Eric R. Larson 1 *, Rachael V. Gallagher 2, Linda J. Beaumont 2 and Julian D. Olden 3

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1 Diversity and Distributions, (Diversity Distrib.) (2014) 20, A Journal of Conservation Biogeography Diversity and Distributions BIODIVERSITY RESEARCH 1 Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA, 2 Department of Biological Sciences, Macquarie University, Sydney, NSW 2109, Australia, 3 School of Aquatic and Fishery Sciences, University of Washington, Seattle, WA 98195, USA *Correspondence: Eric Larson, Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN 37996, USA. lars9570@uw.edu Generalized avatar niche shifts improve distribution models for invasive species Eric R. Larson 1 *, Rachael V. Gallagher 2, Linda J. Beaumont 2 and Julian D. Olden 3 ABSTRACT Aim Species distribution models are an invaluable tool for anticipating the potential range of invasive species. These models often improve when both native and non-native occurrences are available for model development and validation. Therefore, how might ecologists anticipate the potential distributions for emerging invasive species that lack any or abundant non-native range occurrences? Here, we evaluate the recent suggestion of transferring niche shifts from well-established avatar invaders to emerging invaders by testing if ensemble niche shifts from a group of globally invasive plants improve model predictions when each of these species is iteratively treated as an emerging invader. Location Global. Methods We built species distribution models using Mahalanobis distance and four climatic predictors (maximum and minimum temperature and precipitation) for 26 invasive terrestrial plants from an Australian priority list of weeds. Models using only native range occurrences for each species were modified with avatar niche shifts from the remaining ensemble of 25 species based on both a typical (median) niche shift and a large (extreme) niche shift (or niche expansion). Native range and both median and extreme avatar models were then compared with total range models (developed with both native and nonnative occurrences) for performance by measures of discrimination and an approximation of calibration. Results Avatar niche shifts reduced errors of omission for known non-native occurrences relative to native range models, with a trade-off of increased errors of commission of lesser magnitude. Further, our approximation of model calibration measured relative to total range models improved with avatar niche shifts. Differences between native range and avatar models were most pronounced for the larger extreme avatar niche shifts (or expansion) based on increased niche size and decreased (towards 0) covariance among climatic axes. Main conclusions We suggest that researchers and managers evaluating risk of invasion of their jurisdiction by emerging data-poor invaders modify native range models with observed avatar niche shifts from ensembles of well-studied invaders. Alternative implementations of the avatar invader concept are discussed and research needs for methodological improvements proposed. Despite these opportunities for improved implementation of avatar niche shifts, ample evidence now supports that researchers should expect models based on only native ranges to underestimate or misrepresent the total range for data-poor emerging invaders. Avatar niche shifts (and specifically expansion) from wellstudied species offer a precautionary means to anticipate the extent to which native range models may underestimate total ranges. DOI: /ddi ª 2014 John Wiley & Sons Ltd

2 Avatar niche shifts for emerging invaders Keywords Australia, ecological niche models, Mahalanobis distance, niche conservatism hypothesis, non-native species, weeds. INTRODUCTION When Joseph Grinnell (1917) used the term niche to describe an organism s place in its environment, he probably did not anticipate the many methodological advances that would move quantitative characterization of his niche concept, in the guise of species distribution models (SDMs), to the forefront of basic and applied ecology (Pearman et al., 2008; Soberon & Nakamura, 2009). One recent application that has both challenged and advanced our basic understanding of the Grinnellian niche is the use of SDMs to anticipate potential geographic ranges and environmental associations for invasive species (Peterson, 2003). Some researchers have observed that models based on only native or non-native ranges of species can have poor reciprocal transferability (e.g. Broennimman et al., 2007). This may reflect genuine niche shifts with ecological or evolutionary mechanisms (Callaway et al., 2011) or may arise due to methodological issues such as failure to account for non-analogue climates between disparate geographic regions (Petitpierre et al., 2012). Regardless of cause, the potential inability of native range distribution records to anticipate non-native distributions is problematic, particularly for emerging invaders that lack sufficient non-native range data to parameterize models or evaluate reciprocal transferability (Jimenez-Valverde et al., 2011). As a potential solution to this problem, Larson and Olden (2012) suggested transferring the magnitude and character of observed niche shifts (sensu Pearman et al., 2008; see Discussion) from well-studied avatar invaders to data-poor emerging invaders. The term avatar was proposed in this context to represent the way that a well-established invader could emulate Grinnellian niche implications of the invasion process for an emerging invader; akin to how an avatar in a videogame or on the internet allows its human user to explore a simulated or remote environment (but see Damuth, 1985 for a previous application of avatar to evolution). Larson and Olden (2012) argued that the degree and character to which native range models underestimate the observed total range (i.e. modelled from combined native and non-native occurrences) from one or many avatar invaders could be transferred as a precautionary estimate of native range model underestimation for an emerging invader. In introducing this avatar invader concept, the authors suggested that a first step to evaluating its usefulness would be to determine whether observed niche shifts from established invasions are represented or predicted by niche shifts from other well-established avatar invaders. Here, we evaluate the avatar invader concept using a published dataset of 26 plant species introduced to Australia that were previously evaluated for potential Grinnellian niche shifts (Gallagher et al., 2010). We treat each individual species as an emerging invader and ask if ensemble niche shifts from the remaining 25 avatars improve model performance relative to a model using only native range occurrences. Accordingly, we provide the first empirical test of the capacity of the avatar invader concept to improve SDMs for emerging invaders, a result with important implications for the prevention and management of species invasions. METHODS Study species We selected 26 terrestrial plants from an Australian national list of priority weeds that have well-defined native and nonnative ranges; see Appendix S1 and Table 1 in Gallagher et al. (2010) for more detailed species information. Occurrence records were collated from a variety of sources, with the present manuscript differing from Gallagher et al. (2010) by inclusion of occurrences from all non-native regions globally rather than only Australia. One feature of this dataset (and many others) is that the number of species occurrence records is often imbalanced between native and non-native ranges. To avoid either range having a disproportionate influence on total range models, a random sample of occurrences was extracted from the more abundant range such that it equalled the number of occurrences in the less abundant range (Appendix S1). This step may not be necessary for similar studies with other SDM methodologies (see below and Discussion), and permutations of the randomization procedure (above) could be used to evaluate model sensitivity to this methodological decision. Climate data Larson and Olden (2012) suggested a minimal set of environmental predictors and a transparent modelling methodology for transferring niche shifts between avatar and emerging invaders. Accordingly, we used the following four climatic predictors from the WorldClim database (Hijmans et al., 2005) at a five arc-minute resolution: maximum annual temperature of the warmest month (MaxT; C); minimum annual temperature of the coldest month (MinT; C); maximum precipitation of the wettest month (MaxP; mm); minimum precipitation of the driest month (MinP; mm). Data from WorldClim are based on average monthly temperature and precipitation from a network of meteorological stations centered on 1975 (generally from the period ) and representing current climates (Hijmans et al., 2005). We Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd 1297

3 E. R. Larson et al. anticipate that these climatic variables are all associated with thresholds for survival of terrestrial plants at a global extent and coarse grain. Species distribution modelling There are a number of presence-only SDM tools currently available which differ in ease of use, model complexity and data requirements (Franklin, 2009). Multimodel comparisons have repeatedly concluded that there is no single best SDM (Elith et al., 2006; Lawler et al., 2006). As such, the availability of data and the goals of the study should guide SDM choice (Segurado & Araujo, 2004; Elith & Leathwick, 2009). Given the aims of the current paper, we selected Mahalanobis distance, which is a simple measure of multivariate similarity that accommodates covariance structure between all variables (Mahalanobis, 1936). An alternative implementation of this approach has been developed (partitioned Mahalanobis distance; Browning et al., 2005), although we hypothesize based on its past use that it may be better suited for studies of habitat selection within subsets of distributions rather than modelling the extent of entire distributions. Mahalanobis distance is calculated from the means, variances and covariances among predictor variables, and hence, Larson and Olden (2012) suggested that it is highly suitable for capturing changes in niche position (mean), size (variance) or structure (covariance; Soberon & Nakamura, 2009). Further, Mahalanobis distance is a true presence-only SDM approach that does not require pseudoabsence data for model parameterization (e.g. VanDerWal et al., 2009; but see below for use of pseudoabsences in evaluation of model performance). We implemented this tool using the Jenness et al. (2012) extension for Arc GIS 10.0 (ESRI, 2010). Because Mahalanobis distance uses covariance to account for relationships between predictor variables, authors like Farber and Kadmon (2003) have noted that this approach may cause errors when extrapolated in space or time if relationships between variables change. This is a concern for any SDM that allows for interaction between predictor variables; exceptions would include rectilinear modelling of independent climate variables through approaches like BioClim (Nix, 1986). The complexity of predictor variable interactions allowed in machine-learning or other SDM applications has likely contributed to findings of poor model transferability in space or time with increasing model complexity (Wenger & Olden, 2012). As such, Mahalanobis distance is representative of current challenges in the SDM literature with respect to trade-offs between model complexity and generality (Warren & Seifert, 2011) but represents an intermediate step between models that allow for no interaction between climate variables (e.g. BioClim) and those SDMs with a complex array of potential interactions between variables (e.g. Maxent, Warren & Seifert, 2011; Classification and Regression Trees, Elith et al., 2008; Artificial Neural Networks, Wenger & Olden, 2012). Characterizing niche shifts Following Larson and Olden (2012), we calculated Mahalanobis distance from means, variance and covariances of the four climatic niche predictors (above) from both native and total range (combined native and non-native) occurrences for 26 focal species (Fig. 1). Niche shifts were then represented by calculating ratios between total and native ranges for each statistic (Fig. 2). In a minority of cases, we found that the sign of covariance (positive or negative) could change between native and total ranges, an event not anticipated by Larson and Olden (2012) (see Appendix S2 for visualization of sign changes by climate predictors). We have not identified a method for anticipating these sign changes that might be transferable from avatar to emerging invaders. Hence, for this exercise, we characterized changes in covariance between native and total ranges as the absolute magnitude in covariance relative to zero (Fig. 2); when transferring avatar niche shifts (below), we allowed covariance to increase (away from zero; reduced orthogonality) or decrease (towards zero; increased orthogonality) but not change sign. This modelling simplification is one area where future work may improve on our implementation of the avatar invader concept. Transferring niche shifts We treated each species as an emerging invader for which we modelled potential niche shifts using two ensemble scenarios based on the remaining 25 avatars. The first of these ensemble niche shifts was based on the median observed changes in means, variances and covariances from the 25 avatars (Fig. 2). The second ensemble niche shift was termed the extreme avatar model and anticipated to represent a large, pronounced niche shift (e.g. Broennimman et al., 2007) by always increasing variance (increasing niche size) and decreasing covariance (towards 0 or increasing orthoganality; Larson & Olden, 2012). This was performed by using the median observed change in climatic means in combination with the upper or 75th quartile of change in variances (an increase) and the lower or 25th quartile of change in covariances (a decrease; or towards 0 regardless of sign) from the 25 avatars (Fig. 2). Accordingly, the extreme avatar model might best be described as niche expansion rather than a niche shift. Niche shifts were transferred by multiplying the observed native range means, variances and covariances for emerging invaders with the proportions derived from total to native ratios for either median or extreme avatar ensembles. Importantly, we emphasize that the following mathematical constraint must always be met in transferring niche shifts: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi covariance ðx; yþð variance ðxþvariance ðyþþ If this inequality is violated, an impossible correlation between climatic variables greater than 1 (or < 1) occurs. In 1298 Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd

4 Avatar niche shifts for emerging invaders Figure 1 Conceptual figure representing species distribution modelling with Mahalanobis distance, and the avatar invader concept of transferring niche shifts from well-studied and established invaders to data-poor emerging invaders. (1) Native occurrences of the avatar species are used to calculate means and variances for climatic predictors, and covariance between them, which is then applied to calculate Mahalanobis distance and produce a resulting species distribution model (SDM). (2) The addition of non-native occurrences for the avatar invader often changes our understanding of its climatic niche relationships; we re-calculate means, variances and covariances from these total occurrences (native and non-native occurrences combined) and again calculate Mahalanobis distance to produce an SDM. The ratio of total to native range means, variances and covariances (absolute value; see main text) is calculated as the niche shift. (3) For the emerging invader, native range occurrences are also used to find means, variances and covariances; calculate Mahalanobis distance; and generate an SDM. (4) This native range information can be transformed by the avatar niche shift above; we multiply native range means, variances and covariances against the avatar ratios to produce new means, variances and covariances. These are then used to calculate Mahalanobis distance and produce an SDM that represents the distribution for the data-poor emerging invader. See manuscript text for issue of sign changes in covariance between native and total ranges, as well as discussion of ensemble avatar niche shifts. We use a threshold of chi-square P 0.05 to represent species presence following conversion of Mahalanobis distance to chi-square P-values. no cases did our transferred ensemble niche shifts violate this inequality, but an exploration of some niche shifts as transferred between individual species produced this error in a minority of cases. Larger ensembles of avatars may buffer individual emerging invaders from impossible niche shifts, but we urge researchers implementing the avatar invader concept to carefully evaluate the means, variances and covariances produced from niche shifts and reject those that violate the above relationship (see Discussion). Evaluating model performance Native range, median avatar, extreme avatar and total range SDMs were produced for all species using Mahalanabois distance (above). Mahalanobis distance values for each species were converted to chi-square P-values with a threshold of P 0.05 representing suitable habitat; the conversion of Mahalanobis distance to chi-square P-values assumes multivariate normality, but is also useful for re-scaling to a shared 0 Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd 1299

5 E. R. Larson et al. Figure 2 Total range to native range ratios of the means, variances and covariances of four climate variables for 26 invasive plant species (logarithmic scale for readability only). Red arrows denote the third or upper quartile for variance and the lower or first quartile for covariance used in extreme avatar models (see text). Medians are reported in box plots. to 1 scale (Clark et al., 1993; Larson & Olden, 2012). An example of the variance/covariance matrices used in Mahalanobis distance models and accompanying species distribution maps is given for Thunbergia alata (Fig. 3). We used total models as the best available estimate of the fundamental niche of each species after invasion and evaluated performance of the native range, median avatar and extreme avatar models against these total range models. We recognize that species occurrences as modelled above do not represent the fundamental niche (but rather the realized niche including both native and non-native occurrences), but we share Jimenez-Valverde et al. s (2011) perspective as summarized by Elith (2013) that presence records from the invaded range... are likely to expand the range of environments and biota represented in the data, and hence can potentially edge the modelled niche towards the fundamental niche (but see Elith, 2013 for criticisms of inclusion of non-native occurrence data in SDMs). We also acknowledge that the use of simulated data and species, as opposed to our empirical example, offers an alternative approach to evaluating the avatar invader concept in which the simulated fundamental niche could be known (see Discussion). Model performance as discrimination (i.e. species presence or absence) was evaluated as errors of omission for nonnative occurrences (proportion omitted), errors of commission for random global pseudoabsences generated in equal number to non-native occurrences (proportion included), and area under the receiver operating characteristic curve (AUC). We used pseudoabsences (or background points) at a global extent following the recommendations of Capinha et al. (2011) but recognize that the choice of extent and number of pseudoabsences can affect measures of model performance (e.g. Webber et al., 2011). We also report the proportion of global area predicted as suitable from each model. Comparisons were made as the difference between native, median avatar and extreme avatar models and the total range model of the niche. Model performance can be evaluated as both discrimination (categorical prediction of presence/absence; above) and calibration (continuous prediction of probability of presence; Phillips & Elith, 2010). Although true calibration can only be evaluated in cases of presences and actual absences by evaluating how well estimated probability of presence explains observed proportions of presences (Jimenez-Valverde et al., 2013), we sought to report an analogue of calibration to capture how well our native range and avatar models approximated probabilities of presence predicted by total range models. We did this by regressing chi-square P-values for native, median avatar and extreme avatar models against total model chi-square P-values, our best available estimate of true probability of presence. These regression models used chi-square P-values from non-native occurrences and global pseudoabsences. We evaluated our approximated calibration performance as similarity of intercepts, slopes, and R 2 values between native range or avatar models and the total range models. For both measures of discrimination and approximated calibration, performance relative to total models for native range, median avatar, and extreme avatar models were compared using Kruskal Wallis ranked ANOVAs (H statistic), with Mann Whitney U-tests (U statistic) for post hoc pairwise comparisons. RESULTS The total range models used as a baseline for the evaluation of native range and avatar models had good performance by measures of discrimination, with mean errors of omission of 1300 Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd

6 Avatar niche shifts for emerging invaders Figure 3 Native range, median avatar, extreme avatar and total range models for Thunbergia alata as variance-covariance matrices (10,000 random points for computation time) by four climate variables and maps of global suitability for this species. Mahalanobis chi-square P-values 0.05 are considered suitable (see legend). MaxP is reported on a logarithmic scale for readability only. Some scatter on edges of predicted distributions in scatterplots is caused by chi-square P-values being influenced by all climate variables and their combinations rather than only the bivariate relationships visualized in each separate plot. only 0.11 ( 0.07 SD), mean errors of commission of only 0.16 ( 0.11 SD) and mean AUC values of 0.93 ( 0.05 SD; Appendix S1). This result is perhaps expected as non-native range occurrences were included in development of total range models and also used for model validation (i.e. lack of independence between development and validation data). Yet a fivefold random cross-validation of the total range Mahalanobis distance models supported our interpretation of Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd 1301

7 E. R. Larson et al. generally good performance (Appendix S3) in accordance with past evaluations of Mahalanobis distance for SDMs (Tsoar et al., 2007; Larson & Olden, 2012). Avatar models, and extreme avatar models in particular, out-performed native range models by measures of both discrimination (Fig. 4) and approximated calibration (Fig. 5), although these models rarely approached performance of the baseline total range models (above; Appendix S1). Particularly relevant for anticipating potential distributions of invasive species, avatar models significantly reduced errors of omission for confirmed non-native range occurrences relative to native range models (H = 19.92, P < 0.001). Although median avatar models did not differ significantly from native range models for errors of omission (U = 431, P = 0.089), extreme avatar models had lower errors of omission than both native range and median avatar models (U = 508 to 575, all P < 0.002). This reduction in errors of omission from native to avatar models was accompanied by a tradeoff of increasing errors of commission for global pseudoabsences (H = 26.51, P < 0.001). Errors of commission were significantly higher for median avatar over native range models (U = 215.5, P = 0.025), as well as extreme avatar models relative to both native range and median avatar models (U = 84.5 to 137.5, all P < 0.001). Importantly, the increase in errors of commission (e.g. from SD for native range models to SD for extreme avatar models) was of smaller magnitude than the decrease in errors of omission (e.g. from SD for native range models to SD for extreme avatar models); applied managers may often prefer distribution models for invasive species to be slightly conservative, valuing omission over commission errors (Lobo et al., 2008; Jimenez-Valverde et al., 2011). This result was supported by the general but non-significant (H = 2.875, P = 0.240) trend of increasing AUC values from native to extreme avatar models and a failed equal variance test (Bartlett K 2 = 8.685, P = 0.013) caused by a reduction in variance in AUC with avatar models (Fig. 4). This reduction in AUC variance was caused by fewer models with very poor AUC values in the case of extreme avatar models relative to native range models; native range models with higher AUC values saw little change with avatar niche shifts, whereas native range models with lower AUC values saw improvement with avatar niche shifts (Fig. 4). The proportion of global area predicted as suitable for species also increased from native to extreme avatar models (H = , P < 0.001), with all pairwise comparisons significantly different (U = 69 to 174.5, all P < 0.003). Native range models predicted less global surface area as suitable relative to total range models, whereas median avatar models generally predicted a comparable proportion of global surface area as suitable and extreme avatar models a greater area of global surface area as suitable (Fig. 4). For approximated calibration, R 2 generally increased from native range to extreme avatar models, although not significantly (H = 3.56, P = 0.169). However, similarity of regression slopes to total range models did improve from native range to extreme avatar models (H = 12.50, P = 0.002), although pairwise comparisons were only significant between native and extreme avatar models (U = 151, P = 0.001). The comparison of intercepts produced a significant difference (H = 27.44, P < 0.001); native range and median avatar models were significantly different (U = 181, P < 0.004) but extreme avatar models had higher intercepts than both (U = 84.5 to 148, all P < 0.001). These higher intercepts for extreme avatar models often exceeded zero, illustrating that extreme avatar models regularly predicted higher probability of suitability for species at locations where total range models predicted low probability of suitability (Fig. 5). This provides another perspective on the tendency for extreme avatar Figure 4 The difference between native and avatar (median and extreme) models and total models for 26 plant species for errors of omission (false negatives), errors of commission (false positives), area under the curve (AUC) of the receiver operating characteristic, and proportion of total global area predicted. Zero values and dashed lines represent agreement with total models Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd

8 Avatar niche shifts for emerging invaders Figure 5 Summarized linear regressions (left) based on mean slopes and intercepts (right) of Mahalanobis chisquare P-values from native or avatar (median and extreme) models regressed against total models for 26 invasive plant species (see text). A 1:1 line (grey) indicates the threshold at which native and avatar models predict higher or lower probability of suitability than the total model. Box plots of R 2 values, slopes and intercepts for all 26 individual comparisons of total to native or avatar models are given (right). models to over-predict global area suitable relative to total range models while committing related errors of commission (Fig. 4). However, we interpret approximated calibration for extreme avatar models as improved relative to the underprediction of suitability from native range models (Fig. 5): corresponding reductions in errors of omission are likely more important to identifying areas for prevention of species invasions than the accompanying increases in errors of commission (Fig. 4). DISCUSSION The applied goal of anticipating potential distributions for invasive species has advanced our understanding of the Grinnellian niche, by clarifying what a niche is conceptually (Soberon & Nakamura, 2009) and introducing new methods to quantify it (e.g. Araujo & Peterson, 2012). Combining both conceptual and methodological concerns, Petitpierre et al. (2012) argued that it is inappropriate to characterize as niche shifts incidents where invasive species establish in regions with climates or environments that are non-analogous to (i.e. unavailable in) their native range (but see Webber et al., 2012 for a critique). By this standard, many of the Grinnellian niche shifts reported by Gallagher et al. (2010) and similar papers would likely be disqualified as invalid. Yet for many applied resource scientists, expansion of the native range realized niche into potentially non-analogue climates of their own management jurisdiction is the process of interest and remains frustratingly unpredictable. This is a matter over which Gallagher et al. (2010) and Petitpierre et al. (2012) only disagree on the definition of niche shift ; both manuscripts document many cases in which SDMs developed from only native range data would almost certainly underestimate non-native ranges owing to non-analogue climates. Petitpierre et al. (2012) even acknowledge that SDMs are anticipated to be effective only if study areas have comparable environments, an assumption regularly violated based on an abundance of studies that have found poor reciprocal transferability between native and non-native ranges (e.g. Fitzpatrick et al., 2007; Larson et al., 2010; Medley, 2010). Few papers have offered recommendations for generating precautionary SDMs when native and proposed non-native regions lack comparable environments and species of interest are early in the invasion process (but see Elith et al., 2010; Vaclavık & Meentemeyer, 2012). Addressing this issue remains an urgent management need as data-poor but potentially invasive species will continue to emerge due to the dynamic nature of invasion pathways and implications of climate change (Bradley et al., 2012). In response, Larson & Olden (2012) offered the pragmatic suggestion that niche shifts from well-established invaders could be transferred to data-poor emerging invaders as a precautionary estimate of the extent to which native range data may underestimate total ranges. This recommendation makes no distinction between expansion of the realized niche into previously inaccessible areas of the fundamental niche (e.g. Pearman et al., 2008; Gallagher et al., 2010) or shifts in the fundamental niche itself (Petitpierre et al., 2012) and differs from the more typical practice of treating native and non-native range occurrences of a single species as two separate niches for reciprocal comparisons (e.g. Broennimman et al., 2007; Medley, 2010). Instead, the avatar invader concept of Larson and Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd 1303

9 E. R. Larson et al. Olden (2012) interprets the niche as an attribute of the species, not geographically disjunct populations of the same species, and proposes that the most informative question from a management perspective is using the invasion process to explore the magnitude and character to which native range data under-estimates or misrepresents the total range. Here, we tested this avatar invader concept by evaluating whether typical (median) or large (extreme) niche shifts (or expansion) from an ensemble of well-studied global invaders improved models developed from native range occurrences. We found that avatar models provided superior approximated calibration, as measured relative to total range models, over native range models and that avatar models produced a reduction in errors of omission that outweighed a corresponding increase in errors of commission. These differences were particularly pronounced between our large or extreme avatar niche shifts and native range models. As such, we suggest that resource scientists interested in screening emerging invaders for the risk of establishment in their management jurisdiction include defensibly large niche shifts or expansion from an ensemble of similar invaders as a precautionary method of accounting for the often poor performance of native range models. Our implementation of the avatar invader concept has room for improvement. Although avatar models reliably outperformed native range models, in some instances avatar models still performed poorly as measured against our total range models, with poor approximated calibration, high errors of omission, and low AUC values. Larson and Olden (2012) made a number of suggestions for potentially modifying and improving the avatar invader concept, including the use of ecological traits or phylogenetic similarity to match avatars to emerging invaders. Accordingly, we attempted to produce smaller and more precise ensembles of avatars based on shared characteristics of our 26 focal species, as well as similarity of their native range climates. Unfortunately, these smaller, characteristic-matched avatar ensembles did not improve on performance of our full ensemble model (Appendix S4). Like Gallagher et al. (2010) and Petitpierre et al. (2012), we note that the many idiosyncrasies of the invasion process may override our capacity to anticipate niche shift character or magnitude from ecological traits or other characteristics (but see Donaldson et al., 2014 and Appendix S4). We support further inquiry into this question, but would not be surprised if using large ensembles of general niche shifts remains preferable over close matches of avatars to emerging invaders based on ecological traits, phylogenetic relatedness or similarity of native range climates. This is because data quality issues may erratically misrepresent the niche for either the native or non-native range independent of any species characteristics, and the invasion process is likely ongoing for many species and accordingly different proportions of the fundamental niche are being represented through time (e.g. Vaclavık & Meentemeyer, 2012). We also acknowledge that there are alternative means of transferring knowledge of model performance between native and total ranges from avatar to emerging invaders. For example, the appropriate selection of thresholds to delineate suitability for species presence in distribution models has been an active area of inquiry (e.g. Liu et al., 2005). Avatar invaders could be used to identify the threshold of environmental suitability from models developed using only native range occurrences that also succeed in capturing all or a significant proportion of non-native occurrences. Typical or extreme relaxations of these suitability thresholds between native and total ranges could then be transferred to emerging invaders, allowing use of native range models without the potentially problematic or difficult transformations of niche position, size or structure used here and by Larson and Olden (2012). Alternatively, hierarchical Bayesian models (e.g. Liermann & Hilborn, 1997) could be used to inform potential total range models for data-poor emerging invaders using the total range models of well-studied established invaders, perhaps on the basis of phylogenetic groups or trait similarity (but see above). And finally, mechanistic models based on the physiology, life history and/or dispersal processes of focal organisms are important alternatives to correlative SDMs (e.g. Webber et al., 2011), although their data demands may limit applications to the poorly studied emerging invaders we have proposed the avatar invader concept to address. However, Elith (2013) suggests that generalized versions of such mechanistic models could be developed to serve as templates for sets of physiologically similar species under data or time-limited circumstances, a proposal we suggest is akin to mechanistic avatars. Further, many of these proposed implementations of the avatar invader concept (above) might best be evaluated using simulation studies. The use of simulated data (and simulated species ) has been extremely productive in developing and evaluating methodologies in SDMs (Hirzel et al., 2001; Reese et al., 2005; Elith & Graham, 2009), and simulation studies could be used to explore the range of conditions over which the avatar invader concept is (or is not) a viable idea. Specific needs might include identifying causes and commonality of sign changes in covariance between climate predictors from the native to total range; exploring the range of conditions over which avatar niche shifts might lead to violations of the variance/covariance inequality (see Methods); evaluating the influence of invasion stage or invasion pathway on utility of avatar invaders; assessing the best climate predictors, and perhaps the optimal number of climate predictors, to use in an avatar invader context; and determining the influence of native range climatic similarity on niche shift similarity between invaders (Appendix S4). Challenges to developing simulation studies to test the avatar invader concept include the need to not only simulate species and their niches, but also variable invasion processes for these species (differing patterns of introduction, establishment and spread), but this approach would surely offer interesting and important insights to our methodology. Regardless of implementation, the vision of the avatar invader concept is that more could be learned from well-studied and well-established invaders with respect to 1304 Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd

10 Avatar niche shifts for emerging invaders anticipating the potential total distribution of emerging invaders for which few or no non-native occurrences are yet available. With respect to applied management, we suggest that this may be more useful than the typical correlative SDM approach of splitting native and non-native ranges into separate niches for reciprocal comparisons (e.g. Larson et al., 2010; Medley, 2010) or recent suggestions to exclude from analyses climates that are non-analogous between regions (Petitpierre et al., 2012). We invite further evaluations and critiques of the utility of the avatar invader concept, but urge researchers and managers to treat with suspicion SDMs for emerging invaders that only use native range occurrences, as under-estimation and misrepresentation of the total range is likely more rule than exception. ACKNOWLEDGEMENTS This manuscript was improved by comments from J. Elith, P.R. Armsworth, A.G. Boyer, B.L. 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Methods in Ecology and Evolution, 3, SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article: Appendix S1 Species characteristics (Table S1) and model results (Table S2) for each of the 26 focal non-native plants. Appendix S2 Correlations visualizing sign changes between climatic predictors. Appendix S3 Five-fold cross-validation of total Mahalanobis distance models. Appendix S4 Species characteristics and native range climates for narrowing avatar ensembles. BIOSKETCH Eric R. Larson is a post-doctoral researcher at the University of Tennessee s Department of Ecology and Evolutionary Biology. He is interested in applied ecology with a focus on freshwater species and ecosystems, the prevention and management of species invasions, and understanding and improving conservation in practice. Author contributions: The idea was conceived by E.R.L.; R.V.G and L.J.B. developed the datasets; E.R.L. analysed the data; E.R.L. led writing of the manuscript with significant contributions from R.V.G., L.J.B. and J.D.O. Editor: Jane Elith 1306 Diversity and Distributions, 20, , ª 2014 John Wiley & Sons Ltd