” cells. This metric uses a resistance-weighted spread algorithm to determine the area that can be reached from each cell in a focal patch. The focal cell gets an organism-specific “bank account,” which represents, say, an energy budget available to the organism for dispersal from the focal cell. The size of the account is selected to reflect the organism’s dispersal or movement ability, and translates into ecological neighborhood size around a focal cell. Each patch type (including the focal patch type) is assigned a cost, based on a user-specified resistance matrix. Specifically, relative to a each focal patch type, each patch type is assigned a resistance coefficient in the form of weights ranging from 1 (minimum resistance, usually associated with focal patch type) to any higher number that reflects the relative increase in resistance associated with each patch type. The index is computed at the individual cell level as follows. The metric is computed by simulating movement away from the focal cell in all directions, where there is a cost to move through every cell. Even a cell of the same patch type will have a cost, usually set to 1, so that under the best circumstances (i.e., minimum resistance), there will exist a maximum dispersal area based on the specified account or energy budget. Note that assigning a (small) cost for traveling through the focal community (typically a cost of 1) results in a linearly decaying function. Moving through more resistant cells costs more and drains the account faster. Thus, depending on the resistance of the actual landscape in the vicinity of the focal cell, there will be a certain area that a dispersing organism can access. This area represents the least-cost hull around the focal cell, or the maximum distance that can be moved from the cell in all directions until the “bank account” is depleted. This dispersal area, given as a percentage of the maximum dispersal area under conditions of minimum resistance, provides a measure of the traversability of the landscape in the vicinity of the focal cell. Averaging this index across cells at the patch, class, or landscape level provides an index of traversability.