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FUNCTIONAL VS. MEASURED HETEROGENEITY
FunctionalHeterogeneity
Measured Heterogeneity
Figure 2.--Relationship of measured heterogeneity (composition of parts of different kinds) to functional heterogeneity (how
an organism perceives and reacts to its environment). Note that measured heterogeneity for the left and right matrices
is the same, but the functional heterogeneity is different.
Interpretation of the significance of index values in the mid-range of the gradient is difficult. The intermediate
heterogeneity conditions are also the most difficult to interpret from the behavioral perspective of the organism, i.e.,
it is difficult to predict how an organism will react to conditions of intermediate heterogeneity.
landscape pattern. Application of the procedures involves (i) classification of land elements based on ecological function, (ii)
tiling of the landscape data (usually maps or images), and (iii) quantification of spatial pattern. Following is a brief description
of each index along with an explanation of the calculation procedure. These methods apply for any NxN array of
weighted landscape elements. We are currently investigating the sensitivity of these indices.
The Angular Moment of Inertia Index (AMI). The AMI is an index that is sensitive to variation in the dispersion
of landscape elements. It is the normalized product of a second moment calculation. The index is a measure of the dispersion
of weighted matrix elements about the centroid of the landscape area. The AMI is calculated using the following
procedures. First, the centroid of the weighted surface (matrix) is calculated. Because each element, a_j,within the matrix has
a value and locational indices attached, the horizontal (Xo)and the vertical (Yo) centroids can be calculated by
Xo = (_j_i(aij),j) / _i_j aij
Yo= (£_Zj(aij).i) / £,Ej aij
Second, Xoand Yo are used to derive the second moment (M) about the centroid
M = Z_jc(o. Xo)2 + (i - Yo)2) • au)
However, because each element in the matrix represents a cell that has a real extent, the second moment for each cell :
must be calculated. The equation becomes
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M = Z_i