Spread and current potential distribution of an alien grass, Eragrostis lehmanniana Nees, in the southwestern USA: comparing historical data and ecological niche models
ABSTRACT
The potential distribution of alien species in a novel habitat often is difficult to predict because factors limiting species distributions may be unique to the new locale. Eragrostis lehmanniana is a perennial grass purposely introduced from South Africa to Arizona, USA in the 1930s; by the 1980s, it had doubled its extent. Based on environmental characteristics associated with its introduced and native range, researchers believed that E. lehmanniana had reached the limits of its distribution by the early 1990s. We collected data on E. lehmanniana locations from various land management agencies throughout Arizona and western New Mexico and found new records that indicate that E. lehmanniana has continued to spread. Also, we employed two modelling techniques to determine the current potential distribution and to re-investigate several environmental variables related to distribution. Precipitation and temperature regimes similar to those indicated by past research were the most important variables influencing model output. The potential distribution of E. lehmanniana mapped by both models was 71,843 km2 and covers a large portion of southeastern and central Arizona. Logistic regression (LR) predicted a potential distribution of E. lehmanniana more similar to this species current distribution than GARP based on average temperature, precipitation, and grassland species composition and recorded occurrences. Results of a cross-validation assessment and extrinsic testing showed that the LR model performed as well or better than GARP based on sensitivity, specificity, and kappa indices.
INTRODUCTION
Predicting the potential distribution of an alien species in its introduced habitat is difficult. Despite knowledge of factors constraining alien species in their native range, the same rules do not apply to the introduced range. Often, alien species may remain relatively obscure then rapidly spread to new areas in unpredictable patterns (Moody & Mack, 1988). Niche opportunities will vary (Shea & Chesson, 2002) as alien species share no evolutionary history with and may not be limited by competitors (Callaway & Aschehoug, 2000), predators, or pathogens (Keane & Crawley, 2002). Alien species may undergo rapid evolution or human selection that allows them to exist under differing environmental limits (Thompson, 1998). Therefore, predicting the distribution of an alien species using data from its native range may not provide adequate information about where the species can exist in its new location (Mau-Crimmins et al., 2006). It is difficult for land managers to make reliable decisions regarding native plant communities that are at risk of invasion when the outcomes of abiotic and biotic interactions of the alien species in the new environment are often unknown. Additionally, questions such as current extent, abundance, and direction and rate of spread have not been answered for many species (Mack, 2000). This is a particularly pressing issue for land managers in Arizona in regard to Eragrostis lehmanniana Nees, because we only know the conditions under which E. lehmanniana exists in its native range and have yet to investigate the abiotic conditions associated with its invaded range. Recent interest in land management issues, such as the use of fire in grassland restoration and impacts of current drought conditions, has made understanding E. lehmanniana's potential distribution important in identifying and prioritizing areas for restoration as well as aiding in the understanding of drought impacts.
To overcome our lack of knowledge, records of alien species occurrences must be continually updated. Data pertaining to species occurrences often exist in disparate sources that have not been compiled to create a unified picture of species distribution. Synthesized, the data may reveal new patterns of species distributions and stimulate the development of experiments to test biotic and abiotic limits to the extent of alien species in their introduced ranges.
Eragrostis lehmanniana, an alien perennial grass from South Africa introduced to Arizona in the 1930s, offers a unique opportunity to follow the introduction and spread of an invasive alien species. Unlike most alien species, the introduction history of E. lehmanniana, including initial seeding sites, area seeded, and genotype, is well documented (Crider, 1945; Cox & Ruyle, 1986; Schussman, 2002). In an effort to rehabilitate Arizona's grasslands that were damaged by drought and overgrazing in the 1900s, a worldwide search for grasses suitable for seeding in the southwestern USA was undertaken. Numerous grasses collected around the world were grown in trials in southeastern Arizona; the most successful species, E. lehmanniana, was selected in the 1930s and distributed throughout southern Arizona. Just 50 years later, E. lehmanniana had expanded to an area twice the area to which it was originally planted (1450 km2) and was reported to have reached the limits of its range based on analysis of abiotic factors that limit its distribution in South Africa (Cox & Ruyle, 1986). However, E. lehmanniana has expanded beyond initial seeding sites to areas beyond its predicted environmental limitations (Cox & Ruyle, 1986) and into undisturbed areas (Anable et al., 1992). Additionally, E. lehmanniana is associated with the alteration and decline of native ecosystems (Cable, 1971; Bock et al., 1986; Williams & Baruch, 2000). Its spread is expected to continue under current climate conditions and land-management practices (Anable et al., 1992; Cox & Ruyle, 1986; McClaran & Anable, 1992).
Given the projected spread of E. lehmanniana our research objective was to identify locations where E. lehmanniana currently exists and use these data to (1) compare current E. lehmanniana locations with 20-year-old distribution maps, and (2) identify potential habitat of E. lehmanniana in Arizona and western New Mexico, USA using ecological niche models.
METHODS
Model input data
We obtained 1180 unique occurrences of E. lehmanniana in our study region of Arizona and western New Mexico from several sources including the Santa Rita Experimental Range, Bureau of Land Management, The Nature Conservancy (TNC), US Department of Defense, US Fish and Wildlife Service, US Forest Service, US Geological Survey, and the US National Park Service. We randomly selected occurrences that were greater than 1 km apart (resulting in 186 points) to minimize spatial autocorrelation and disproportionate influence of intensively sampled areas. From this pool of 186 occurrences, we used 100 points to build models of the species’ potential distribution and retained the remaining points for extrinsic model testing. Base environmental data consisted of 13 geographical layers in raster format at 1-km resolution covering Arizona and western New Mexico. Topographical data obtained from a digital elevation model (USGS, 2001) and its derivatives included: elevation, slope, and cosine of aspect. Edaphic data included depth to bedrock and textural data (Miller & White, 1998) averaged across the soil horizons up to 1-m in depth to estimate the percentage of sand, clay, and silt in the soil profile. Climatic data were available for the period 1980–97 and included: average summer precipitation (June, July, August), average winter precipitation (December, January, February, March), average annual precipitation, average solar radiation in Mega joules (MJ m−2 day−1), and average maximum and average minimum annual temperatures (Thornton et al., 1997, 2000). We avoided the conventional designation of 3-month seasons to capture the unique seasonality of precipitation in Arizona based on Sheppard et al. (2002).
Logistic regression modelling
We used retrospective sampling, case-control logistic regression (LR) (Christensen, 1997) to differentiate between E. lehmanniana sites (n = 100) and random locations (n = 100) based on environmental variables, a technique commonly used to model species distributions (e.g. Fielding & Bell, 1997; Franco et al., 2000; Kleinschmidt et al., 2000; Barbosa et al., 2003). Random points drawn from the entire study area allowed us to differentiate between presence locations (cases) and random locations (controls) across the entire study area in order to justify inferences to the entire study area. Random points were generated for the study region using a random-point generator in ArcInfo 9.1 (ESRI, 2005; Jenness, 2005).
We excluded four of 13 environmental variables prior to analysis because of correlations higher than 0.75 in a pairwise correlation analysis. We explored the inclusion of polynomial terms within the model and found no significant model improvement, as determined by model Akaike Information Criterion scores, and so did not include higher order terms in the model. Final model parameters included nine environmental variables (slope, cosine of aspect, depth to bedrock, percentage of silt, percentage of sand, average summer precipitation, average winter precipitation, and average maximum temperature) and all first-order interactions.
We used a stepwise procedure in SAS 9.0 (SAS Institute Inc., Cary, NC, USA), which is appropriate for determining the variables and interactions between variables that best distinguished between E. lehmanniana locations and the random locations based on statistical criteria (Hosmer & Lemeshow, 2000). We assigned a P-value to enter the model of 0.30 and a P-value to stay in the model of 0.10.
Creation of the probability surfaces
To build the visual representation of the potential distribution of E. lehmanniana, we calculated the probability response at every cell location in the study area using the raster array of explanatory variables to estimate the probability of potential E. lehmanniana presence. Using ArcInfo (ESRI, 2005), we multiplied each coefficient by the cell value in the appropriate environmental grid, summed the resulting grids at each cell location, and then solved the logit function for the probability at each cell location. Given that we had a balanced sample of presence and random points, we considered a location to be E. lehmanniana habitat when probability was greater than 0.5 (Manel et al., 1999).
Genetic Algorithm for Rule-Set Prediction modelling
GARP (Genetic Algorithm for Rule-Set Prediction) is a niche-based model receiving wide application (Stockwell & Noble, 1992; Stockwell & Peters, 1999). GARP uses an iterative process of rule selection, evaluation, testing, and incorporation or rejection to create a rule-set that best represents the environmental conditions under which the species is found (Peterson & Cohoon, 1999). We ran the model 300 times and selected all combinations of four types of rule types (atomic, range, negated range, and logit), which resulted in 15 combinations; we then ran each combination 20 times. For each run, the algorithm ran either for 1000 iterations or until convergence. We then projected the final rule-set, or ecological niche model, onto a digital map as the species’ potential geographical distribution and imported it into ArcView 3.2 (ESRI, 1999) using the Spatial Analyst extension for visualization.
To choose the best subset of the 300 native range models created, we adopted a best subsets selection procedure (Anderson et al., 2003; Peterson et al., 2003). Following this method, we selected the best subset of models by eliminating all models that had non-zero omission error based on independent test points, calculated the median area predicted present among these zero-omission points, and then identified the 10 models closest to the overall median area predicted. We summed these 10 models to create an output grid of model agreement, ranging from 0 (areas not predicted as E. lehmanniana habitat by any of the 10 models) to 10 (areas predicted as E. lehmanniana habitat by all 10 models). Finally, we considered areas predicted by seven out of 10 models to show the potential distribution of E. lehmanniana.
Model performance assessment
For LR we used a jackknife (cross-validation) procedure, which excluded each datum in turn and then recalculated the maximum likelihood estimates of the coefficients to assess the accuracy of the model. Also, we calculated the proportion of true positives (sensitivity) and true negatives (specificity) correctly predicted, as well as the proportion of specific agreement corrected for agreement by chance alone (kappa) using original and extrinsic data for both LR and GARP models (Manel et al., 2001). We calculated and compared kappa statistics in addition to using extrinsic testing points in order to alleviate any error associated with the prevalence of species locations (Fielding & Bell, 1997; Manel et al., 2001).
The LR and GARP models required slightly different input data for model development. Logistic regression utilized presence and random information, whereas GARP used presence only information. The predictive power indices and overall accuracy measurements required presence, random, and absence information. Given that there was slightly different information needed for model creation and assessment, we divided our presence points into two groups, those to be used in model creation and those for extrinsic testing. Also, we generated two groups of random points, one for model building (n = 100) and one for testing (n = 86). Finally, we obtained absence points (n = 265) from TNC's extensive field survey of grasslands across Arizona and southwestern New Mexico (Gori & Enquist, 2003; Schussman & Gori, 2004); this information did not represent the entire study area and therefore we used these data solely for model assessment. In addition, we calculated percentage agreement of E. lehmanniana distribution between LR and GARP maps and compared these maps with the field-based grassland assessment map produced by TNC, which identified areas currently dominated (frequency > 20%) by E. lehmanniana.
Environmental variables associated with potential distribution
We obtained key environmental drivers from LR model output. To determine important environmental factors influencing the GARP model, we performed a series of sequential jackknife manipulations on environmental coverages. Specifically, jackknifing uses all possible combinations of a reduced set (e.g. N − 1) of N environmental coverages to generate models. We assessed model quality by exploring correlation between variable inclusion and omission error (Peterson & Cohoon, 1999). We considered variables that were positively correlated with improvement in avoiding omission error to be most important in defining E. lehmanniana's environmental niche.
Because predictions of species habitat are a function of many variables, it is difficult to easily interpret the individual variables’ influence on predicting species potential distribution. To enable interpretation of multiple variables simultaneously, we used Principle Components Analysis (PCA), bivariate plots, and descriptive statistics to explore differences between the two distribution maps.
To compare models, we used a random-point generator in ArcView 3.2 (Jenness, 2005) to generate random points from across the study region. Based on the distribution maps we identified the random points as predicted present by both models, LR only, GARP only, or areas dominated by E. lehmanniana. We performed a PCA on the correlation matrix for the environmental variables associated with random points identified by both models, LR only, and GARP only using primer version 5 (PRiMER-E Ltd., Plymouth, UK). Prior to analysis, we transformed variables using the log or square-root transformation if distributions visually appeared skewed. We also used bivariate plots and descriptive statistics to compare the similarities and differences of the 13 environmental input variables in each model and areas known to be dominated by E. lehmanniana.
Comparison of distribution maps
We scanned and rectified Cox and Ruyle's 1986 map of seeding locations (n = 143) and areas occupied (5830 km2) by E. lehmanniana to obtain a spatial coverage of E. lehmanniana's distribution as of 1986. Additionally, we obtained a spatial coverage of areas dominated by E. lehmanniana from TNC's 2003 grassland assessment for Arizona (Gori & Enquist, 2003). Spread of E. lehmanniana was evaluated by visually assessing changes in E. lehmanniana locations as well as areas identified as occupied by E. lehmanniana in 1986, 2003, and our predicted distributions.
RESULTS
Eragrostis lehmanniana distribution
The LR model predicted E. lehmanniana to occur throughout a large portion of 10 counties in Arizona and New Mexico, totalling 80,822 km2 (Fig. 1a). The distribution was limited to areas in the southeastern half of Arizona and the corner of New Mexico. GARP predicted E. lehmanniana to occur throughout a large portion of 16 counties in Arizona and New Mexico, totalling 120,678 km2 (Fig. 1b). The distribution spans from the northwest corner of Arizona, through the central part of the state, to the southwest corner of New Mexico. A comparison of E. lehmanniana potential distribution mapped by both models shows 71,843 km2 of overlapping area, 8875 km2 of LR-only predicted area, and 63,664 km2 of GARP-only predicted area (Fig. 2). The Nature Conservancy assessment (Gori & Enquist, 2003) found 5948 km2 dominated by E. lehmanniana; these regions fell within LR and GARP distribution maps, with both models predicting an extent of E. lehmanniana well beyond TNC's assessment (Fig. 2). Cox & Ruyle (1986) estimated the area occupied by E. lehmanniana as 1450 km2. Seeded at 143 locations, primarily along major roadways, the areas where E. lehmanniana existed in 1986 overlap with about half the areas currently dominated by the grass according to the TNC assessment and these areas all are located within areas predicted by both models. Only four seeding locations sites are not found within an area predicted by one or both models (less than 7 km from any predicted location) while 123 are within the area predicted by both models (Fig. 2). Of the 100 E. lehmanniana location points used for building models, 19 were located in areas at least 38 km beyond 1986-recorded seeding locations. Most of the new E. lehmanniana locations extend toward the northwest from the heavily seeded areas in the southeast; the farthest location is 258 km from the nearest seeding location.
Distribution of Eragrostis lehmanniana across Arizona and western New Mexico as predicted by (a) logistic regression (LR) and (b) Genetic Algorithm for Rule Set Prediction (GARP). Maps are in Universal Transverse Mercator projection and show a subsample of points used to create and test the model. Input points are the 100 presence locations for model building by LR and GARP (input random points used in LR are not shown). Extrinsic points of presence (not shown), absent, and random locations were used to test the model performance.
Model output comparison showing Eragrostis lehmanniana distribution as predicted by GARP (7 of 10 best models) and LR (probability > 50%), GARP only, and LR only. These models were compared to a field assessment of areas dominated (as compared to simple presence/absence) by E. lehmanniana as well as seeding locations. Maps are in Universal Transverse Mercator projection.
Environmental variables associated with potential distribution
The main environmental variables driving the potential distribution for the LR model were winter precipitation, summer precipitation, slope, average high temperature, and the interaction between summer precipitation and average high temperature. Soil variables (silt, sand, depth to bedrock), aspect, and radiation were removed by the stepwise analysis. Jackknife manipulations of the different environmental coverages suggested that summer precipitation, winter minimum temperature, elevation, summer maximum temperature, solar radiation, and clay were the critical variables, in decreasing magnitude, influencing the GARP model. These variables correlated positively with improvement in avoiding omission. The differences in variables highlighted by the two models correspond with the differences in portions of the state predicted as suitable habitat by the two methods.
Principal components analysis of the correlation matrix showed points predicted as present by both models falling closely together in ordination space. Along the first axis, elevation and average temperature were the main environmental variables related to the potential distribution modelled along the first axis (Table 1). Radiation, slope, sand, and winter precipitation explain most of the variation on the second axis (Table 1). On both axes, locations predicted as E. lehmanniana habitat by LR-only or GARP-only ordinated marginally outside the cluster of points predicted by both models. Analysis of bivariate plots and a visual comparison of locations predicted as E. lehmanniana habitat by both LR and GARP models also showed little difference between the models. Only a few LR-only points had slightly higher average high temperatures and higher average winter precipitation than GARP-only points (Fig. 3). Similarly, a comparison of minimum, maximum, and mean values for points falling within the 50% predicted probability of occurrence for LR, seven out of 10 best subset GARP models, and TNC's E. lehmanniana-dominated areas showed comparable values for the 13 environmental variables (Table 2).
| Variable | PC1 | PC2 | PC3 | PC4 | PC5 |
|---|---|---|---|---|---|
| Silt | 0.069 | 0.198 | −0.094 | −0.495 | −0.590 |
| Sand | −0.164 | −0.336 | 0.580 | 0.182 | −0.046 |
| Radiation | 0.099 | 0.542 | 0.185 | 0.302 | −0.141 |
| Elevation | 0.460 | 0.038 | 0.149 | −0.002 | −0.035 |
| Depth to bedrock | −0.184 | 0.283 | 0.137 | 0.108 | 0.037 |
| Clay | 0.134 | 0.248 | −0.589 | 0.092 | 0.383 |
| Average temperature | −0.464 | 0.001 | −0.162 | 0.065 | −0.107 |
| Average low temperature | −0.450 | −0.094 | −0.183 | 0.037 | −0.091 |
| Average high temperature | −0.456 | 0.090 | −0.135 | 0.089 | −0.118 |
| Cosine of aspect | −0.055 | 0.002 | 0.020 | −0.607 | −0.065 |
| Slope (log) | 0.142 | −0.402 | −0.257 | 0.081 | −0.275 |
| Winter precipitation (log) | 0.165 | −0.472 | −0.257 | 0.155 | −0.054 |
| Summer precipitation (log) | 0.134 | 0.100 | −0.149 | 0.445 | −0.604 |
| Eigen values | 4.3 | 2.2 | 1.6 | 1.2 | 1.1 |
| % variation | 33.4 | 16.7 | 12.2 | 9.1 | 8.5 |
| Cumulative % variation | 33.4 | 50.1 | 62.3 | 71.4 | 79.9 |
Bivariate plot of winter precipitation and average high temperature for presence locations predicted by both models (light grey circles), LR only (black crosses), or GARP only (open diamonds).
| Variable | LR | GARP | TNC | |||
|---|---|---|---|---|---|---|
| Mean (SE) | Range | Mean | Range | Mean | Range | |
| Winter precipitation (mm) | 480.0 (5.0) | 200–1062 | 442.0 (0.2) | 137–986 | 373.4 (2.5) | 233.7–723.9 |
| Summer precipitation (mm) | 470.0 (5.0) | 241–1001 | 419.0 (0.1) | 152–901 | 551.2 (2.5) | 343–1115 |
| Average temperature (°C) | 16.4 (0.1) | 8.3–21.5 | 14.9 (0.1) | 9.3–21.0 | 16.5 (0.0) | 13.4–19.0 |
| Average low temperature (°C) | 8.1 (0.1) | 0.8–13.2 | 6.5 (0.1) | 1.2–12.4 | 7.9 (0.0) | 5.0–11.1 |
| Average high temperature (°C) | 24.8 (0.1) | 15.7–30.5 | 23.3 (0.1) | 16.1–30.0 | 25.0 (0.0) | 20.2–27.6 |
| Radiation (MJ m−2 day−1) | 17.8 (0.0) | 14.8–18.6 | 17.8 (0.0) | 16.1–18.9 | 18.0 (0.0) | 16.1–18.5 |
| Elevation (m) | 1241 (13.0) | 478–2316 | 1402 (9.0) | 563–2196 | 1306 (6.0) | 917–1961 |
| Cosine of aspect | 0.0 (0.0) | 1.0–(−1.0) | 0.0 (0.0) | 1.0–(−1.0) | 0.15 (0.0) | (−1.0)−1 |
| Slope (%) | 4.2 (0.1) | 0.0–25.7 | 4.5 (0.1) | 0.1–29.7 | 3.2 (0.1) | 0.2–24.7 |
| Depth to bedrock (cm) | 107.4 (1.8) | 0.0–152 | 102.6 (1.4) | 21.0–152.0 | 131.1 (1.6) | 20.0–152.0 |
| Clay (%) | 20.1 (0.3) | 0.0–47.0 | 21 (0.3) | 5.0–48.0 | 20.7 (0.3) | 9.0–47.0 |
| Sand (%) | 46.1 (0.4) | 0.0–82.0 | 45.0 (0.3) | 15.0–82.0 | 45.7 (0.3) | 17.0–64.0 |
| Silt (%) | 33.9 (0.2) | 0.0–58.0 | 34.7 (0.2) | 13.0–54.0 | 34.3 (0.2) | 27.0–54.0 |
Despite the slight differences in the amount of precipitation and temperature predicted by LR and GARP to drive E. lehmanniana distribution, in both models these factors are critical in expressing the range of the species. According to the models, E. lehmanniana is typically not found where winter precipitation is below 280 mm or summer precipitation is below 330 mm. Average low temperatures did not range below 0.8 °C and average highs did not rise above 30 °C. Temperature values calculated for TNC's E. lehmanniana-dominated areas were on the high end of the range observed for both models (Table 2). We did not observe an effect of soil texture variables or aspect on the distribution of E. lehmanniana.
Model performance
We assessed model performance based on sensitivity, specificity, and kappa. Kappa values range from −1 to 1 with 0.0 to 0.4 = slight to fair model performance, 0.4 to 0.6 = moderate performance, 0.6 to 0.8 = substantial model performance, and 0.8 to 1.0 almost perfect performance (Manel et al., 2001). Results of the cross-validation assessment for the LR model showed that the model performed well for all three indices, with sensitivity, specificity, and kappa values of 84%, 84%, and 0.68, respectively (Table 3). Extrinsic testing of the LR model showed an increase in sensitivity measures to 94% for both extrinsic random and absence points, whereas specificity decreased to 81% and 78% and kappa decreased to 0.76 and 0.72 for random points and absence points (Table 3). Extrinsic testing of the GARP model showed similar patterns as those seen in the LR model. Sensitivity measures were high, with values of 94% for extrinsic random and absence points and with lower values for specificity (69% and 45%) and kappa (0.61 and 0.40) (Table 3).
| Logistic regression | GARP | ||||
|---|---|---|---|---|---|
| Model | Extrin rand | Extrin abs | Extrin rand | Extrin abs | |
| Sensitivity | 84% | 94% | 94% | 94% | 94% |
| Specificity | 84% | 81% | 78% | 69% | 45% |
| Kappa | 0.68 | 0.76 | 0.72 | 0.61 | 0.40 |
- Extrin rand, extrinsic random; Extrin abs, extrinsic absence.
DISCUSSION
Distribution maps
Considering the introduction history and ecological characteristics of E. lehmanniana, we were not surprised to find E. lehmanniana in more locations in northwest-central Arizona in early 2000 than in the mid-1980s, with areas of high probability of E. lehmanniana presence occurring around locations where the grass was seeded. One-fifth of the points representing current locations used for model input were found outside of areas sown to E. lehmanniana, with models predicting a potential distribution well beyond E. lehmanniana's current occupation. This expanded distribution may not be unreasonable considering new reports of presence locations outside of our study area including northern California; Central Chihuahua, Mexico; and central Texas. These reports suggest that the species is still capable of spreading even beyond areas identified by the models we considered. However, four of the 143 seeding locations appear to be classified as unsuitable habitat for E. lehmanniana. Anable et al. (1992) suggests that E. lehmanniana does not survive in areas that receive less than 89 mm of precipitation in 40 days.
Ecological modelling
Whereas many studies have compared modelling methodology and assessment measures (Fielding & Bell, 1997; Guisan & Zimmermann, 2000; Pearce & Ferrier, 2000a,b; Manel et al., 2001; Olden & Jackson, 2002; Stockwell & Peterson, 2002; Loiselle et al., 2003; Thuiller et al., 2003; Segurado & Araújo, 2004), few papers discuss and compare the resulting distribution maps (see Austin & Meyers, 1996; Thuiller et al., 2003, 2005; Thuiller, 2004). Given that model performance varies by species distribution and available data, models should be chosen and assessed based on type of input data, species range, and the research question being addressed (Guisan & Zimmerman, 2000; Manel et al., 1999; Thuiller et al., 2003; Segurado & Araújo, 2004). Multiple modelling approaches may be necessary to obtain a realistic model prediction (Olden & Jackson, 2002; Thuiller, 2004), and assessing model performance within an ecological context is essential (Fielding & Bell, 1997). Visual comparisons of model output also are necessary to assess model accuracy and appropriateness. In this study, we aimed to use well-tested methods appropriate for our question and interpret the results in light of our knowledge of the species.
Accuracy assessments for both LR and GARP models showed that both models performed equally well at predicting known E. lehmanniana locations (sensitivity). However, LR was more successful than GARP at predicting known E. lehmanniana absence locations (specificity) and the proportion of specific agreement (kappa) (Table 3). Results of accuracy assessments suggest that the LR model has a more realistic prediction of E. lehmanniana's current distribution than does GARP. However, given that we were modelling a wide-ranging species for which microclimate may play a large role in determining presence or absence, at least in the southeastern part of the state, the drop in accuracy based on known E. lehmanniana absence locations is not unexpected (Guisan & Zimmerman, 2000; Segurado & Araújo, 2004). In addition, other factors should be considered when interpreting these maps and metrics. Specifically, the two models operate differently. Logistic regression fits a generalized linear model with a logit link to the data points, thereby highlighting areas that are most similar to the input points. In contrast, GARP is an expert system that selects among several rule types to fit best the relationships between data sets. Designed to work with presence-only data, GARP avoids over-fitting the distribution by selecting among a variety of rule sets while minimizing rule complexity (Kriticos & Randall, 2001). However, GARP has been shown to over-predict potential distributions (Pearson et al. in press). Second, E. lehmanniana is an introduced species that continues to spread to new habitats in Arizona (D. Robinett, pers. comm.; G. Ruyle, pers. comm.) and beyond, therefore regression methods may miss potential habitat that is outside the range of conditions currently captured by the location points used to build the model.
In our study, both LR and GARP predict presence on nearly 72,000 km2 in southeastern Arizona (Fig. 2). The primary area of disagreement between the two distributions occurs in the northern half of Arizona, which is predicted by the GARP model (Fig. 2). Although this portion of Arizona is a grassland ecosystem, it supports cool-season grasses and receives more of its precipitation during the winter months than southeastern Arizona (Finch, 2004). Eragrostis lehmanniana is not found in northern Arizona but dominates many grasslands in southeastern Arizona (Schussman & Gori, 2004). This difference in area predicted reveals a slight difference in the interaction of precipitation and temperature in influencing the predicted distributions between the two models.
Regardless of the differences in predictions by the models, 20% of the recent data points of E. lehmanniana exist well beyond the area delimited by Cox & Ruyle (1986). Eragrostis lehmanniana is a widely distributed species in Arizona that disperses readily via copious small seed that spreads easily via wind, water, and vehicles (Kincaid et al., 1959; McClaran & Anable, 1992). Until the late 1980s it was seeded by livestock producers, along many highways by the Arizona Department of Transportation, and used in ‘restoration’ seed mixes following forest fires (Cox & Ruyle, 1986; D. Robinett, pers. comm.). Areas receiving frequent disturbance near roads and trails are most likely to become invaded first, with populations spreading from these loci. These models correlate with what expert knowledge and field studies have suggested: that E. lehmanniana has become dominant in semidesert grasslands, which once supported native plants. The core area predicted by both models is supported by existing data, and those predicted areas at the edges of the range are increasingly supported by first-time E. lehmanniana sightings.
Model limitations
Correlative models such as niche-based or bioclimatic envelope models have been criticized for not capturing interactions between species (Davis et al., 1998 but see Guisan & Thuiller, 2005). Competitive interactions can limit the geographical distribution realized by a species; models built on known locations under these conditions can underestimate the environmental niche that the target species has the ability to occupy (Peterson et al., 2002). Environmental niche models that do not account for these relationships can lead to incorrect predictions of future species distributions (Pearson & Dawson, 2003).
Current knowledge of E. lehmanniana in the USA suggests that this plant is not limited by competition with other species. Instead, it has been observed to spread aggressively into native grasslands and shrublands from seeded areas, both in response to and independent of disturbance (Anable et al., 1992). Cable (1971) predicted that the spread of E. lehmanniana into new habitat would be limited only by the ability of viable seed to reach these locations. Biotic interactions operate at a local scale, on the order of metres to kilometres (Willis & Whittaker, 2002; Pearson & Dawson, 2003), the scale of the model presented in this paper. However, because E. lehmanniana appears to move across the landscape independently of other species, this criticism of correlative models unlikely pertains to the present models.
In addition to excluding biotic interactions or the influence of dispersal, the models are limited by input data. For example, the scale of the environmental data put into the models may be too coarse to represent the variables truly influencing the species’ presence. In addition, the layers selected may not represent all the abiotic factors important to E. lehmanniana at a location. Additionally, inherent error in the input data arising from interpolation could contribute to distribution inaccuracies. Likewise, both models assume E. lehmanniana is at equilibrium with the environment and hence represent an accurate prediction of potential habitat. Even with these limitations, it can be argued that for the identification of the potential distribution of an invasive alien, it is more important that our models identify accurately where the species could occur rather than where it is likely not to occur (Thuiller et al., 2005). Given that both models had 94% accuracy for predicting E. lehmanniana presence, both models yield valuable and interpretable distribution predictions.
Environmental variables
Eragrostis lehmanniana was selected for its drought tolerance and can easily persist at average high temperatures of 25 °C (Crider, 1945). Our study supports the finding that E. lehmanniana is rarely found in areas with an average low temperature of less than 0 °C (Cox & Ruyle, 1986). As a consequence of this environmental limitation, the Soil Conservation Service introduced other species of Eragrostis (specifically, E. curvula and E. curvula var. confertifolia) that survive at higher elevations and colder temperatures than E. lehmanniana (Crider, 1945). With respect to precipitation requirements, the models we evaluated predicted suitable habitat in regions with almost equal amounts of summer and winter precipitation. This highlights the ability of E. lehmanniana to utilize both warm and cool season precipitation even though it still may be limited by cold temperatures. It has been observed to photosynthesize and even reproduce during the winter months (Fraiser & Cox, 1994).
Interestingly, points located within E. lehmanniana-dominated areas, as indicated on TNC's map, exhibited a warmer and wetter range compared to the model predictions (Table 2). However, it is difficult to know if this suggests that areas that become dominated by E. lehmanniana fall within a slightly narrower abiotic range or if these values are not at equilibrium due to E. lehmanniana's continued expansion. Perhaps E. lehmanniana is not as good of a competitor at the tails of its distribution in the different variables (temperature and precipitation) and thus does not dominate communities in those areas.
The lack of effect of soil texture variables on the distribution of E. lehmanniana may be due to the resolution of our input data. Whereas climatic variables may be represented well at 1 km resolution, soil variability occurs over a much smaller scale, hence biologically meaningful variability probably was not captured in our models. In addition, soil characteristics are more likely to affect abundance than presence at a particular site (Anderson et al., 1957; Cable, 1971; Cox & Martin, 1984; Cox & Ruyle, 1986; Cox et al., 1988). Specifically, Cox & Ruyle (1986) found that E. lehmanniana could spread to many soil types but only predominates where surface soils are sandy. Likewise, aspect would be expected to alter microhabitat and thus again would be more important in determining dominance on a local scale (< 1 km).
Beyond the abiotic factors associated with E. lehmanniana existence and spread, factors such as land use, climate change, and phenotypic plasticity may also be important players in E. lehmanniana's continued spread. Increases in the use of automobiles and road access may have been important vectors in the spread of E. lehmanniana as its small seed is easily transported via cars. A period of above-average precipitation occurring after 1976 (Swetnam & Betancourt, 1998) also may help explain increases in E. lehmanniana distribution as increased precipitation allowed for increases in abundance and expansion to new areas. Finally, the phenotypic plasticity of this apomictically reproducing grass is outstanding, with E. lehmanniana being shown to exist in a wide range of ecological conditions with little to no genetic variation (Schussman, 2002).
ACKNOWLEDGEMENTS
We would like to thank Dan Robinett and George Ruyle for their insights and on-the-ground knowledge of the current distribution of Eragrostis lehmanniana. Additionally, we thank Tom Boxler and Alfonso Sanchez for their identification of E. lehmanniana in Modoc county, California and Central Chihuahua, Mexico. Thanks to Bob Steidl for statistical advice. Insightful reviews of this manuscript were provided by Guy McPherson, Wilfried Thuiller, and an anonymous reviewer. Financial support of this project was provided by the Center for Invasive Plant Management and T&E, Inc.
