(C114) Percentage of Like Adjacencies

pladj_c.jpg  

gii =    number of like adjacencies (joins) between pixels of patch type (class) i based on the double-count method.

gik =    number of adjacencies (joins) between pixels of patch types (classes) i and k based on the double-count method.

Description

PLADJ equals the number of like adjacencies involving the focal class, divided by the total number of cell adjacencies involving the focal class; multiplied by 100 (to convert to a percentage). In other words, the percentage of cell adjacencies involving the corresponding patch type that are like adjacencies. All background edge segments are included in the sum of all adjacencies involving the focal class, including landscape boundary segments if a border is not provided. Cell adjacencies are tallied using the double-count method in which pixel order is preserved, at least for all internal adjacencies (i.e., involving cells on the inside of the landscape). If a landscape border is present, adjacencies on the landscape boundary are counted only once, as are all adjacencies with background.[gii = intLike+extLike][gik = intTrue+intLike+extTrue+extLike]

Units 

Percent                                                                          

Range

0 ≤ PLADJ ≤ 100


PLADJ equals 0 when the corresponding patch type is maximally disaggregated (i.e., every cell is a different patch) and there are no like adjacencies. This occurs when the class is subdivided into one cell patches. Note, this condition can only be achieved when the proportion of the landscape comprised of the focal class (Pi) is ≤ 0.5. When Pi = 0.5, this occurs only when the class is distributed as a perfect checkerboard. When Pi > 0.5, the checkerboard begins to fill in and there will exist like adjacencies. PLADJ increases as the corresponding patch type becomes increasingly aggregated such that the proportion of like adjacencies increases. PLADJ = 100 when the landscape consists of single patch and all adjacencies are between the same class, and the landscape contains a border comprised entirely of the same class. If the landscape consists of single patch but does not contain a border, PLADJ will be less than 100 due to the background edge segments in the tally of adjacencies involving the focal class. Finally, PLADJ is undefined and reported as “N/A” in the “basename”.class file if the class consists of a single cell.

Comments

Percentage of like adjacencies is calculated from the adjacency matrix, which shows the frequency with which different pairs of patch types (including like adjacencies between the same patch type) appear side-by-side on the map. PLADJ measures the degree of aggregation of the focal patch type. Thus, it is a measure of class-specific contagion. Regardless of how much of the landscape is comprised of the focal class (Pi), this index will be minimum if the patch type is maximally dispersed (or disaggregated), and it will be maximum if the patch type is maximally contagious. However, this index does not account for the fact that the percentage of like adjacencies for a random distribution equals Pi. If the percentage of like adjacencies is less than Pi, then the patch type is more dispersed than expected of a random landscape. Conversely, if the percentage of like adjacencies is greater than Pi, then the patch type is contagiously distributed. Note, this metric measures only dispersion and not interspersion, and thus may be a useful index of fragmentation of the focal class when interpreted in conjunction with Pi.