(C116) Aggregation Index 


g_{ii} = number of like adjacencies (joins) between pixels of patch type (class) i based on the singlecount method. maxg_{ii} = maximum number of like adjacencies (joins) between pixels of patch type (class) i (see below) based on the singlecount method. 

Description 
AI equals the number of like adjacencies involving the corresponding class, divided by the maximum possible number of like adjacencies involving the corresponding class, which is achieved when the class is maximally clumped into a single, compact patch; multiplied by 100 (to convert to a percentage). If a_{i} is the area of class i (in terms of number of cells) and n is the side of a largest integer square smaller than a_{i}, and m = a_{i}  n^{2}, then the largest number of shared edges for class i, maxg_{ii} will take one of the three forms: maxg_{ii} = 2n(n1) , when m = 0, or maxg_{ii} = 2n(n1) + 2m 1, when m ≤ n, or maxg_{ii} = 2n(n1) + 2m 2, when m > n. Note, because of the design of the metric, like adjacencies are tallied using the singlecount method, and all landscape boundary edge segments are ignored, even if a border is provided. 

Units 
Percent 

Range 
0 ≤ AI ≤ 100 Given any P_{i} , AI equals 0 when the focal patch type is maximally disaggregated (i.e., when there are no like adjacencies); AI increases as the focal patch type is increasingly aggregated and equals 100 when the patch type is maximally aggregated into a single, compact patch. AI is undefined and reported as “N/A" in the "basename".class file if the class consists of a single cell. Note, AI is closely related to the Landscape Shape Index (LSI), only the latter is based on perimeter surfaces as opposed in internal like adjacencies. Both metrics can be normalized to reflect the fact the minimum and maximum values vary depending on P_{i}; the range of possible values is greatest when P_{i} = 0.5. The normalized versions of LSI and AI are completely redundant; thus, FRAGSTATS only computes the normalized LSI (nLSI) metric. 

Comments 
Aggregation index is calculated from an adjacency matrix, which shows the frequency with which different pairs of patch types (including like adjacencies between the same patch type) appear sidebyside on the map. Aggregation index takes into account only the like adjacencies involving the focal class, not adjacencies with other patch types. In addition, in contrast to all of the other metrics based on adjacencies, the aggregation index is based on like adjacencies tallied using the singlecount method, in which each cell side is counted only once. Consequently, the tallies given in the “basename”.adj output file are not correct for this metric. Further, because of the design of the metric, landscape boundary edge segments are ignored, even if a border is provided FRAGSTATS handles this case by distinguishing between internal like adjacencies (i.e., like adjacencies involving cells inside the landscape) and external like adjacencies (i.e., like adjacencies between cells inside the landscape and those in the border). Only internal like adjacencies are used in the calculation of this metric; a landscape border has no affect on this metric. The aggregation index is scaled to account for the maximum possible number of like adjacencies given any P_{i}. The maximum aggregation is achieved when the patch type consists of a single, compact patch, which is not necessarily a square patch. 