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The Connectivity Index (CI). The CI index is based on a run-length encoding strategy that is commonly used to
encode raster (matrix) data. Run-length encoding is a good compression technique for rasters that have a high degree of
spatial autocorrelation. Run lengths are measured geometrically rather than arithmetically, giving more than linear value to
longer runs. The computational procedures for the CI index are given below.
First, count the runs of matrix elements with the same value (i). For example, 1l 11 would be a run of length L(1) =
4. A row, column, or diagonal may have several runs. For example, vector 111222233333 has three runs. There can be
multiple runs for a given i.
For each row, column, or diagonal, we sum the runs for each distinct element value. For example, vector
1112222211111 has three runs and two values. Converted to run values, the vector is 123, 12345, 12345. The sum of runs,
by element value, for this vector is ES(1) = 21 and ZS(2) = 15. For a given run i of length L, the run value is S(i) = L * ( L +
1 ) / 2. For a given element value i, all possible S(i) are calculated by row, column, and diagonal, with the diagonal S(i)
divided by 2.2 to compensate for separation distance. The total run value for a matrix and a given i is simply the ZS(i) for
that matrix.
For the general NXN matrix, the smallest possible ZS(i), i = 1 to n where n is the number of different values, is
ZSmin(i) = 2 ( N2+ N2/2 -2).
ZSmin(i) exists where all run lengths are 1. The largest possible value, ZSmax(i), must be calculated using NXN
matrix of constant i.
Thus, the range is
The unweighted CI is calculated as
ESmax(i) = NZ(N+I) + 2(Z K(K+I))/2 z - N(N+I)/2 2
R = ZSmax(i) - ZSmin(i).
H = (ES(i) - ESmin(i)) / R.
The CI for a matrix where i values are relative to a function (i.e., hazard rating or probable use) can also be computed.
The run values are calculated as weighted sums (WCI).
WCI = 1; i(_:S(i)), i = 1,2 .....
The Spatial Interaction Index. The third index of heterogeneity is based upon the gravity model and is sensitive to
fragmentation of the highest valued landscape elements. When applied to geographic analysis, the gravity model is called
spatial interaction. Therefore, we have called this index spatial interaction (SI).
SI is based on Newton's law of attraction between masses. It states that attraction is proportional to the product of
two masses (assigned weight) and inversely proportional to the distance between them. For a matrix of landscape elements
represented in matrix form:
, k = 1, where
mkand ml are distinct elements of the matrix representing the attraction measure, r is the distance separating mk and m,, and t is
the maximum value in the matrix.
Functional Heterogeneity of Forest Landscapes and Host Defenses
In this section we examine functional heterogeneity of forest landscapes in relation to epidemiology of D. frontalis.
Our approach is to provide (i) a general overview of the procedure used to characterize functional heterogeneity, (ii) illustrate
how the methodology facilitates integration of intbrmation on landscape structure and natural history of D. frontalis, and (iii)
conclude with an interpretation of how host defenses influence epidemiology of the insect. 277