(L9) Landscape Shape Index

E =                  total length of edge in landscape in terms of number of cell surfaces; includes all landscape boundary and background edge segments.

min E =           minimum total length of edge in landscape in terms of number of cell surfaces (see below).

Description

LSI equals the total length of edge in the landscape, given in number of cell surfaces, divided by the minimum total length of edge possible, also given in number of cell surfaces, which is achieved when the landscape consists of a single patch. If A is the landscape area, including all internal background (in terms of number of cells), and n is the side of the largest integer square smaller than A (denoted ) and m = A - n², then the minimum edge or perimeter of the landscape, min-E, will take one of the three forms (Milne 1991, Bogaert et al. 2000):

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

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

min-E = 4n + 4, when A > n(1+n).

Units

None

Range

LSI ≥ 1, without limit.

LSI = 1 when the landscape consists of a single square (or almost square) patch; LSI increases without limit as landscape shape becomes more irregular and/or as the length of edge within the landscape increases.

Comments

Landscape shape index provides a standardized measure of total edge or edge density that adjusts for the size of the landscape. Because it is standardized, it has a direct interpretation, in contrast to total edge, for example, that is only meaningful relative to the size of the landscape. LSI can also be interpreted as a measure of patch aggregation or disaggregation, similar to the class-level interpretation. Specifically, as LSI increases, the patches become increasingly disaggregated.