(C9) Landscape Shape Index

e_i =                  total length of edge (or perimeter) of class i in terms of number of cell surfaces; includes all landscape boundary and background edge segments involving class i.

min e_i =          minimum total length of edge (or perimeter) of class i in terms of number of cell surfaces (see below).

Description

LSI equals the total length of edge (or perimeter) involving the corresponding class, given in number of cell surfaces, divided by the minimum length of class edge (or perimeter) possible for a maximally aggregated class, also given in number of cell surfaces, which is achieved when the class is maximally clumped into a single, compact patch. If a_i is the area of class i (in terms of number of cells)[note, this is equivalent to the sum of patch areas across all patches of class i] and n is the side of the largest integer square smaller than a_i (denoted ) and m = a_i - n², then the minimum edge or perimeter of class i, min-e_i, will take one of the three forms (Milne 1991, Bogaert et al. 2000):

min-e_i = 4n, when m = 0, or

min-e_i = 4n + 2, when n² < a_i ≤ n(1+n), or

min-e_i = 4n + 4, when a_i > n(1+n).

Units

None

Range

LSI ≥ 1, without limit.

LSI = 1 when the landscape consists of a single square or maximally compact (i.e., almost square) patch of the corresponding type; LSI increases without limit as the patch type becomes more disaggregated (i.e., the length of edge within the landscape of the corresponding patch type increases).

Comments

Landscape shape index provides a simple measure of class aggregation or clumpiness and, as such, is very similar to the Aggregation index. The differences lie in whether aggregation is measured via class edge (or perimeter) surfaces (as in LSI) or via internal like adjacencies (as in AI). Since these surface counts are inversely related to each other (i.e., holding area constant, as the perimeter count increases, the internal adjacency count must decrease, and vice versa), these metrics largely measure the same thing. Note, previous versions of FRAGSTATS used a slightly different definition of LSI; hence, the results will differ from previous runs.