Occurrences

Occurrence records of starry stonewort were published in Escobar et al. [8], which used data from digital repositories including the Global Biodiversity Information Facility (GBIF) [24] and the Global Invasive Species Information Network [25] using the keywords “Nitellopsis obtusa,” “Nitellopsis obtusa var. ulvoides,” and “Chara obtusa”. Occurrences from invaded areas in the US were also derived from additional reports and publications [1,4,9,26]. Minnesota records were updated based on 2016 reports of new localities from the Minnesota Department of Natural Resources (MDNR, http://www.dnr.state.mn.us/invasives/ais/infested.html).

Occurrences were individually inspected to assure credibility and geospatial accuracy. All Minnesota, Wisconsin, and New York records have been confirmed by a Characeae expert (Ken Karol, New York Botanical Garden). Michigan has the most records and not all have been verified by experts. It is possible that reports from Michigan (and GBIF or other databases) include false records. Unfortunately, this is the best information that is available at this time. We chose to include all records based on the expectation that the error rate is relatively low and that the invaded region most likely to include false records (Michigan) is in the center of the species’ invaded range, such that false occurrences would be unlikely to have a strong influence on niche estimation.

Oversampled areas, as a form of sampling bias, can generate model overfit [27]. To prevent this, we calibrated present-day models using occurrences filtered to one-per-cell according to the spatial resolution of cells in our environmental layers [28]. All the remaining occurrences were used for modeling. From the initial pool of 2,260 occurrences, 84 single occurrences (i.e., occupied pixel cells) remained in the entire species’ range: 29 in the native range (34.5%; 2 in Japan, 27 in Europe) and 55 in the invaded range in the US (65.5%; Fig 2).

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Fig 2. Model calibration region, M, explored in this study.

Models were calibrated in three regions (red lines in A, B, and C) based on the distribution of starry stonewort populations (green points). A. Model calibration region based on an invasive population approach focused on starry stonewort populations in the invaded area of the United States and a high dispersal potential (i.e., 2,200 km), M_i. B. Model calibration region considering the entire or global species’ range in the United States, Europe, and Japan and a high dispersal potential (i.e., 2,200 km), M_g. C. Model calibration region considering the entire or global species’ range in the United States (left map), Europe (central map), and Japan (right map) and a reduced dispersal potential (i.e., 700 km), M_d.

https://doi.org/10.1371/journal.pone.0180930.g002

Model calibration region M

The selection of M, the model calibration region, has a strong influence on ecological niche model predictions [29]. For instance, considering only invasive populations can result in incomplete information about the environmental preferences of the species [13], or be insufficient to characterize environmental tolerances [30]. Explicitly testing different extents of the calibration region facilitates comparison of models and informs interpretation of results [31]. Recent new records for starry stonewort in North America suggest that it may be expanding in North America from east to west and from south to north [8]. As a proxy of the dispersal potential of the species we used two distances for three M scenarios. First, we used the maximum distance between all known starry stonewort populations in the US (~2,200 km), as suggested by the data available (i.e., MDNR surveillance: http://www.dnr.state.mn.us/invasives/ais/infested.html) [23]. Considering that the species has been dispersing between distant lakes, we assumed that spatial barriers could be overcome in the model calibration regions. We used this distance as a buffer around starry stonewort occurrences to generate a model calibration region for the invaded range in the US (M_i). This area corresponds to a model based on the invasive populations.

Furthermore, to account for starry stonewort environmental preferences across its entire range, we focused on two additional model calibration areas, including both native (Europe and Japan) and invasive populations (US). One of these calibration areas was based on the same maximum distance between all known starry stonewort populations in the US (~2,200 km; M_g) and the other was a proxy of the maximum distance between closer neighbors populations in the US (~700 km; M_d), which in our case corresponded to the distance between the last detection in Wisconsin and the first detection in Minnesota. We used these distances to generate a buffer around occurrences across the entire species’ range (Fig 2). The M_i scenario encompasses inland and coastal regions of central and eastern Canada and all states in the continental US except those in the far west: California, Nevada, Oregon, Washington, and western portions of Arizona and Idaho. The M_g scenario encompasses all of those areas in addition to Europe, parts of northwestern Africa and Asia (Japan, North and South Korea, and parts of eastern China and Russia). The M_d scenario includes the Upper Midwest region in the US and southeastern Canada, portions of Southern, Northern, and Western Europe, and a small portion of Eastern Europe, and also Japan except by the Hokkaido island (Fig 2). All M scenarios included the area of interest for this study (Minnesota).

Environmental variables

As a proxy of A, we used the present-day Ecoclimate dataset (1950–1999) at 50-km spatial resolution [32]. Since starry stonewort occurs in both coastal and inland areas, we used climate variables covering both regions. This climate dataset is derived from the Coupled Model Inter-comparison Project (CMIP5) and combines climatic patterns from multiple general circulation models from inland and marine ecosystems; thus, final climatic layers have global coverage. The role of oceanic dispersal in the invasion process of this species remains uncertain, however, we assumed that marine dispersal could play a role and include climate conditions in terrestrial and marine ecosytems in our model calibration regions. We used climatic variables likely to influence starry stonewort’s macroscale distribution, selecting uncorrelated variables based on correlation coefficients ≤0.80 (Table A in S1 File). Specifically, we used annual mean temperature (°C), mean diurnal temperature range (°C), isothermality (%), temperature seasonality (°C), maximum temperature of the warmest month (°C), mean temperature of the wettest quarter (°C), annual precipitation (mm/m²), and precipitation seasonality (%) [32].

Climate models are considerably variable, thus, adding more scenarios of future climate would provide more information regarding the plausible variability in forecasts. Future climatic conditions for the end of the 21^st century (2080–2100) were obtained from Ecoclimate, including four representative concentration pathways (RCPs; i.e., 2.6, 4.5, 6, and 8.5 W/m²; here after numbers are shown without units) [32]. Each RCP scenario represents potential trajectories of greenhouse gas emissions projected to the future, ranging from the most optimistic (i.e., 2.6) to the worst-case scenario (i.e., 8.5) [32]. RCPs are the most updated climate scenarios from the Intergovernmental Panel on Climate Change (IPCC), Fifth Assessment Report (AR5), and replaced the SRES scenarios previously implemented by the IPCC AR4 [33]. The four RCP scenarios were estimated based on five different future general circulation models (GCM): CCSM, GISS, IPSL, MIROC, and MRI, allowing us to capture the variability in emissions (i.e., RCP scenarios) and climate simulations (e.g., CCSM vs. MRI).

Non-analogous climate evaluation

We explored areas with non-analogous (novel) climatic conditions between present-day climate in the calibration regions vs. future climate in the projection region of Minnesota. This resulted in a present vs. future comparison and calibration vs. projection regions. This analysis was done using the extrapolation detection (Exdet) tool developed by Mesgaran et al. [34]. Exdet identifies non-analogous environments between calibration and projection regions denoted as type I novelty [sensu 34]. Accounting for these non-analogous or novel environments enables a more confident interpretation of models [18,35,36].

Ecological niche models

Qiao et al. [37] proposed that multiple ecological niche modeling algorithms should be employed to identify the model that best fits with the available data, the study system, and the research question. We used Maxent to perform niche modeling because it enables the use of different variable transformations (features), i.e., linear (L), quadratic (Q), product (P), threshold (T), and hinge (H), and allows for different parameterizations (regularization values). In addition, Maxent allows automatic truncation in novel climates to avoid predictions in non-analogous environments.

Maxent is an occurrences-background algorithm, which estimates the most uniform probable distribution of the occurrences across a selected calibration region [13,38]. The background represents the summary of environmental conditions across the model calibration region. Because we explored two calibration regions (invaded range and two areas from the entire species’ range) the available background varied. We developed models based on 5,000 and also 10,000 background samples.

Here, we tested 20 different regularization coefficient values ranging from 0.1 to 2. The regularization coefficients regulate the complexity of the model, higher values penalize for complexity and thus, produce simpler models (avoiding complex relationships between the data and the variables) that, in general, tend to have larger predictions [39]. Because assessing different configurations is recommended [39–41], we explored models based on six feature combinations reported in the literature: L, LQ, H, LQH, LQHP, and LQHPT [40].

We used raw values from Maxent to assess model fit according to Akaike’s Information Criterion values corrected for small sample size (AICc), which ranks models based on their information content and complexity [42]; the model with the lowest AICc was selected (i.e, ΔAICc = 0) as best reconciling the goals of fitting occurrences with environmental input data and minimizing model complexity [41]. In addition, because low AICc does not represent the ability of the model to predict independent data, we also assessed predictive performance based on the full (AUC_total) and mean (AUC_mean) of the area under the curve of the receiver-operating characteristic (AUC) and the difference between training and testing AUC and its variability. These metrics assess if models can discriminate between occurrence and background points, with AUC values ≤0.5 consistent with randomly generated models unable to differentiate between backgrounds and occurrences. Because AUC has been questioned [43,44], we also used independent data to calculated mean omission rates (OR) from binary models based on using 100% (OR_100%) and 90% (OR_90%) of training occurrences as thresholds. These metrics enable the proportion of independent occurrences predicted incorrectly to be quantified [40]. Evaluation of model predictions was performed using independent data obtained via dividing the occurrences in two sets, one for model calibration and one for evaluation. Calibration and evaluation data sets were developed based on four different data splitting configurations: (i) using one point at a time for model evaluation (i.e., Jackknife); (ii) apportioning the occurrences into four groups, each with an off-diagonal set for calibration and another for evaluation (i.e., block; as in [45]); (iii) selecting clusters of points and using half for calibration and the other half for evaluation (i.e., Checkerboard1 [40]), and (iv) partitioning the occurrences via cross-validation (k-fold; see [40]). Model evaluations were conducted using the R package ENMeval [40].

Model projection to Minnesota

Once the best regularization coefficient, feature configuration, and number of background points were determined for the calibration regions (Fig 2), the three selected models were projected to environmental conditions in Minnesota. Maxent allows strict model transference during model projection via ‘extrapolation’ and ‘clamping’ being deactivated [36,46]. This practice prevents unrealistic extrapolations of models into non-analogous (novel) environments that could be present in the projection region but absent from the calibration region [46].

In all, to identify the best model by calibration region (M_i vs. M_g vs. M_d), we explored 120 parameter configurations (20 regularization coefficients × 6 feature combinations), and two background samples for each regions M_i and M_g: 5,000 and 10,000; and 10,000 for M_d which was not explored due to the reduced extent of this calibration area (Table B in S1 File). The best models were projected to 20 future climate scenarios (4 RCP × 5 climate models). To inform interpretation of forecasts, we also estimated uncertainty of all final models. We parameterized final models based on our previous evaluations and generated surfaces of uncertainty using 80% of occurrences in Maxent and performed 25 bootstrap replications using random starting seeds. For final models, we selected the logistic output format in Maxent with clamping and extrapolation deactivated. We used the standard deviation of replicates as an indicator of uncertainty [38,47] (Fig 1) and developed a t-test (α = 0.05) to compare the continuous suitability values of pixels among models in Minnesota.

Finally, we created an ensemble of models for different future climate scenarios in Minnesota. We averaged the final logistic models and calculated the standard deviations to identify areas where models were consistent (low SD) or diverged (high SD). There is debate about use of model ensembles, due to issues regarding interpretation of continuous units from different algorithms (e.g., general linear models vs. regression trees vs. Maxent) (see [13]). Here, we overcame such discrepancies by using the same suitability value (i.e., Maxent logistic), from the same parameterization so that differences only reflected differences in future climate models for Minnesota. We also estimated the number of lakes in Minnesota comprising the lowest and highest predictions of suitability using lake inventory data from the National Wetlands Inventory of the US Fish & Wildlife Service [48].

Model predictions

We used a BAM ecological niche modeling framework to predict present-day and future climatic suitability throughout Minnesota for the aquatic invasive species starry stonewort. Under most future climate scenarios, the available range is predicted to shrink relative to present-day conditions. Based on the data available and the assumption of niche conservatism [49,50], all future climatic models under all RCP scenarios showed a decrease in suitable range relative to present-day conditions, with the exception of future climatic models: CCSM 2.6 and 4.5, and MRI RCP 4.5, 6, and 8.5 for M_i, GISS RCP 6 for M_g, and CCSM 2.6 and MRI 8.5 for M_d, which showed increased areas of suitability with plausible range shifts. All these predictions, however, showed considerable uncertainty (Figs 7–9).

It is possible that our findings underestimate the potential invasiveness of starry stonewort by not capturing the full extent of its climatic tolerance [23]. Escobar et al. [8] recently described environmental tolerances of starry stonewort in its invaded and native ranges and found that invasion was associated with a shift in its realized niche, suggesting niche expansion, i.e., there were environmental conditions occupied by starry stonewort in the invaded range that lacked analogues in the native range [51]. This suggests that invasion potential may exceed what would be anticipated based on past performance alone, and starry stonewort may be able to expand into previously unoccupied environmental space [49,51]. Models could also be underestimating invasion due to overfitting from oversampled areas (i.e., sampling bias) and spatial autocorrelation in climatic variables; however, we minimized this risk by resampling occurrences to one per pixel and using coarse-resolution climatic variables, including data from remotely sensed imagery, to counter high spatial lag associated with data derived solely from climate stations [32,52,53].

The consensus areas of suitability across models (Fig 10) showed a pattern of reduced suitability across all M regions, suggesting a potential decline of the starry stonewort under warming climates in terms of the climates where the species is found to date. Model ensembles highlight areas of agreement across predictions, but their interpretation requires caution [17]. The lack of consensus of suitable areas for starry stonewort under future climate in Minnesota reflects the diversity of possible trajectories of future climate (Figs 7–9).

We note that our findings are based on estimated climatic tolerances and a proxy of establishment [23]. Numerous other factors, such as water chemistry, dispersal limitation, and agonistic interactions with resident biota, could limit starry stonewort expansion. However, a recent study of macrophyte communities in invaded lakes suggested plausible dominance of starry stonewort, with native species richness decreasing as starry stonewort increases in biomass [2]. These fine-scale, potentially complex and interacting factors cannot be accounted for in climate-based models, experiments would be needed to test the influence of these factors on starry stonewort population dynamics. Future research should assess how finer-scale abiotic variables (e.g., pH, conductivity, water clarity), biotic interactions, dispersal potential (via boater movement or natural water connectivity), and landscape factors (e.g., densities of roads and boat accesses) influence lake-level risk of starry stonewort invasion. Emergence of sexually reproductive populations could add new and longer-distance dispersal vectors due to small oospores that could potentially be spread by waterbirds or survive overland transport longer than bulbils [21].

Environmental variables

The environmental variables derived from the Ecoclimate repository are a promising alternative for modeling species distributed across inland and coastal/marine ecosystems [32], providing robust data on climatic variability needed for ecological niche models [54]. The 50-km spatial resolution of Ecoclimate variables mitigate the high spatial lag of finer-resolution climatic layers [52,53], which can produce flawed estimates due to high spatial autocorrelation from statistical downscaling [32,53]. We argue that during exploratory analyses, coarse-scale variables are useful for identifying plausible constraints for species establishment. Subsequent work can then incorporate finer-scale environmental variables (derived from remote sensing or habitat data) to complement climate-based models. Additionally, we developed analyses incorporating five future climate models: CCSM, GISS, IPSL, MIROC, and MRI, and four RCP emission scenarios: 2.6, 4.5, 6, 8.5. This allowed us to investigate a broader range of plausible climate scenarios. Ecological niche modeling of species invasions under future climates should incorporate alternative climate models and emission scenarios to reflect the uncertainty in future conditions.

The calibration region M

In agreement with previous studies using virtual species [29], our models based on empirical data suggest that a careless definition of the calibration region, M, may produce flawed results [23]. Restricting the model calibration region only to the invaded region, M_i, in present-day climate (Fig 2), narrowed geographic predictions to southeastern Minnesota—all actual occurrences to date are outside of this region—as a result of the incomplete information provided to the algorithm (Fig 3). In contrast, considering the entire species’ range for the two calibration regions M_g and M_d (Fig 2) included portions of central and central-north Minnesota where starry stonewort has known occurrences (Fig 3). We found that increasing the model calibration area generated an increase in AUC values, but from a practical perspective, accounting for environmental conditions available in the entire range produced forecasts that were more reliable and more precautionary [30]; this suggests that AUC may not accurately reflect model performance due to high sensitivity of this metric to the extent of the model calibration region [29].

From a theoretical perspective, niche estimations should be guided by modern ecological niche theory [23]. According to Hutchinson [13,55], ecological niches occur in multidimensional environmental space, and species may not occupy all suitable abiotic environments (A) due solely to limiting biotic interactions (B; e.g., competition) (Fig 11 top). However, Soberón and Peterson [23] propose that Hutchinson’s ideas were incomplete and that, in addition to B, a species can also be limited by its dispersal potential (M) (Fig 11 bottom). They propose that species rarely occupy their entire environmental potential and that the Hutchinsonian framework needs to be expanded. The BAM framework proposes that for a realistic A estimation for an invasive species, studies should include delimitations of M allowing a representative characterization of the dispersal potential of the species [23]. In other words, models aiming to estimate a good proxy of A should include all the areas where the species occurs, including the full native and invaded ranges. Thus, we stress that ecological niche modeling to forecast current and future biological invasions are dependent upon M (Fig 10 bottom). Ecological niche models calibrated in only a portion of the species’ range or under a single M scenario may underestimate invasive potential (Fig 3). In this vein, our estimation of dispersal potential based on distance between populations in the invaded range may be confounded by search effort and may not reflect the actual directionality of spread. Genetic/genomic analyses could be used to reconstruct dispersal potential, invasion pathways, and directionality.

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Fig 11. Conceptual framework used for interpretation of predictions.

Top: The “Hutchinson Fallacy” expressed as the intersect of abiotic (A; dashed line) and biotic factors (B; dotted line) showing the environments that a species can occupy (gray) or not (white area inside the dotted circle), based on biotic interactions solely (e.g., competitors). Note that under the Hutchinson’s proposal, all the areas environmentally suitable can be reached by the species (i.e., entire circle), suggesting that the movement and dispersal potential of the species (M; solid line) is effective to occupy all the suitable conditions (i.e., A is contained in M). Bottom: The “BAM Framework” proposed by Soberón and Peterson [23] to explain that dispersal limitations (M) can also restrict the species to occupy (gray) only a portion of all the suitable environments (A). Note that in this example, the species can occupy a portion of the environmental conditions suitable due to the limited dispersal potential (i.e., half circle). A (abiotic) = environmental conditions suitable for the species; B (biotic) = interaction with other species; M (move) = movement or dispersal potential of the species.

https://doi.org/10.1371/journal.pone.0180930.g011

The extent of the calibration region was also crucial to establish the presence or absence of novel environments between calibration and projection regions, and between present-day and future climates [34,46]. Models M_i calibrated from the invaded range only, and models M_d calibrated based on a small dispersal potential (Fig 2), showed high levels of truncation of prediction in non-analogous novel climatic conditions across Minnesota, limiting our ability to project models to future scenarios (Figs 4 and 6). Conversely, M_g models from the entire species range with a hypothetical high dispersal identified suitable areas for starry stonewort in Minnesota under present-day and most future climate scenarios (Figs 5 and 9). This provides additional evidence that the calibration region extent plays a key role in ecological niche model projections for species invasions. Thus, model calibration regions should include the full distribution of the studied species under different M scenarios to capture the fullest possible set of environmental determinants of physiological tolerance of the organism, providing a firmer biological foundation for calibration region selection [13,31]. We urge researchers and reviewers to put special attention to the justification and biological support of the M area selected for model calibration in past and future ecological niche modeling studies.

Maxent and model evaluation

Current literature advocates Maxent for niche modeling due to its accessibility, user-friendly interface, and supporting literature [39]. However, the potential of Maxent to overestimate or overfit predictions to the data available must be considered [18,27,38,39,41]. Maxent must be fitted for each study case considering the natural history of the species, the data available, and the assumptions involved. The results from our approach to control the extent of the calibration region, which included use of regularization coefficients, information-theory model selection, strict model evaluation, and strict model transference, support the contention that using the default parameterizations of Maxent, while convenient, is an inappropriate approach that can lead to inaccurate conclusions [29,41,46]. Thus, each modeling effort should include detailed individualized parameter selection, and model results should be critically assessed to determine if they are biologically sound, avoiding reliance on single model estimates [37].

Although predicted suitability from our present-day models ranged from minimal to broad across Minnesota (Fig 3), models with the two different calibration regions performed well in terms of omission rates and AUC values [40]. The heterogeneous suitability predicted under the two configurations reflects the sensitivity of ecological niche models to experimental design decisions (Fig 2) [13]; therefore, we propose that uncertainty estimation must be included as an essential component of ecological niche model estimations.