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Approach for Application of the Indices to Define Functional Heterogeneity of Forest Landscapes
Use of the indices of heterogeneity is predicated on having a spatially referenced database that embraces the features
of landscape structure essential to D. frontalis. Typically, development of GIS databases requires a substantial commitment
to map and image processing in order to identify and reference pertinent landscape variables. In the case ofD. frontalis, we
are particularly interested in the habitat of the insect, i.e., patches of pines (graded by vulnerability) and lightning-struck
hosts.
In addition to the spatially referenced database, it is also necessary to define how the organism interacts with its
environment, i.e., to relate the natural history of the insect to habitat structure. We indicated earlier that a great deal is known
about the interaction of D. frontalis and its hosts. Literature on this subject was reviewed in our treatme:nt of host defenses.
An essential feature of D. frontalis/host interaction centers on the process of dispersal. The parameters for this process
determine how the network of population centers (infestations) can be connected to habitat patches and lightning-struck
hosts. Although the dispersal process as a whole is poorly understood, certain elements of it have been studied in great detail,
e.g., response of the insect to semiochemicals (Smith et al. 1993). We define boundaries for the dispersal process, based on
estimates available from the published literature (Coulson et al. 1979, Pope et al. 1980, Wagner et al. 1984).
With the GIS database and information on how the insect interacts with its environment, we can use the indices to
examine •functional heterogeneity of the forest landscape. The general approach involves development of three types of
maps: hazard, modified hazard, and heterogeneity. The hazard map is an abstract of the variables associated with different
degrees of vulnerability of forest stands to infestation by D. frontalis. The modified hazard map includes additional information
on location of lighming-struck hosts, infestation centers, and insect behavior. The heterogeneity map integrates these
variables, i.e., information on habitat units, population centers, and insect behavior. This map represents a view of how D.
frontalis might interact with its environment. The map is produced by applying the indices of heterogeneity to the modified
hazard map. A moving-window calculation (Fig. 3) is used. The moving-window approach is a common technique in
landscape ecological studies (Turner et al. 1991). It is particularly useful in defining functional heterogeneity, as window
size and shape can be changed to accommodate different spatial scales (Weins 1989, Levin 1992) (Fig. 4). In the particular
application, we are interested in the spatial scale used by D. frontalis, which is largely set by the distribution and abundance
of habitat units and population centers and the dispersal capability of the insect.
MOVING-WINDOW ANALYSIS
J - . n
i I J' +1 n-1
-{ii{ i i
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........ 1 ....... !...........
---Inaut Array .... Output Array--
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Figure 3.--The moving-window analysis applied to an array. The arrays can be raster renditions of landscape maps. Each cell
(i,j) represents a 2-d sample of the landscape. In this example the window is 3X3 cells. In our methodology functional
heterogeneity is calculated for land attributes in the windows of the input array and placed in the output array.
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