Gap analysis is based on the comparison of maps of land cover and selected animal species with current patterns of land ownership and management activities. In practice, there have been no preexisting sources for these three spatial data layers at scales compatible with regional land use planning. Of necessity, the state and national Gap Analysis Programs have developed several new approaches to mesoscale (e.g., 1:100,000) mapping of land cover and the predicted distributions of terrestrial vertebrates. A detailed explanation of Gap Analysis methods for development of all data layers is presented by Scott et al. (1996). One important product of the Oregon Gap Analysis effort is an Atlas of Oregon Wildlife. The process of building data sets to create polygon maps for this publication also provided the data for the analyses described below.
The data layers reflecting the distribution of various elements of biodiversity that state Gap Analysis programs develop have multiple uses, but they were primarily intended to provide information about the conservation status of species and ecosystems and to and make spatially explicit recommendations about future changes in land ownership and management that would lead to the long-term maintenance of biodiversity (Kiester et al. 1996, Csuti and Kiester 1996). The ultimate product of a gap analysis isn't a list of "gaps," but a map showing priority areas for conservation action.
"The concept [of gap analysis] is deceptively simple, if not simplistic: within a particular country or region, first identify and classify the various elements of biological diversity in several ways. Then examine the existing and proposed systems of protected areas and other land-management units that help conserve biological diversity. Finally, using various classifications, determine which elements (e.g., major ecosystems, vegetation types, habitat types, species) are unrepresented or poorly represented in the existing system of conservation areas. Once this is known with reasonable precision, priorities for the next set of conservation actions can be established" (Burley 1988:227-228). Gap analysis objectives therefore include:
1. Identify which species and natural communities are unprotected or inadequately protected on existing areas that are managed primarily for their natural values.
Adequate protection means multiple representation in areas managed for their natural values that are large enough to support very viable populations of animals and plants and contain multiple examples of all seral stages of their dominant vegetation cover type. Adequately protected species or vegetation cover types should not be used to identify additional areas to manage for their natural values.
2. Identify which areas in each biological region contain the largest number of unprotected or underprotected species or natural communities (Caicco et al. 1995). These areas are candidates for changes in management status to insure that all species and natural communities are adequately represented in the network of areas managed primarily for biodiversity.
3. Identify which other areas must be managed for their natural values to insure the persistence of unprotected or underprotected species or natural communities not found in areas with concentrations of unprotected or underprotected species or natural communities.
Gap analysis addresses both coarse and fine filter conservation planning strategies. The first level of analysis assesses the adequacy of representation of ecosystems (vegetation types) in reserves and makes recommendations for changes in land management to address inadequacies. A coarse filter conservation strategy assumes that most species will be represented if all ecosystems (described by vegetation types, in our case) are represented in protected areas. Because a coarse filter conservation strategy based on vegetation cover is intended to capture samples of all common species, including plants and invertebrates, the concept behind a vegetation-based coarse filter reserve network is superior to a reserve network based only on a biased subset of species (like terrestrial vertebrates).
This integration involved three data sets: the Oregon hexagon data set, a set of Oregon vegetation polygons (O'Neil et al. 1995), and a table listing the vegetation types which constitute appropriate habitat for each species. The set of Oregon vegetation polygons was first intersected with the hexagon boundaries in ArcInfo to provide a new set of potential habitat polygons. For efficiency these polygons and the table of species habitat types were then processed using a program written in C++ and built upon our in-house object-oriented GIS software library tclib. For each species, this program identified those polygons of appropriate habitat for that species which occur in hexagons where the species is present. Often these polygons were part of a larger parent polygon which extended beyond the boundary of a given hexagon prior to the intersection of the parent vegetation polygons with the hexagon grid. In these cases it was felt that the species range might extend past the boundary of the hexagon into other portions of the original large vegetation polygon, since the hexagon boundaries do not themselves represent boundaries to species movement. However, extending the range too far into hexagons where expert opinion had decided that the species did not occur would in effect overrule that expert opinion. As a compromise, it was decided that species ranges would be extended into adjacent non-occurrence hexagons in cases where the majority of the original parent polygon lay in an occurrence hexagon. Conversely, if the majority of the parent polygon lay outside an occurrence hexagon, then it was felt that the expert opinion had in effect ruled-out the occurrence of the species in that polygon, and thus the species range did not include sub-polygons of that parent polygon occurring in an occurrence hexagon.
Once a set of polygons representing the adjusted species range was found, the built-in capabilities of our software library tclib were exploited to output these polygons both as a raster layer for incorporation in the Oregon Wildlife Atlas and as an ArcInfo generate file for importation into ArcInfo and other off-the-shelf GIS.
The purpose of prioritization analysis is the determination of areas that have the greatest positive cumulative impact for further research and management of biological diversity (Kiester et al. 1996). The procedure uses an integer programming approach applied to reserve selection (Camm et al. 1996, Church et al. 1996, Csuti et al. 1997) and IBM's Optimizing Subroutine Library. This approach uses a regular 640 square kilometer hexagonal grid (White et al. 1992) covering the entire area of concern. Each hexagon contains a list of species found within the bounds of that hexagon. The prioritization procedures determine the maximum nth partial coverages by calculating the maximum number of species that could be found in 1, 2, up to n hexagons (n is usually the maximum number of hexagons needed to represent all the species within a class or category). The first partial coverage begins with the selection of the hexagon with the most species. Then, all pairs, triplets, and so on of hexagons are found that have the greatest combined number of species until one or more sets of hexagons are found that contains all species. These further combinations need not include the hexagon with the maximum number of species in it because, two hexagons' lists when combined may contain more species than the richest hexagon combined with any other hexagon (Kiester 1996). In other words, the analysis finds the sequence of hexagons at each step that adds the most new diversity and determines the minimum number of hexagons that taken together, have an example of every species (Kiester 1996). Many sequences may, and often do, give the same integer maximum number of species. This procedure keeps track of ties so that all equivalent solutions are generated.
The hexagonal grid currently used for mapping biodiversity in Oregon is the U.S. Environmental Protection Agency Environmental Mapping and Assessment (EMAP) grid which covers the contiguous United States (White et al. 1992). This Lambert azimuthal equal area map projection is composed of grid cells approximately 640 square kilometers in size. This size was selected as a "suitable compromise between the desired spatial resolution of sampling and the projected available financial resources" (White et. al., 1992, p. 18).
Species richness mapping requires a logical union of sets. Changes in scale will result in different unions of species sets, not numerical averages that can be calculated for a species richness map at any other scale. Variance at different scales, therefore, can only be determined by performing logical unions at all scales of interest and calculating variance directly (Stoms 1994:347). Two geometries exist for the composition and decomposition of hexagonal grids. New grids will have grid cells some factor of three or four times the size of the original grid. Composing a hexagonal grid by a factor of 3 involves taking a central hexagon and one third of all six neighboring hexagons. The resulting hexagon will be rotated by 30 degrees with respect to the original. Composing a hexagon by a factor of 4 involves taking a central hexagon and one half of all neighboring hexagons. The resulting hexagon shows no rotation with respect to the original. A third geometry allows for the composition of a central hexagon with its six complete neighboring hexagons. Although the resulting polygon is not a hexagon, this polygon has many important properties of a hexagon (e.g. equal distance to all neighboring polygons). Hexagonalgrids cells can be made smaller or decomposed in a similar manner. No seven fold decomposition is possible. This study will look at variations in species richness associated with three fold and seven fold compositions and decompositions of the original EMAP hexagonal grid.
A seven fold compsoition will result in grid cells larger by some factor of seven. In this analysis, grids cells 7 and 49 times as large as the EMAP grid are constructed. Original mapping of the range of terrestrial vertebrates in the state of Oregon was based on the EMAP grid. Because species were either assigned to hexagonal grid cells or not, all data could be selected and manipulated outside of ArcInfo. This was accomplished by setting up a matrix file. Rows represent the 422 terrestrial vertebrates present in Oregon, and columns the 441 EMAP hexagons overlying Oregon. C++ code was written to select a central hexagon and all six of its adjacent neighbors. Then, points defining the outline of the new polygon are selected from the original hexagonal grid's ArcInfo generate file and written to a new polygon file. A union command is performed on rows from the data matrix for the seven selected hexagons. These data are then written out to a new hexagon file. Species richness values in the resulting data are statistically compared with original values.
Three fold compositions or decompositions were not possible on the original data. Three fold (de)composition requires taking one third of all adjacent hexagons. The EMAP hexagon, however, is the minimum mapping unit of the original range maps. Species are either assigned to hexagons or not, without information of where within the hexagon they exist. Thus, range maps based on the EMAP grid cannot be subdivided for three fold (de)compositions.
Three fold analysis instead uses a second generation of species range maps developed for the state of Oregon. Construction of these range maps begins with LANDSAT Multi-spectral Scanner (MSS) imagery. Kagan and Caicco (1992) visually interpreted boundaries of vegetation cover types using MSS false color infrared positive prints at a scale of 1:250,000. The minimum mapping unit was 130 ha. A total of 6916 vegetation polygons were mapped in vector format, with the average size being 3296 ha. These 6916 polygons represent 130 different vegetation types.
O'Neil et. al. (1995) then used a process involving wildlife-habitat relationships (WHR) to assign 420 breeding species to the 130 vegetation types. The wildlife species similarity between each pair of vegetation types was then calculated using the Jaccard coefficient. Vegetation types were then clustered into 30 classes using an algorithm that "minimizes the within-cluster variance relative to the between-cluster variance at each step" (O'Neil et. al. 1995:1484). The clustered vegetation map was entered into ArcInfo and the UNION command was performed with the EMAP hexagonal grid to create a vegetation/hexagon coverage. A generate file was created for the vegetation/hexagon coverage. See Butterfield et al. (1994), Csuti 1996, Scott and Csuti 1997, and Scott et al. (1993) for overviews of the Gap Analysis approach of using habitat relationships to develop predicted distribution maps for vertebrate species.
Besides WHR, the other important factor in determining the range of species is the general area in which they exist. C++ programming took combined WHR information with species range hexagons to create maps of species ranges. This code was modified to output ArcInfo generate files capable of being used in future spatial analysis.
The minimum mapping unit for this three fold analysis will be a triangle compromising one twelfth of the smallest hexagonal grid cell to be mapped. This study will begin at a scale four levels below the EMAP grid. Each hexagon, therefore, with be one eighty-first the size of an EMAP hexagon, or approximately 8 square kilometers. Each triangle will be one twelfth of this size, or approximately 0.67 square kilometers. The resulting hexagonal grid created with C++ programming contains over 400,000 triangular grid cells. This grid was brought into ArcInfo as a coverage and combined with the vegetation/hexagon coverage using the UNION command. A list of triangle-id's and vegetation/hexagons was exported using the ArcInfo Tables UNLOAD command. This list will allow species to be associated with each triangle. Once these matrix values are assigned, a C++ program similar to the seven fold composition program can be used to compose all three fold species richness maps. Use of this program will be more efficient than overlaying new hexagonal grid coverages directly on the vegetation/hexagon coverage in ArcInfo.
Multi-scale analysis of species richness involves integrating a number of spatial selection and overlay commands. Although ArcInfo can be a useful tool for such manipulations, object oriented programming can often be much more efficient. This is especially true if analysis involves repeated selection at one or multiple scales.