GIS/EM4 - An Analytical Assessment Tool for Predicting Changes in a Species Distribution Map Following Changes in Environmental Conditions

An Analytical Assessment Tool for Predicting Changes in a Species Distribution Map

Following Changes in Environmental Conditions

GIS/EM4 No. 104

William W. Hargrove
Forrest M. Hoffman

Abstract

We have developed a GIS-based statistical technique which empirically predicts changes in the spatial distribution of habitat for a plant or animal species over a geographic area that has undergone a scenario of change in specified environmental conditions. The technique is illustrated with Pinus taeda L., loblolly pine, and Acer saccharum Marsh., sugar maple, under two future climate change scenarios for the continental U.S.

We use a new Multivariate Spatio-Temporal Clustering (MSTC) approach that we developed for application on raster data within a GIS. MSTC employs non-hierarchical clustering on the individual pixels in a digital map from a GIS for the purpose of classifying the cells into types or categories. Our technique uses the standardized values of each environmental condition (e.g., temperature, rainfall, soil) for every raster cell in the map as a set of coordinates that together specify a position for that raster cell in a data space having a dimension for each of the included environmental characteristics. Two raster cells from anywhere in the map that have similar combinations of environmental characteristics will be located near each other in this data space. Their proximity and relative positions in data space will quantitatively reflect their environmental similarities, allowing these cells to be classified into environmentally similar groups. MSTC combines aspects of traditional GIS and statistical clustering techniques.

Using the classification abilities of MSTC, we compared and grouped map cells by selected environmental conditions found within the present continental U.S. with conditions predicted to occur here according to two alternative future climate scenarios. Environments were specified in terms of 25 condition characteristics. We obtained high-resolution simulation forecasts for conditions within the continental U.S. in the year 2099 according to two global climate simulation models that are recognized by the U.S. National Assessment: the Canadian Climate Centre model, and the Hadley UKMO model. The VEMAP program has made yearly data sets for these models available for the period between 1994 and 2099 at 0.5 degree resolution for the continental United States.

From these models, we obtained the simulated forecasts for monthly minimum and maximum temperature, monthly solar irradiance, and monthly precipitation. We calculated differences between present and future conditions predicted in the year 2099 by each of the two models. Difference layers were applied to our high resolution maps of current conditions within the United States in order to obtain predicted conditions. Thus, sixteen of the 25 environmental conditions were altered to represent the conditions forecast to occur within the continental U.S. in the year 2099 by each model.

A variant of the MSTC procedure can be used to generate a model of the environmental envelope or niche of a particular species. We use the current distribution of Pinus and Acer to define their respective niches, then alter the map, and use the niche definition to classify map pixels and delineate the new distribution of habitat suitable for these tree species within the map. This technique is significant for assessing predicted effects of changes in environmental conditions (i.e., global warming) on the potential distribution of suitable habitat for both plants and animals.

Making a special prediction of the current geographic range of a species allows us to test the robustness and adequacy of the niche model. Conditions present within the current U.S. are used to predict a current geographic range for the species, which can be compared with the known actual geographic distribution. When the fitness prediction obtained for each species when the current conditions within the United States are tested against the hypervolume definitions, the predicted distributions strongly resemble the known current distributions for both of these tree species. The niche model-based geographic predictions are somewhat more extensive in terms of the outer, low-fitness peripheral areas, but still strongly resemble the original geographic ranges which were used as input to the model development process.

Predictions for a simple uniform climate warming scenario are surprising. Habitat distributions for the tested tree species generally dissapate and evaporate, without visible northward migration. We speculate that environmental conditions in many cells of the new maps may represent new combinations never seen in the present U.S. The performance of species cannot be predicted inside such cells, since the cells have left the inference space of the training data set. Methods for identifying such unpredictable cells, and speculation about their abundance and distribution are discussed.

Keywords

Acer, Bailey, CCC, climate, clustering, ecoregion, geographic distribution, habitat, Hadley UKMO, Hutchinson, hypervolume, MSTC, niche, Omernik, Pinus, range, regionalization, tree, warming

Introduction

Locating borders between ecoregions is truly a multivariate decision process that must make reference to a number of large geographic data sets, one for each environmental condition which is to be considered (Hargrove and Hoffman 1999). We have developed an objective technique combining multivariate statistics and a Geographic Information System (GIS) which objectively computes the placement of borders between ecoregions, given maps of all environmental conditions that one wishes to consider. Rather than relying on expertise, our technique uses the standardized values of each environmental condition for each individual raster cell in the map as a set of coordinates that specify a position for that raster cell in a data space having as many dimensions as the number of included environmental characteristics. Two raster cells from anywhere in the map having similar combinations of environmental characteristics will be located near each other in data space, and their nearness and relative positions will quantitatively reflect their environmental similarities.

Methods

The steps of the process are shown in Figure 1. After their disassembly from geographic space, the map cells are re-plotted in environmental data space like stars in a data universe. Because the density of these cells in data space is not uniform, we use an iterative classification procedure to group various nearby ``stars'' into clusters having similar combinations of environmental conditions. This procedure begins with the specification by the user of the desired number of ``galaxies'' or clusters into which the stars are to be grouped. All observations are examined sequentially to find the most widely separated set of stars which will provide this number of initial cluster ``seeds.'' Thus, the number of ecoregions which result from the process is under the user's control.

Figure 1. The Multivariate Spatio-Temporal Clustering procedure. The left half of the flowchart is in geographic or map space, and the right half is in abstract data space. If performed on multiple maps representing a chronosequence, the same clustered combinations are identified whenever and wherever they occur.

Each map cell is then compared against all cluster seeds, and the map cell is assigned membership to the cluster whose seed is closest to it in terms of Euclidean distance. After all map cells have been assigned, new cluster centroids are calculated to be the mean of each coordinate over all cells assigned membership to that cluster (Hartigan and Wong 1979). Then the iterative assignment procedure repeats. Stars do not move in environmental data space; rather, the centroids of the cluster ``galaxies'' slowly slew until an equilibrium classification is obtained. When fewer than a specified number of map cells change cluster assignment in a particular iteration, the process converges and halts.

Map cells with their final cluster assignments can then be re-assembled into their proper geographic positions, and the resultant ecoregion map can be color-coded by the cluster assignment. Because raster cells adjacent in the map are likely to have similar environmental values, ecoregion clusters are often geographically contiguous. However, because the geographic location is not used for clustering, clusters can be spatially disjoint, and two map cells with similar environments could be classified in the same ecoregion even though they are widely separated geographically. Two widely-spaced mountain tops, for example, could be classified in the same ecoregion cluster if their environments are similar enough. We have used the MSTC procedure to create objective ecoregions for many different areas.

We call this empirical process Multivariate Spatio-Temporal Clustering (MSTC), and have implemented it in a parallel algorithm coded in C using the Message Passing Interface (MPI). Our code is dynamically load-balancing, fault-tolerant, and performs both initial seed-finding and iterative cluster assignment in parallel (Hoffman and Hargrove 1999b). The clustering algorithm is inherently parallelizable, since individual nodes can independently classify subsets of cells, then combine results at the end of the iteration. We developed the Multivariate Geographic Clustering parallel algorithm and code on a heterogeneous Beowulf-class parallel machine constructed from surplus 486- and Pentium-based personal computers (Hoffman and Hargrove 1998, Hoffman and Hargrove 1999a, Hoffman and Hargrove 1999c. We have also performed MSTC across multiple supercomputers interconnected via GLOBUS (Mahinthakumar et al. 1999).

Clustering through time

MSTC can also be used to consider not just a single map, but a chronological sequence of two or more maps coded with multiple environmental attributes changing through time. Individual maps at each single point in time are comprised of cells with which are associated a particular set of environmental characteristics relevant to human health concerns. All cells from all maps in the chronosequence, each with their specified ``mix'' of attributes, are submitted to a single MSTC analysis.

MSTC objectively and empirically organizes the cells into groups which have similar combinations of environmental characteristics, regardless of where in space or time the cell originally began. The number of groups is specified beforehand by the user. Although not used directly by MSTC, the spatial and temporal location of each cell is stored, so that the grouped cells can be re-assembled, now with their clustered combination assignment, back into the original chronosequence of maps. Thus, the MSTC process objectively identifies and creates groups of similar cells sharing similar environmental conditions across all maps in the sequence, i.e., across time and space.

Since all spatial cells in the chronosequence are submitted to a single MSTC analysis, the particular unique combination of conditions represented by each group is retained across all maps in the time series. After map re-assembly, a particular clustered combination of environmental conditions may be present in all, a few, or only one map in the chronosequence. Because cells with similar combinations of environmental characteristics are likely to be adjacent in geographic space, clustered combinations often (but not always) form contiguous regions in each map in which they are present. Across maps in the time sequence, these regions representing a particular environmental combination may change in size, shape, and location. Even though they may grow or shrink in area, or even appear and dissappear during the chronosequence, each of the clustered combinations is a discrete and unique entity which can be tracked across space and through time.

Data on environmental characteristics

We characterized environments in terms of the combination of 25 variables listed in Figure 2. The factors included elevation, maximum, mean, and minimum annual temperature, monthly precipitation, several soil parameters, number of frost-free days, and solar aspect and input. Each of these layers represents a data map which was developed for the continental United States, at a resolution of 1 km². There are over 7.8 million map cells in each of the 25 layers. Each layer was developed from different public-domain data sources or surrogates in a unique way, but the detailed description of the data development methods is beyond the scope of this manuscript. Rather, we will concentrate on the MSTC method here, which can be used with any combination of data from any source.

Figure 2. Environmental characteristics considered in the Multivariate Spatio-Temporal Clustering procedure. Each of the 25 characteristics represents a 1 km resolution map of the continental U.S. containing more than 7.8 million cells.

Comparing the present with two alternative futures

We analyzed three maps simultaneously using MSTC in order to regionalize a time series of maps into a set of common environmental regions which are comparable across the series. We compared the present environment of the U.S. in terms of the 25 variables with two alternative future versions of the U.S. at a point 99 years in the future. We implemented two global climate models by altering 16 of the 25 variables in spatially explicit ways, and then used MSTC to find 100 common environmental combinations across this set of three maps. One prediction is from the Hadley United Kingdom Meterological Office (UKMO), and the other is from the Canadian Climate Centre (CCC). Both predictions are for the year 2099. Thus we are intercomparing the present with two alternative versions of the future, three maps in the set, each 25 layers deep, each layer with 7.8 million cells.

We obtained high-resolution simulation forecasts for conditions within the United States in the year 2099 according to two global climate simulation models which are recognized by the U.S. National Assessment: the Canadian Climate Centre model, and the Hadley UKMO model. The VEMAP program has made yearly data sets for these models available for the period between 1994 and 2099 at 0.5 degree spatial resolution for the continental United States.

We obtained the simulated forecasts for for monthly minimum and maximum temperature, monthly solar irradiance, and monthly precipitation. We used an IDL program to calculate differences between present and future conditions predicted in the year 2099 by each of the two models. Because particular years could be unusual, we averaged over a five-year interval beginning with 1994, and over a five year interval ending with 2099, and took the difference between the means as the predicted change. We also needed mean annual temperature differences. These were obtained by lumping all 12 monthly minimum and maximum temperatures for each of the five years in the starting and ending intervals, and calculating an average difference between the intervals. Difference layers were applied to our high resolution maps of current conditions within the United States in order to obtain predicted conditions.

Sixteen of the 25 environmental conditions were altered to represent the conditions forecast to occur within the United States in the year 2099 by each model. Because of the inherent spatial coarseness of the modeled conditions (0.5 degree) relative to the high resolution of the present-day conditions (1 km²), there were some ``slivers'' near the coastline of the United States which extended beyond the edge of the predictions. Areas in these small ``slivers'' remained unchanged.

The first pair of the triad of maps, the present and the CCC scenario for the future, are compared in Figure 3. Geographic regions having the same clustered mix of environmental conditions are colored randomly, but, because the SAME random color table is used for all maps, changes in the location and area affected by different environmental conditions can be traced between maps. This level of division makes visual identification of the same area relatively easy across maps. The northeast, for example, experiences very little change, although conditions within the northeast shrink somewhat in Pennsylvania. The red cluster of the coastal plain divides into a Mississippi valley component and an Atlantic seaboard component. A green coastal Texas cluster shrinks to a tiny area near Galveston Island. Many severe changes are predicted for California by this model, making artefacts of the coarse resolution of the prediction visible there.

Figure 3. Comparison of the environment within the present-day U.S. and that predicted for the year 2099 by the Canadian Climate Centre (CCC) GCM for the VEMAP program. One hundred common environmental combinations were identified across three versions of the U.S., the present and two alternative future scenarios for 2099, using Multivariate Spatio-Temporal Clustering. This figure compares the first pair only. Random colors of the regions are common across the triad of maps. Comparison of any color across maps indicates how that environmental combination will change in size and shift geographically according to this future climate scenario.

The second pair of the three maps, shown in Figure 4, compare the environmental conditions at present with those predicted by the Hadley UKMO model for 2099. Because the random colors are standardized and refer to the same combinations, regions in these maps can also be compared with Figure 3. The red coastal plain dissolves into a number of small remnant clusters around the periphery of a new cluster combination according to this forecast. The lime green coastal Texas cluster grows to become the dominant cluster in eastern Texas. The maps are much higher resolution than is evident in the images shown here, and areas of interest can be enlarged to see much additional detail.

Figure 4. Comparison of the environment within the present-day U.S. and that predicted for the year 2099 by the Hadley United Kingdom Meterological Office (UKMO) GCM for the VEMAP program. One hundred common environmental combinations were identified across three versions of the U.S., the present and two alternative future scenarios for 2099, using Multivariate Spatio-Temporal Clustering. This figure compares the second pair only. Random colors of the regions are common across the triad of maps. Comparison of any color across maps indicates how that environmental combination will change in size and shift geographically according to this future climate scenario.

Area changes for particular environments

We can depict the area changes in particular environments, whether they grow in size, stay the same, or shrink in area, using a map with stoplight colors. Red indicates a shrinking environment, yellow is no change, and green is a growing environmental combination. Of course, these environments may not remain in the same geographic locations. Nevertheless, examination of Figure 5 for area changes, along with Figure 3 for geographic area shifts gives a complete picture of the changes forecast by the CCC scenario. Figure 5 makes it clear that most present-day environments will decrease in area, and will yield to a nearly complete environmental changeover.

Figure 5. Changes in area for each of the clustered combinations from the present to the year 2099 as predicted by the CCC GCM. Red indicates that the geographic area in the clustered environmental combination decreases in the future, green indicates that the clustered environment increases with time. Yellow areas do not change in area, though they may shift geographic locations. Almost every present environmental combination gives way to something new, resulting in a complete changeover by 2099.

Figure 6 shows results when we take this trend of geographic change in area to the extremes. The top map shows two clusters presently in the Texas panhandle which represent environmental combinations which will go extinct according to the CCC model. These combinations of the 25 environmental variables cease to exist entirely by the year 2099 according to this forecast. The bottom map shows clusters that are entirely new combinations in the year 2099. Environments within these areas represent new mixes of the 25 variables, and are environments which do not exist today. Clusters in the top map give geographic clues about locations for possible species extinctions, while clusters in the bottom map represent locations for possible new speciations. We have also used the MSTC technique to compare present environments with those estimated for the period of the Last Glacial Maximum, 20-18 thousand years ago.

Figure 6. Environmental extinctions and new combinations predicted by the CCC GCM. Clusters in the top map represent combinations of the 25 environmental variables which have no analog by the year 2099. These environments become extinct in the future. Clusters in the bottom map have no analog in the present. These areas represent new environments, with different mixtures of the 25 environmental conditions which do not currently exist.

Environmental niche modeling with MSTC

A simple variant of the MSTC technique permits the creation of a model of the Hutchinsonian niche or environmental envelope within which a species can grow and reproduce (Figure 7). The process begins with a current geographic distribution for a particular species (in this case, Pinus taeda L., loblolly pine). Rather than specifying the number of clusters to be found, we instead specify a within-cluster variance. Geometrically, this is equivalent to specifying a fixed radius for all clusters; clusters with a large radius have greater within-group variance.

Figure 7. Niche hypervolume modeling using MSTC. Environmental combinations from all map cells within the known geographic range of a species are plotted in environmental data space, and fixed-radius, variance-based clustering is used to identify as many fixed-radius clusters as necessary to ensure that each occupied map cell is contained within at least one of the clusters. Mean fitness or performance measures within each cluster are associated with the cluster centroid. All clusters, taken together like volumetric pixels, serve to locate and define the environmental envelope for the species. A prediction can be made for a new environmental scenario by plotting the new cells in data space, and then constructing a map only from those cells which are internal to one of the clusters. Fitness predictions are made by assigning the productivity from that centroid to all member map cells.

To develop a niche model for a particular species, as many fixed-radius clusters are specified as necessary to ensure that each map cell within the geographic range of the species is contained within at least one cluster. When all resultant clusters are taken together, they serve as volumetric pixels which locate and define the shape of the permissible niche for this species within environmental space. Selecton of the fixed radius defines the resolution; using a smaller radius will result in the specification of more clusters, and will describe the niche envelope in greater detail.

Surrogate measures of performance of the species measured at each location are associated with each environmental cluster combination comprising the niche model. The mean performance among all map cells assigned to a cluster is assigned to that cluster, and any new map cell falling within that cluster is assigned that productivity. In this way, geographic predictions can be made which are not just binary presence/absence, but include a projected estimate of how well the species will perform at each location. Multiple performance metrics can be associated with a single niche definition; here we use production of woody tissue in terms of m³/ha/yr. To predict changes in a geographic distribution under a scenario of environmental change, each map cell in the new scenario is plotted in data space. Only map cells which fall within existing clusters are retained as permitting growth, and projected performance under that combination is assigned.

Results

Each niche was defined in terms of 25 environmental condition gradients, including detailed climatic, physiographic, and soil factors. We selected a within-cluster variance radius of 0.75, which resulted in a niche definition for loblolly comprised of 49,324 clusters, and a niche definition for sugar maple comprised of 45,490 clusters.

Testing the adequacy of niche models

When the current conditions within the United States are compared with the hypervolume definition predictions, the predicted distributions strongly resemble the known current distributions for both of these tree species (Figure 8). It is as important for this verification that areas outside the current geographic distributions of these species are NOT predicted by the niche hypervolume model as it is that cells within the distribution ARE predicted. The geographic predictions from the hypervolumes are slightly more extensive in terms of the marginal areas (redder), but the more optimum core areas (yellower and greener) strongly resemble the original geographic ranges that were used as input to the prediction process.

Figure 8. Present and predicted present geographic range productivity for Pinus taeda L. and Acer saccharum Marsh. Niche hypervolume models were defined by analyzing 25 environmental axis combinations from 1 km² cells within the current geographic distributions (A, B, top row). Niche models were then used to predict current distributions within the continental U.S. (C, D, bottom row) as a test. Colors indicate woody production (m³/ha/yr). The ranges predicted under current conditions strongly resemble the known ranges for both species; more area is indicated in suboptimal parts of the range. No optimal unoccupied-but-suitable areas are indicated for either species.

Sensitivity of MSTC to sample size

How sensitive is the niche model to sample size? What if we randomly delete half of the cells where the species occurs? What effect will that have on the model, and on the map that is predicted by the model? At least as many cells will be identified as habitable in a predicted range map as are included in the current location ``training'' set. A substantially similar current geographic distribution is also forecast for these two species using niche models developed when half of the occurrence locations are deleted (Figure 9). The niche hypervolume technique could potentially be used even for species with limited geographic ranges (or limited occurrence data), i.e., rare or endangered species.

Figure 9. Present and predicted present geographic range productivity for Pinus taeda L. and Acer saccharum Marsh when half of the cells from the original tree ranges are randomly discarded. There is very little difference in the geographic ranges predicted from a niche model constructed from only half of the data. The technique could potentially be used successfully for species with limited ranges, e.g., threatened or endangered species.

Figures 10 and 11 show sequential geographic range predictions for loblolly and sugar maple, respectively, under a simple climate warming scenario in which mean, minimum and maximum annual temperature are increased in a geographically uniform manner. It was surprising to see a generalized evaporation of the geographic range of these two species rather than a northward migration with increased warming. Highly productive green areas do not transition with warming to yellow, and then red, but instead simply dissappear. We were particularly surprised to see instances where dark green, highly productive geographic areas were present within a ``sea'' of locations classified as unsuitable (e.g., loblolly, +3.5 degrees). One would expect a gradually decreasing fitness or productivity, as combinations slowly reduced in suitability, rather than an abrupt changeover from highly suitable to unsuitable.

Figure 10. Niche model geographic range prediction sequence for loblolly pine under a climate scenario of geographically uniform increase in mean, maximum, and minimum annual temperature, by half degree increments.

Figure 11. Niche model geographic range prediction sequence for sugar maple under a climate scenario of geographically uniform increase in mean, maximum, and minimum annual temperature, by half degree increments.

Discussion

We suspect that the combinatorics of 25 axes are becoming important here. With 25 axes, there are a lot of ways to be different, and it is easy to leave the inference space of the training data set. The niche modeling technique could be thought of as creating a file drawer filled with a file folder for each combination of the 25 variables under which loblolly is known to grow. Inside each folder, the observed (and expected) productivity of this species under this environmental combination is filed. Some of the folders in the drawer will contain productivities of zero, i.e., loblolly has not been observed to grow under this combination. If the combination of 25 variables from a new cell is not matched by a file folder in the drawer (within the radius tolerance), the prediction will be made that loblolly will not grow at this new location. If we think of the 25 descriptor variables in each cell as the combination to a lock, there are many ways to get the combination wrong, and the lock is difficult to open. It would be easier to pick a lock whose combination had fewer numbers.

We need to further distinguish in the predictive maps the cases where we find a file folder, but it contains a zero productivity, from cases where there is no file folder for this new combination in the drawer. In the former case, this is an environmental combination that we have seen before, and we can safely predict that loblolly will not grow under this set of conditions. In the latter case, we have encountered a new combination, and we simply have no observational basis for making a prediction. We need to indicate and distinguish such new combinations geographically as regions within which we cannot predict, perhaps by shading them in gray to distinguish them from areas where we predict no loblolly.

The Venn diagram in Figure 12 illustrates the relationship among the sets. The large circle on the left indicates the set of all environmental combinations present within the current U.S. The small shaded circle within it represents the subset of combinations within the present U.S. within which loblolly is known to grow. Areas outside the species niche circle but within the larger U.S. set are not currently suitable locations/combinations for this species, i.e., are outside its current geographic range or environmental envelope.

Figure 12. Venn diagram showing the set relationships between the inference space of the training set (Current U.S), a new climate scenario, and the current environmental niche envelope for a particular species. There is a need to geographically identify not only the shaded area within the overlap, but also to distinguish the locations where the species won't grow from the areas where prediction is not possible due to combinations which have never been encountered before.

Now the current U.S. undergoes an environmental shift, as indicated by the arrow at the bottom, to some future scenario. Whatever portion of the small shaded circle now falls within the overlap represents the subset of combinations where loblolly can grow under the new scenario. This is the portion of the set that we have previously mapped. The species goes extinct within the remainder of its shaded niche circle, since these combinations no longer occur. The remainder of the overlapped area represents environmental combinations which HAVE been seen before within the current U.S., and within which loblolly is known NOT to occur.

Only areas within the overlap are predictable using the niche modeling technique. As the environmental shift is more extreme, and the right circle moves further and further from the current conditions, the area of overlap decreases. If the environmental shift is so far and complete that the new set of environmental conditions shares no members with the current set and there is no overlap, then no prediction is possible. Under such a scenario, the entire new U.S. is comprised of unpredictable new combinations. All areas within the right circle outside the overlap area represent new environmental combinations not present within the current U.S. training set. Because the niche hypervolume predictions are based on empirical observations, no predictions are possible within this subset. These are the areas we wish to ``gray out'' as unpredictable in the maps.

Future directions for research

Our expectation is that there will be more gray areas in the maps as the warming sequence in Figs. 10 and 11 become more extreme, since more of the new map cells will leave the part of the diagram representing combinations of the 25 occurring in the present U.S. We also predict that, as the length of the prediction interval increases and present and future conditions continue to diverge, more combinations will become unpredictable. Similarly, as one increases the dimensionality of a niche model, one increases the accuracy and specificity of predictions for combinations not too different from present ones, but limits areas where prediction is possible as the degree of environmental change becomes more pronounced. It may be that areas where species would be expected to migrate will be increasingly obscured by unpredictable gray zones, or that gray areas will form an unpredictable matrix around the islands of high productivity which we now see.

How can we identify such formerly unencountered unpredictable areas? We intend to construct a single ``super niche'' model which describes and contains all of the environmental combinations everywhere within the current U.S. This reference niche model will serve to describe the leftmost circle in the Venn diagram, and will represent the known inference domain for niche-based predictions. Environmental conditions outside this ``super niche'' represent new combinations for which no species predictions can be made. A single-pass clustering on this niche model will provide the gray-shaded areas on the maps within which no prediction is possible. This approach is generic, and does not depend on the particular species niche of interest. The same ``super niche'' can be used to identify unpredictable areas when predicting any species within the U.S.

Acknowledgements

This research was sponsored by the Oak Ridge National Laboratory (ORNL) Seed Program. ORNL is managed by UT-Battelle, LLC, for the U.S. Department of Energy under contract DE-AC05-00OR22725. Valuable comments were provided by Andrew Schiller and Yetta Jager.

List of references

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Hoffman, F. M., and W. W. Hargrove. 1998. "Making Soup from Stones." Troubleshooting Professional, Vol. 2, Issue 5.

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Kittel, T.G.F., N.A. Rosenbloom, T.H. Painter, D.S. Schimel, H.H. Fisher, A. Grimsdell, VEMAP Participants, C. Daly, and E.R. Hunt, Jr. November 1996 (revised August 1999). The VEMAP Phase I Database: An integrated input dataset for ecosystem and vegetation modeling for the conterminous United States. http://www.cgd.ucar.edu/vemap/users_guide.html.

Mahinthakumar, G., F. M. Hoffman, W. W. Hargrove, and N. T. Karonis. November 13-15, 1999. Multivariate Geographic Clustering in a Metacomputing Environment Using Globus. Proceedings of the ACM/IEEE SC99 Conference, Portland, OR.

Authors

William W. Hargrove,Landscape Ecologist
Computational Physics and Engineering Division
Oak Ridge National Laboratory, Oak Ridge, TN 37831-6274
Email: hnw@fire.esd.ornl.gov
Tel. 865/241-2748, FAX 865/241-3870
Webpage: http://research.esd.ornl.gov/~hnw/

Forrest M. Hoffman, Research Scientist
Environmental Sciences Division
Oak Ridge National Laboratory, Oak Ridge, TN 37831-6036
Email: forrest@esd.ornl.gov
Tel. 865/576-7680, FAX 865/576-8543
Webpage: http://research.esd.ornl.gov/~forrest/