A Technique for Representing Diminishing Habitat Occupation: Feathering Predicted
Species Distributions Near Range Limits in Maine
Randall B. Boone1,2 and William B. Krohn3
1Department of Wildlife Ecology and 3Cooperative Fish and Wildlife Research Unit, University of Maine, Orono
2Current address: Natural Resource Ecology Laboratory, Colorado State University, Fort Collins
Introduction
Species ranges are typically portrayed in Gap Analysis as binary maps, showing areas occupied and not occupied by species. If occupied habitats are predicted by simply identifying suitable habitat within a species’ range, a sharp boundary can occur along that predicted distribution. There are times when a species’ potential habitat has a sharp boundary (e.g., riparian species occupying wetlands in arid landscapes, or habitats abutting ocean). In Maine, inland boundaries are more often a synthetic representation of unknown accuracy. Range boundaries represent an arbitrary small-scale line within a declining probability gradient where the animal is judged sufficiently rare to disregard its occurrence (Krohn 1996). Ranges also can change rapidly and frequently (Hengeveld 1989; Krohn 1996; Brown and Lomolino 1998), suggesting that fixed sharp boundaries between potentially occupied and unoccupied habitats are inappropriate.
Modelers using habitat maps with 100-ha minimum mapping units (MMUs) avoided these artificial boundaries by including in their predictions habitat polygons that overlapped any portion of the species’ range (Scott et al. 1993). Habitat polygons extended varying distances beyond the range limit, essentially blurring the sharp boundary. If polygons were very large (e.g., matrix habitat), they would cause predicted distributions to extend too far into areas outside the species’ range. Modelers therefore subdivided habitat polygons using some convenient tessellation such as counties (Scott et al. 1993) or watersheds (e.g., B. Thompson, pers. comm.), reducing the size of habitat polygons.
These methods worked well when habitat maps had large MMUs, but MMUs of 2 ha are now suggested. For example, the 1994 vegetation map of Colorado has 16,618 polygons, whereas the map for Maine has 1.45 million polygons and covers one third the area (84,113 ha) of Colorado. Equally important is the contrast in habitats throughout a state. In Colorado, differences in factors such as elevation, precipitation, and snowfall lead to strong patterns in vegetation patches. In Maine, small patches of given habitats are relatively evenly distributed throughout the state. Whereas predicted distributions of species in Colorado tend to be more naturally segmented by contrasting landscape types, predicted distributions of Maine species are often fairly uniform across their range limits. For example, the habitats of Three-toed Woodpeckers (Picoides tridactylus) in Colorado are naturally segmented, having no sharp range boundary, whereas the range limit of the species in Maine is distinct (Figure 1).
 Figure 1. The predicted habitat for Three-toed Woodpeckers in Colorado (a) and Maine (b). Fragmented habitats in Colorado mask range limit boundaries, whereas in Maine the range limit boundary is distinct. |
Methods Used to Feather Habitat Maps
Given that range limits represent gradients in the probability of species occurrences and that maps of a species’ predicted distribution seemed to unnecessarily show sharp range boundaries, we sought to feather Maine’s habitat maps along their boundaries. To do so required the assumption that randomly selected patches along a species’ range limit could be considered valid nonhabitat. We made this assumption because: 1) vertebrates tend to be rare along their range limits (Brown 1995); 2) doing so would portray predicted habitat at 1:100,000 scale more fairly than nonfeathered maps; and 3) conservation decisions should be made only after on-the-ground surveys have been conducted (Scott et al. 1993) so these fine-scale changes in habitat suitability would not affect management decisions.
First we attempted to turn habitat patches to nonhabitat based upon a stratified-random selection. Selection was stratified by the distance to the range limit. Within a given buffer distance (e.g., 50 km), habitat patches distant from the range limit were very likely to remain habitat. Patches nearer the range limit were progressively more likely to be changed to nonhabitat. Steps involved in processing a given raster-based habitat map where to: 1) calculate the Euclidean distance to the species’ range limit; 2) identify habitat patches within the feathering distance; 3) identify patches to be retained; 4) discard the patches within the feathering distance that were not selected; and 5) merge the resulting feathered habitats with the remaining habitats within the state. Despite several attempts, we could not generate acceptable feathered habitat maps using this process, and all attempts required too much processing time to be practical. Even modest-sized feathering buffers included tens of thousands of habitat patches. Lists of patch identifiers (i.e., nonspatial scalers) could be generated and a subset of identifiers selected quickly, but using the resulting list of identifiers to select the spatial patches to retain was computationally intensive. A similar technique we tested identified patch centroid cells (yielding one cell per patch, which simplified logic), and randomly selected habitats to conserve. Patches with centroids selected were retained. A final technique assigned a random number to each cell, then inspected the maximum value assigned to each patch to determine if it should be retained. Each of these methods generated fairly reasonable, but not ideal, maps. Regardless of the method, the resulting feathering effect also varied spatially based upon the size of habitat patches, which we judged inappropriate.
In our second attempt, we used a cell-based rather than patch-based method to feather habitat maps along range boundaries for Maine Gap Analysis. Whether to retain a habitat cell or not is a simply binary decision without the complexities of patch selection. We used four levels of habitat quality in our modeling before converting maps to presence/absence. We used these levels of quality while feathering habitats; cells ranked high quality were less likely to be converted to nonhabitat than sites of low quality. As a species’ range limit was approached, probabilities across quality scores converged until at the range limit all patches were converted to nonhabitat. Many functions were assessed that controlled the relationship between the distance from range limits and the probability of cells being selected [e.g., log(distance), sqrt(distance), sqrt(sqrt(distance))]. A simple linear relationship was judged most effective (Figure 2). The steps in analysis were similar to those described above: 1) a Euclidean distance to the range limit was calculated for each cell and standardized to 0-1; 2) a random-value grid was generated, multiplying each random value by a score based upon the habitat quality for the cell [i.e., quality 4 = x * 1.8; 3 = * 1.4; 2 = * 1.0; 1 = * 0.7]; 3) cells were selected to be retained or discarded based upon the random-value grid being greater than another random value, and the distance to the range limit; and 4) results within the feathering distance were merged with the remainder of the state.
 Figure 2. The probability of cells remaining used habitat, across the feathering distance, which is species-specific. Most cells remain suitable habitat at the maximum feathering distance, whereas most cells are judged nonsuitable habitat nearest the range limit. |
Results
An example of maps for Three-toed Woodpecker (Figure 3) demonstrates that range limits were less obtrusive and maps seemed more reasonable after habitat maps were feathered. The distance over which we feathered ranges varied by species, from no feathering for Bald Eagle (Haliaeetus leucocephalus), whose map was based upon essential habitats defined by legislation (Maine Department of Inland Fisheries and Wildlife 1998), to 3 km for rare species with patchy occurrences such as Blanding’s Turtle (Emydoidea blandingi), to 50 km for wide-ranging species such as Three-toed Woodpeckers.
 Figure 3. Predicted habitat for Three-toed Woodpecker. Map ‘a’ is the predicted habitat prior to feathering the range limit boundary. Map ‘b’ is the feathered final map of predicted habitat for Maine. |
Many research questions remain regarding portraying habitats along range limits. For example, while we assumed that the abundance of species decline near range edges, there is evidence that in some cases this is not so. For example, an ungulate population erupting in New Zealand after introduction was described as a "rolling wave of density" moving across space, with relatively high density occurring temporarily at the edge, and the highest density further back in the range (Riney quoted by Caughley [1970]). However, three of the four range edge models outlined by Caughley et al. (1988) assume that population density is lowest near the range edge and highest in the core of the range (also see Caughley and Sinclair 1994:60-64). Thus we believe that our general assumption of low densities near the range edge is a reasonable first approximation, although additional field data are needed.
Our general methods would be most appropriate based upon patch removal versus cell removal. Also the weighted probability for habitats being selected should be sensitive to the habitat types themselves. Finally, ideal models would dispense with range limits entirely, using verified relations with environmental variables instead (as reviewed in Brown and Lomolino 1998). More research is needed to characterize spatial and temporal patterns of distributions along range limits, but the method we used to feather Maine vertebrate potential habitat maps along their ranges was effective, yielding maps that portrayed potential habitats better than unfeathered maps.
Literature Cited
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