Pi = proportion of the landscape occupied by patch type (class) i.
m = number of patch types (classes) present in the landscape, excluding the landscape border if present.
Description MSIEI equals minus the logarithm of the sum, across all patch types, of the proportional abundance of each patch type squared, divided by the logarithm of the number of patch types. In other words, the observed modified Simpson's diversity index divided by the maximum modified Simpson's diversity index for that number of patch types. Note, Pi is based on total landscape area (A) excluding any internal background present.
Units None
Range 0 ≦ MSIEI ≦ 1
MSIDI = 0 when the landscape contains only one patch (i.e., no diversity) and approaches 0 as the distribution of area among the different patch types becomes increasingly uneven (i.e., dominated by 1 type). MSIDI = 1 when distribution of area among patch types is perfectly even (i.e., proportional abundances are the same).
Comments Modified Simpson's evenness index is expressed such that an even distribution of area among patch types results in maximum evenness. As such, evenness is the complement of dominance.