Remote sensing is used to map the actual distribution of some invasive plant species, such as leafy spurge (Euphorbia esula L.), whereas geospatial models are used to indicate the species' potential distribution over a landscape. Geographic data layers were acquired for Crook County, Wyoming, and the potential distribution of leafy spurge presence or absence were predicted with the use of the Weed Invasion Susceptibility Prediction (WISP) model. Hyperspectral imagery and field data were acquired in 1999 over parts of the study area. Leafy spurge presence or absence was classified with the use of the Spectral Angle Mapper with a 74% overall accuracy. However, the user accuracy was 93%, showing that where leafy spurge was indicated in the image, leafy spurge was usually found at that location. With the use of Kappa analysis, there was no agreement between WISP model predictions and either the field data or the classified hyperspectral image. Kappa analysis was then used to compare predictions based on single geographic data layers, to increase the power to detect subtle relationships between independent variables and leafy spurge distribution. The WISP model was revised for leafy spurge based on the remote-sensing analyses, and only a few variables contributed to predictions of leafy spurge distribution. The revised model had significantly increased accuracy, from 52.8% to 61.3% for the field data and from 30.4% to 80.3% for the hyperspectral image classification, primarily by reducing the areas predicted to have potential for invasion. It is generally more cost effective to deal with the initial stages of invasion by only a few plants, compared to an invasion that is large enough to be detected by remote sensing. By reducing the potential area for monitoring, management of invasive plants could be performed more efficiently by field crews.
INTRODUCTION
Invasive species are a world-wide problem affecting maintenance of biodiversity and production of food and fiber. In the United States, annual economic losses from invasive species are about $120 billion (Pimentel et al. 2005). Understanding the potential geographic distribution of an invasive species is important because regions that have not yet been infested require different management strategies compared to regions that are already infested (Rouget et al. 2004). An active area of research is the development of potential distribution models, both as a scientific methodology to understand species' niches (Jackson et al. 2009) and to predict changes in distribution with climate change (Pearson and Dawson 2003; Thuiller et al. 2008). Niche models require a different set of parameters for each invasive species based on its specific ecological characteristics (Peterson 2003; Austin 2007; Hoffman et al. 2008; Stohlgren et al. 2010). A general problem with potential distribution models is that these models are usually tested with only species-presence data, which can result in model errors (Fielding and Bell 1997; Engler et al. 2004; Tsoar et al. 2007). Other studies have shown that using only species-presence data can result in accurate distribution models (Evangelista et al. 2008, 2009; Kumar et al. 2009). On the other hand, species-absence data can be unreliable because a given location can be either unfavorable for the species occurrence or simply the propagules for the species haven't arrived yet at that location.
A major application of remote sensing is to map the actual distribution of invasive species (Everitt et al. 2002; Underwood et al. 2003; Lass et al. 2005). Remotely sensed imagery is often used to provide variables for the prediction of invasive weed distribution (Morisette et al. 2005; Rew et al. 2005). Furthermore, remote sensing can be used to map the locations of plant species that have spectral or phenological differences from the co-occurring native vegetation, which then can be used in lieu of field plots to develop potential geographic distribution models (Bradley and Mustard 2006; Andrew and Ustin 2008, 2009).
Leafy spurge (Euphorbia esula L.) is an invasive weed that renders large amounts of rangeland unfit for horses or cattle (Anderson et al. 2003). For four states, Wyoming, Montana, North Dakota, and South Dakota, the direct economic losses exceed $37 million annually and the indirect economic losses are about $83 million annually (Leistritz et al. 2004). The flower-bracts are distinctively yellow green (Hunt et al. 2004), which can be remotely sensed either with high-spatial-resolution sensors or imaging spectrometers/hyperspectral sensors (Everitt et al. 1995; Anderson et al. 1996; Everitt et al. 2002; Casady et al. 2005; Glenn et al. 2005). The success is mixed for moderate-resolution, multispectral sensors such as Landsat Thematic Mapper (Hunt and Parker Williams 2006; Mladinich et al. 2006; Stitt et al. 2006; Mitchell and Glenn 2009). Therefore, the ability of remote sensing to detect leafy spurge is probably dependent on high amounts of flower-bract cover in a pixel (Hunt et al. 2007), which in turn may be related to leafy spurge's vegetative propagation via adventitious buds on the root system (Messersmith et al. 1985).
Gillham et al. (2004) developed the Weed Invasion Susceptibility Prediction (WISP) model, which uses simple thresholds and categorical variables relating species occurrence to geographic distribution in a landscape. Furthermore, the WISP model was parametrized for leafy spurge with the use of only presence data acquired in Wyoming's Bighorn River Basin, and model performance was assessed with the use of only producer accuracy (Gillham et al. 2004). In this study, the WISP model was used to predict the occurrence of leafy spurge at a new site, Devils Tower National Monument in northeastern Wyoming. Parker Williams and Hunt (2002, 2004) and Hunt et al. (2007) determined the distribution of leafy spurge at Devils Tower National monument with the use of imagery from NASA's Airborne Visible Infrared Imaging Spectrometer (AVIRIS; Green et al. 1998). Over a landscape, the unreliability of absence data may be ameliorated by acquiring a large number of pixels. Similar landscape units that are potentially unfavorable will have relatively few occurrences of leafy spurge, whereas for the similar landscape units that are potentially favorable, some will have leafy spurge and some will not. Both presence and absence data from remote sensing are then used to test and then revise the WISP model.
METHODS
Study Area
The original study was conducted as part of The Ecological Area-Wide Management Leafy Spurge project (Anderson et al. 2003; Hodur et al. 2006). The study area was around Devils Tower National Monument in Crook County, Wyoming, between lat 44.4° and 44.6° N and long from 104.6° to 104.9° W (Fig. 1). Elevations range from 1 219 m to 1 584 m and vegetation is a mosaic of conifer woodlands, northern mixed-grass prairie, riparian zones with deciduous shrubs and trees, and sagebrush shrub lands. Leafy spurge is well established throughout the area (Parker Williams and Hunt 2002, 2004).
Figure 1
Location of Crook County, Wyoming, and coverage of the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) overflights. The two major rivers are the Little Missouri and the Belle Fourche. The location of Devils Tower National Monument is indicated with a dot.
There were two sets of field plots established for validation of remotely sensed imagery. The first set were circular plots (46 m in diameter; n = 109) used for determining the amount of cover, where all plots had some leafy spurge (Parker Williams and Hunt 2002). The second set were square plots (50 m on a side; n = 246) used for classification accuracy of spurge presence or absence (Parker Williams and Hunt 2004). The positions of the center point or corner points were obtained with a Rockwell Precision Federal Global Positioning System (Rockwell International, Cedar Rapids, IA) with a positional accuracy of 5 m. The two sets of plot data were acquired during June and July 1999 (Parker Williams and Hunt 2002, 2004) and were combined for the accuracy assessment of WISP model.
Weed Invasion Susceptibility Prediction Model (WISP)
The WISP model uses a geographic information system (GIS) to predict suitable areas for five invasive plant species with the use of commonly available geospatial data layers and a look-up table of parameters (Gillham et al. 2004). Vector data layers are converted into raster formats. Pixels that are unsuitable for a specific geospatial data layer are labeled with a zero and pixels that are suitable are labeled with a one. Then, the sum of all zeros and ones from the various data layers is calculated for each pixel.
Gillham et al. (2004) used expert opinion to determine the model parameters for leafy spurge (Table 1). Furthermore, because they used nine data layers, pixels with sums of eight or nine were defined as having high susceptibility for invasion by leafy spurge. The GIS data layers for the WISP model were obtained from the Wyoming Geographic Information Science Center, University of Wyoming ( http://www.uwyo.edu/wygisc/). The map scale of the data was 1∶100 000, and the positional accuracy was about 51 m. To match the resolution of the remote-sensing data, the geospatial data layers were converted into 20-m pixels.
Table 1
Original Weed Invasion Susceptibility Prediction (WISP) model variables and parameter values for leafy spurge presence from Gillham et al. (2004).
Image Acquisition and Classification
NASA's AVIRIS was flown in an ER2 aircraft at high altitude (resulting in 20-m pixels) over the study area on 6 July 1999 (Parker Williams and Hunt 2002, 2004). The AVIRIS data were atmospherically corrected to land-surface reflectance with the use of the Atmospheric Correction Now (ACORN) model from ImSpec LLC (Seattle, Washington). Atmospheric spectral transmittance was estimated in the ACORN model by using gas and water vapor absorption bands (Gao et al. 1993, 2009). Then the ACORN model output for each pixel was smoothed with the use of the measured reflectance spectra of a large talus field at the base of Devils Tower (Parker Williams and Hunt 2002). In 1999, high-altitude AVIRIS flights did not have global positioning system and inertial motion sensor data recorded with each scan line of data; hence, the three flight lines were registered to a geospatially rectified SPOT 4 image (20-m pixels) acquired on 11 July 2000. The root-mean-square error between the AVIRIS and SPOT 4 images was 26 m. However, inspection of the overlap between adjacent flight lines showed that some areas were misregistered by up to eight pixels (160 m), which occurred because atmospheric turbulence affected the ER2 aircraft during the overflights.
Kruse et al. (1993) defined the spectral angle between two reflectance spectra based on vector algebra:
where Θ is the spectral angle (degrees), R and T are the reference and target spectra, the numerator is the dot product of two vectors, and the denominator is the product of the normalized vectors. A large field (7.2 ha in size, 182 pixels) with approximately 100% cover of flowering leafy spurge (ocular estimate) located just outside of Devils Tower National Monument was selected as the training area for the reference spectrum of leafy spurge. Classification with the use of the spectral angle mapper (SAM) requires some threshold value of Θ, so spectral angles less than the threshold are classified as leafy spurge present and spectral angles greater than the threshold are classified as leafy spurge absent. A low threshold will increase the number of false negatives (errors of omission), which will lower the producer accuracy, whereas a high threshold will increase the number of false positives (errors of commission), which will lower the user accuracy. The threshold value of Θ was determined to be 3.5°, with the use of simulations from the scattering by arbitrarily inclined leaves model and plot spectral reflectance data (Hunt et al. 2007).
Kappa Analysis
Cohen (1960, according to Congalton and Green 2009) originally proposed Kappa analysis for testing categorical data. The Kappa statistic (κ ˆ) is defined:
where Pc is the percentage of correct predictions (overall accuracy) and Pe is the percentage of correct predictions attributable to chance, which is calculated from the false-positive and false-negative errors (Congalton and Green 2009). One important feature of Kappa analysis is that the variance of κ ˆ can be estimated, so inference tests (Z statistic) can be used to test hypotheses about differences among various classifications (Congalton and Green 2009).
We used the AVIRIS SAM classification of leafy spurge presence and absence to test the WISP model predictions pixel-by-pixel over the landscape around Devils Tower National Monument. However, with 808 557 pixels, there was too much statistical power to accept the null hypothesis, possibly causing a Type II error. Sims and Wright (2005) generally suggested sample sizes up to about 1 600 in order to detect small differences of κ ˆ, so 1 000 pixels were selected at random for calculating κ ˆ and its variance.
The significance of each WISP model variable was tested with the use of the presence/absence predicted by that variable alone with the AVIRIS SAM classification. For the variables distance to water (defined as streams and rivers) and distance to disturbance (defined as roads), we increased the threshold distance incrementally to determine the value that maximized accuracy. New parameters were selected to create a revised model, which was then tested with the field data and AVIRIS classification.
RESULTS AND DISCUSSION
AVIRIS Image Classification
For the three AVIRIS flight lines, about 8% of the area was classified as leafy spurge with the use of the Spectral Angle Mapper (Fig. 2). Three classes of vegetation cover were separated by the value of Θ: high vegetation cover with leafy spurge, high vegetation cover without leafy spurge, and low vegetation cover without leafy spurge. The SAM classification of the AVIRIS data was only 74% accurate, the user accuracy was 93%, and the Kappa statistic was highly significant (Table 2). The high user accuracy indicated that where leafy spurge was by the classified image, it was usually found at that location. Nonflowering leafy spurge has spectral reflectances similar to that of other green vegetation (Hunt et al. 2004), so some of the errors in overall accuracy (Table 2) were probably due to variation in the cover of flowering of leafy spurge (Parker Williams and Hunt 2002).
Figure 2
Spectral angle mapper (SAM) classification for three Airborne Visible Infrared Imaging Spectrometer (AVIRIS) flight lines acquired on 6 July 1999. The spectral angles were divided into three classes: leafy spurge present (red), high vegetation cover with leafy spurge absent (cyan), and low vegetation cover with leafy spurge absent (violet).
Table 2
Accuracy assessment of the Airborne Visible Infrared Imaging Spectrometer (AVIRIS) Spectral Angle Mapper (SAM) classification of leafy spurge presence/absence with the use of the plot data of Parker Williams and Hunt (2002, 2004).
The SAM classification results were not as good as previously reported with a classification based on mixture tuned matched filtering, which uses two subsets of the same AVIRIS and ground data (Parker Williams and Hunt 2002, 2004). Mixture tuned matched filtering separates a single spectral class from an image by comparing the reference and pixel spectra with respect to the variance calculated from all pixels. Because the entire AVIRIS data set was used in this analysis, there were probably many more spectral classes; thus the variance was much larger (J. W. Boardman, personal communication, May 2004), with the result that the classification of leafy spurge was not significantly better than chance (Z = 0.75). However, the SAM classification was significantly better (Z > 3.0) than alternative supervised methods such as Mahalanobis distance and maximum likelihood (data not shown).
WISP Model Results
For Crook County, about 57% of the area was predicted to have high susceptibility to invasion by leafy spurge with the use of the original WISP model (Fig. 3). Accuracy assessment using the field plots in the study area (n = 354) resulted in an overall accuracy of 53%, which was not significantly different from random chance (Table 3). The producer accuracy was 72%, which is somewhat lower than the producer accuracy determined by Gillham et al. (2004). In that study, the WISP model was validated in the Worland District of the Bureau of Land Management, located in Wyoming's Bighorn River Basin. Various state and local agencies collected leafy spurge presence data with global positioning system location (n = 6461).
Figure 3
Weed Invasion Susceptibility Prediction (WISP) model predictions for leafy spurge in Crook County, Wyoming, with the use of the original model developed by Gillham et al. (2004). Data layers include elevation, slope, aspect, precipitation, soil texture, soil pH, distance to streams and rivers, distance to roads or other disturbed areas, and land-cover class. Susceptibility to leafy spurge invasion is the sum of favorable factors for each data layer, so a sum of 8 or 9 factors indicates high susceptibility for leafy spurge (dark gray or red) and sums < 8 indicate low susceptibility for leafy spurge (light gray or cyan).
Table 3
Accuracy assessment of Weed Invasion Susceptibility Prediction (WISP) model predictions for leafy spurge in Crook County, Wyoming, compared to field data and the classified Airborne Visible Infrared Imaging Spectrometer (AVIRIS) image.
Testing the WISP model predictions using the AVIRIS data for the study area resulted in an overall accuracy of 30%, which also was not significantly different from random chance (Table 3). Producer accuracy is similar to that for the field data; however, the user accuracy was only 11%, indicating that the original WISP model could not be used to predict potential habitat for leafy spurge.
WISP Model Evaluation and Modification
Presence or absence of leafy spurge was predicted for each data layer, which was then compared to the AVIRIS SAM classification with the use of Kappa analysis. Based on the parameters of the WISP model, leafy spurge was expected to occur on loamy soil textures; however, loamy soils had a significant negative association with leafy spurge (Table 4). Furthermore, leafy spurge was expected to occur on east-, west-, and south-facing slopes, but there was no significant association with aspect. Also, leafy spurge was expected to occur in grassland and shrub land cover types, which was not found (Table 4). Contrary to expectations, leafy spurge occurrence was significantly associated with clay and silty clay loam soil textures, and riparian and woodland land cover classes (Table 4). Other data layers had little or no variation over the study area precipitation, soil pH, elevation, and maximum slope, so these variables could not be tested for association with leafy spurge. Distance to disturbance (roads) was negatively associated with the occurrence of leafy spurge for all threshold distances from 25 m to 1 000 m (data not shown).
Table 4
Associations between geospatial class and classified Airborne Visible Infrared Imaging Spectrometer (AVIRIS) imagery for three geographic variables with the use of Kappa analysis.
Distance to water was inversely related to leafy spurge susceptibility as expected, with areas close to water having higher occurrence of leafy spurge. The threshold distance to water was varied incrementally from 20 m to 1 000 m (Fig. 4). As the threshold value of distance increased, the 
reached a maximum at 100 m. At a threshold distance of 200 m, 
had the highest level of significance even though the value of 
was lower (Fig. 4). As the threshold distance to water increased, more total area was predicted to have potential for leafy spurge to occur, up to a distance of 1 000 m, where 98% of the area was predicted to be susceptible (Fig. 4). Also shown on Fig. 4 is the producer accuracy from the AVIRIS SAM classification; as the total area increased from thresholds from 20 m to 400 m, the producer accuracy was larger than the fractional area. At larger thresholds, the producer accuracy was about equal to the fractional area (Fig. 4), and the result was high producer accuracies for model prediction simply because of random chance.
Figure 4
Variation in Weed Invasion Susceptibility Prediction (WISP) model accuracy for changes in the threshold distance parameter for the data layer, distance to water. Distances to water less than the threshold are predicted to be leafy spurge present and distances greater than the threshold are predicted to be leafy spurge absent. As the distance to water increases, more area is predicted to be susceptible. Producer accuracy is a measure of false negative errors.
If a large area is predicted to be susceptible, then the producer accuracy will be high even if model accuracy is not significant. Producer accuracies of 100% can be obtained by predicting the entire study area as susceptible to leafy spurge, which could provide some insight to its biology, but then the model would not be useful for prediction. Therefore, the problem with presence-only data for potential distribution models is the possibility that model parameters are determined without respect to total area predicted to be susceptible.
The WISP model was revised with the use of the results of the Kappa analyses. Three of the nine GIS data layers were used in the revised model; the new model parameters were 1) distance to water ≤ 200 m, 2) riparian/woodland land cover, and 3) clay or silty clay loam soil textures. A sum of three was used to identify susceptible pixels. The area of Crook County estimated to be susceptible to leafy spurge was reduced from 43% to 13% (Fig. 5). A few new areas were predicted to be susceptible to leafy spurge compared to the original WISP model.
Figure 5
Comparison of the original Weed Invasion Susceptibility Prediction (WISP) model predictions and the revised WISP model predictions for potential areas of leafy spurge. Variables for the revised WISP model are distance to water, land cover type, and soil texture. New areas predicted by the revised WISP model (orange) had little effect on accuracy; the largest improvement in accuracy was from the reduction of area predicted to be susceptible to leafy spurge (cyan).
For both the field data and AVIRIS SAM classification, the revised model had lower producer accuracies and much higher overall accuracies, which were highly significant (Table 5). With the AVIRIS SAM classification, the revised model had a very low user accuracy of 22%, because there were a large number of pixels where the revised model predicted leafy spurge but the classification indicated leafy spurge was not present (Table 5). These areas could actually have leafy spurge, but the cover of leafy spurge was not high enough to be detected in the AVIRIS SAM classification (Table 2). Also, not all areas that were potentially susceptible for leafy spurge would actually have leafy spurge. Ranchers and farmers in the area have been applying herbicides and biological control methods to reduce the amount of leafy spurge in some areas. Therefore, the low user accuracy of the revised model could be in part attributed to the unreliability of absence data. Use of remote sensing imagery was important for WISP model revision because the large number of pixels allowed associations between leafy spurge and geographic data layers to be detected even when leafy spurge did not occupy all of the potential area.
Table 5
Accuracy assessment for revised Weed Invasion Susceptibility Prediction (WISP) model predictions compared to field data and the classified Airborne Visible Infrared Imaging Spectrometer (AVIRIS) image.
On the other hand, there were about 3 times more pixels classified as leafy spurge in the areas predicted not to be susceptible to leafy spurge, i.e., low producer accuracy (Table 5). These are errors either by the revised WISP model or the geographic data layers. For example, there was a negative association between loamy soil texture and pixels classified as leafy spurge; however, there were some pixels classified as leafy spurge that occurred on loamy soils. Possibly, plants of other species may have had higher productivity on loamy soils, which reduced the cover leafy spurge and created an apparent negative association. This hypothesis may be tested during a drought year, when the deep root system of leafy spurge would increase its relative competitive ability.
The WISP model is a simple version of a potential distribution model in which the probability of occurrence is either 0 or 1. In reality, the probabilities vary between 0 and 1, perhaps with loamy soil textures having a lower probability than clayey soil textures. Advanced potential distribution models use various algorithms to determine the probability of occurrence for an invasive plant's ecological niche (Guisan and Zimmermann 2000; Peterson 2003; Guisan and Thuiller 2005; Austin 2007; Stohlgren et al. 2010). Another general type of potential distribution models are climatic envelope models (Sutherst 2003; Morisette et al. 2005), in which climate or remote sensing variables associated with current invasive plant distributions are used to predict potential distribution globally. One of the potential applications of climatic envelope models is predicting the effects of climatic change (Pearson and Dawson 2003; Thuiller et al. 2008). The original WISP model incorporated a few ideas from climatic envelope models (i.e., precipitation, Table 1), but there was little spatial variation in climatic variables at the county level.
A problem with invasive-species models is the possibility that the models are overtuned to specific locations, increasing agreement between data and model predictions at one location, but sacrificing applicability to other locations. Remotely sensed images, particularly from imaging spectrometers/hyperspectral sensors (Andrew and Ustin 2009), can be acquired at different locations and used to test model performance. However, not all invasive plant species can be detected with remote sensing, and those species that could be detected at some sites may not be detectable at other sites even with imaging spectrometer/hyperspectral data (Andrew and Ustin 2008). The positive and negative associations between geographic variables and classifications of species presence or absence by remote sensing may provide insight into the ecology of those invasive plants that are detectable, which could then be applied to other invasive species.
MANAGEMENT IMPLICATIONS
Imaging spectroscopy/hyperspectral remote sensing has compelling advantages when the target is spectrally distinct from the background, such as the yellow-green flower bracts of leafy spurge (Hunt et al. 2007). There are several different aircraft-borne hyperspectral sensors (besides AVIRIS), and plans are in place for a new generation of satellites deploying hyperspectral sensors (Schaepman et al. 2009). Schaepman et al. (2009) suggest one of the roles of hyperspectral imagery is to serve as a tool to scale field observations to larger scales, a task currently performed with the use of moderate-resolution multispectral satellites (Mladinich et al. 2006). Although software for atmospheric correction and image processing is available, analysis of hyperspectral data requires a high degree of expertise that is not routinely available to land managers. GIS and geographic data layers are routinely available. The results from this study suggest that remote sensing data should be used to test models of potential geographic distribution of invasive species at different locations, and make the GIS models available for land management.
It is generally less expensive to manage an invasive plant species when there are just a few individual plants. Because the cover of a few plants is well below the threshold for detection by remote sensing at moderate spatial resolution, it will still be necessary to look for new infestations of invasive plants by field crews or by very-large-scale aerial photography (Blumenthal et al. 2007). With validated potential distribution models, areas that are more likely to have leafy spurge can be monitored more frequently and areas that are less likely to have leafy spurge can be monitored less frequently, increasing the efficiency of field crews.
Acknowledgments
We thank Amy E. Parker Williams for providing the field data, Ralph T. Roberts for performing the WISP model simulations, and Randy M. Hamilton for discussions. The Wyoming Geographic Information Science Center (University of Wyoming, Laramie, Wyoming) provided the geographic data layers used in the WISP model. Furthermore, we thank the two anonymous reviewers and the associate editor for their comments.
