Introduction

In the recent past, globalization has led to an increase of invasive species, a pattern likely to continue [1]. Besides being one of the biggest threat to biodiversity and ecosystems [2], biological invasions are also very costly to the global economy [3]. This increase of invasive species and their consequences on biodiversity and ecosystems raise numerous management and control issues [4,5]. Preventing an invasive species’ establishment and further spread is recognized as a more efficient and less costly management strategy than eradication, containment and control that may be required when the invasive species has fully established [6]. To that end, species distribution models (SDMs) are increasingly being used in invasion biology, especially to predict invasion risk [7–12] and optimize control strategies [13,14].

SDMs are also widely used in conservation biology, e.g. to predict the potential impact of climate change on genetic diversity [15,16], on species diversity [17–20] and on functional diversity [21,22] or to help reserve planning [23–25]. However, SDMs have been criticized for lacking mechanisms and independent validation, among other things [26]. Besides, two key assumptions of SDMs are often violated in invasion biology. First, niche conservatism is an assumption required for model transferability, whereby climate niches modeled with information from the native area are often projected onto new geographical spaces to estimate the likelihood of successful invasions there. In the context of invasion biology, niche conservatism differs from evolutionary niche conservatism (fundamental niche conserved over evolutionary time), as the question is to know whether the species realized niche is conserved over space. Yet, the assumption of niche conservatism over space is not always met, as the naturalized climatic niches of invasive species can differ from their natives climatic niches [27–29]. Second, until the latest stage of invasion, an invasive species is not yet at equilibrium with its environment [30], so its climatic niche is likely underestimated. Despite such criticisms, the important need of predictive models is such that SDMs are still often used in invasion biology. Indeed, validation studies (i.e., where SDM predictive accuracy is estimated with independent data and not through cross-validation only) being so scarce, SDMs have still not been fully proven to be inaccurate–or accurate -. A few pioneer studies aimed at assessing the predictive accuracy of SDMs in predicting species distribution changes with mixed results: a study showed that models had a good accuracy in predicting the range change of the Eurasian otter in Spain observed between two nation-wide surveys carried out ten years apart [31], whereas a study of deer species in Great Britain showed that SDMs predictions of range changes were no better than dispersal models [32]. Invasive species represent a good opportunity to evaluate SDMs predictive accuracy with independent data, as their invasive range can expand quickly. Indeed, invasive species whose invasion was closely monitored can be used to test whether records from the later stage of the invasion could have been predicted by a model calibrated with records only from the early stages of the invasion. Only very few studies have taken advantage of this opportunity to carry out validation studies with independent data [33–38], but they were carried out with simplistic envelop models or at small spatial scales. Besides, invasive species not being likely at equilibrium makes the use of common evaluation metrics (such as AUC, TSS…) not appropriate as observed absences can either be because of unsuitable environment or because the species did not disperse there yet [39]. More appropriate validation studies are thus very much needed.

Vespa velutina nigrithorax, or Asian hornet, is a perfect candidate species for such validation test. This insect native to China invaded France in 2004 [40] after its accidental introduction from China [41]. It spread rapidly, colonizing most of France at an approximate rate of 60–80 km per year [42,43] and progressively invaded other European countries: Spain in 2010, Portugal and Belgium in 2011, Italy in 2012, Germany in 2014 [44–48], the UK in 2016 [49] and finally the Netherlands where it was first recorded in 2017 (http://frelonasiatique.mnhn.fr/le-frelon-asiatique-detecte-aux-pays-bas/). The spread of this invasive species has been closely monitored since the species was introduced, so it is a perfect example for a validation study. In this study, after investigating whether V. v. nigrithorax is at equilibrium in its invasion range, we used more than 10,000 European invasion occurrences recorded between 2004 and 2015 to test whether occurrences from the later stage of invasion could have been predicted by models calibrated using occurrences from the earlier stage of invasion. We also took advantage of having independent validation data to test whether SDMs would have a better predictive accuracy of the ongoing invasive range if native data were accounted for, thereby responding to another strong question regarding the use of SDMs in invasion biology.

Methods

Results

The climatic niche occupied by V. v. nigrithorax in its invasion range clearly extended during the past few years (Fig 1A and 1B), as there is only a 45% overlap between the climatic niche occupied between 2004 and 2010 and the climatic niche occupied between 2011 and 2015. Statistical tests show that both niches are similar but not equivalent (Fig 1D and 1E). As the climatic niche first occupied by the species in its invasion range is still occupied, we could have expected both niches to be similar. Both niches not being equivalent further shows that part of the climatic niche occupied by the species between 2011 and 2015 was not occupied between 2004 and 2010. This means that in 2010 the species was not yet at equilibrium with its environment in Europe.

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Fig 1. Is V. v. nigrithorax niche at equilibrium in its invaded range?

Climatic niche occupied by V. v. nigrithorax in its European invasion range during 2004–2010 (a) and 2011–2015 (b) along the first two axes of the PCA (see (c) for details), showing an evolution during the two periods. Grey shading depicts the occurrence density of the species. The solid and dashed contour lines represent 100% and 50% respectively of the available (background) climate in Europe. (c) Contribution of the climate variables to the first two axes of the PCA (bio1: annual mean temperature, bio4: temperature seasonality, bio5: mean temperature of the warmest month, bio6: mean temperature of the coldest month, bio12: annual precipitation, bio13: precipitation of the wettest month, bio14: precipitation of the driest month, and bio15: precipitation seasonality). (d) Histograms showing the observed niche overlap D (D = 0.45) (bars with a diamond) and simulated niche overlaps (grey bars) on which tests of niche equivalency and niche similarity were calculated from 1000 iterations [54]: niches are similar but not equivalent.

https://doi.org/10.1371/journal.pone.0193085.g001

Climate suitability predictions differ depending on whether native data were accounted for (Fig 2 & S2 Fig). When accounting only for invasion data, climate suitability is high mainly in the southwestern part of France, where the invasion initiated (Fig 2A). However, when we accounted for both native and invasive data, high climate suitability is further predicted in the north of France, in Belgium, in northern Italy and in northern Spain (S3A Fig). In both cases, the predicted climate suitability of evaluation points (2011–2015, or “late invasion” data) is higher than expected by chance given their distance to the first invasion data (Fig 2 & S2 Fig). Indeed, out of the 2,534 evaluation points that are further away than 150 km from the first invasion record, more than 60% of them have their predicted climate suitability above the 70^th percentile of all background points within the same distance, whereas less than 3% of the evaluation points have their predicted climate suitability below the 30^th percentile (Fig 2 & S2 Fig). Besides, although the predicted suitability of the evaluation points that are the further away (further than 450 km of the first invasion occurrence, but within 850 km) is lower than for closer evaluation points (Fig 2 & S2 Fig), it is still higher than expected given their distance. Indeed, in both cases, more evaluation points have their predicted climate suitability above the 70^th percentile of all background points within the same distance of the first invasion occurrence (31% vs 56% with or without accounting for native data), than below the 30^th percentile (0% in both cases) (Fig 2 & S2 Fig).

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Fig 2. SDMs predictions and predictive accuracy.

(a) Climate suitability gradient map, from 0 to 1, predicted by the model (current ensemble consensus) using invasive data from 2004 to 2010 (blue points). Red points represent invasive data recorded after 2010 (2011–2015) that are used to evaluate the model. The dotted circle around the first invasion data (blue triangle) delimits all points that are within 150km of the first invasion data. (b) Climate suitability of all possible points (between 150 and 850 km of the first invasion data) according to their distance to the first invasion (grey points). The full line represents the median climate suitability according to the distance, whereas the dotted lines represent the 10%, 30%, 70% and 90% quantiles (blue and red points as above). Evaluation (red) points above the median have a higher predicted suitability than expected given their distance to the first invasion occurrence. (c) Boxplots representing the range of climate suitability values for all possible points (grey) and invasive data (calibration data in blue and evaluation data in red) depending on their distance to the first invasion data. In all three cases, the predicted suitability of evaluation points is lower than the predicted suitability of calibration points, but is higher than expected given their distance to the first invasion occurrence (all possible points, in grey).

https://doi.org/10.1371/journal.pone.0193085.g002

Results do not depend on the cut-off year that was used to split the data into calibration data and evaluation data, as results were very similar for the other cut-off years that were tested (S3 & S4 Figs). Such overall results thus mean that climate influences–at least to some extent—the ongoing invasion of V. v. nigrithorax in Europe and that this influence can be predicted by SDMs, despite the species not being at equilibrium yet.

Furthermore, even though modeling methods provide good predictions, the predictions still differ according to whether or not native records were taken into account (Fig 2 & S2 Fig). We can thus further investigate whether one option provides more accurate results than the other. In our case study, percentiles of validation points were significantly higher when the climate suitability was predicted by models accounting for invasive data only (for all cut-off years, except for 2006, opposite result) (Fig 3 & S1 Table). Overall, models thus seem to have a better predictive accuracy when accounting for invasive data only.

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Fig 3. Comparing SDMs predictive accuracy when trained with or without native data.

Percentiles of validation points (further than 150km from the first invasion record) depending on whether or not native data was accounted for to calibrate the models and on the cut-off year that was used to split the invasive data into calibration and evaluation data. Percentiles are obtained by comparing the predicted climate suitability of a given validation point to the distribution of climate suitability values of all points being at the same distance from the first invasion record than the validation point (i.e., grey points in Fig 2B). Percentiles higher than 50^th thus mean that the predicted climate suitability of the validation point is higher than expected given its distance to the first invasion record. For all cut-off years, paired t-test were computed to assess the difference between models with and without native data: a red star indicates significantly higher values (S1 Table).

https://doi.org/10.1371/journal.pone.0193085.g003

Discussion

Using the unique features of an invasion closely monitored in space and time, we demonstrated that despite some known limitations, SDMs can be a powerful tool to predict where invasive species will spread next. In fact, our case study does show that V. v. nigrithorax is not at equilibrium with its environment in its European invaded ranges (Fig 1). This finding is consistent with studies focusing on other invasive species [30,36]. The equilibrium hypothesis being an important assumption, its violation needs to be acknowledged when interpreting SDMs predictions [26]. Indeed, violating the equilibrium hypothesis has some consequences when modeling species distributions, among which underestimating the potential climatic niche of the species, which can in turn lead to underestimating the geographical area the species can invade [36]. However, predicting the full potential invasive range of an invasive species may not be as relevant as accurately predicting the areas that are more likely to be colonized next. Indeed, given the cost of species monitoring and surveillance for the early detection of invasive species, it is more relevant to predict areas that might be invaded next rather than all potential areas that could be reached by the invader if the species achieved its climate equilibrium. Information regarding the areas that might be invaded next could indeed be used by managers for a cost-effective effort on monitoring and controlling such areas. For example, in the case of V. v. nigrithorax, whose invasion can be most efficiently controlled by an early detection followed by nest removal [43,60], monitoring efforts need to be implemented within the highest suitable areas within the already invaded range, as well as within the highest suitable areas that are the closest to the already invaded range. Improved detection techniques would further increase the efficiency and decrease the costs of monitoring/controlling the invasion [61]. Therefore, even if invasive species distribution models cannot predict the full potential invasion range of an invasive species that has just established [36,62], they can still be very valuable for invasive species management. Yet, validation is needed for model reliability and credibility, especially when management decisions are based upon it [63].

Here, we showed that models calibrated with data from the earlier stage of invasion predicted adequately the recent invasive data of V. v. nigrithorax: new invasion observations had higher climatic suitability than expected from their distance to the first invasion occurrence. Although invasive species present a good opportunity to test SDMs predictions with independent data, this has rarely been done so far for the ongoing range expansions of invasive species. The few studies that pioneered this approach used evaluation metrics that have since been shown not to be appropriate when the species is not at equilibrium. Previous studies also showed that SDMs can be used to predict invasions under climate change, through validation from field data [64], as the performance in the field of three plant species was highly correlated with SDMs predicted climate suitability. Although further studies will be needed with other species, our study indicates that SDM can be used in invasion biology to better predict where the species is most likely to spread next, once an invasion has started. It is thus very important to monitor invasive species from the start of the invasion, so as to gather a large enough amount of information to run predictive SDMs. Besides, here we only considered climate variables, but model predictions can likely be improved by also considering non climatic drivers such as land-use variables [65], since predictions depend on the variables used to compute the models [66,67].

Numerous studies on invasive species distribution advocated to use distribution data from both the native and the invasive range [68,69]. In fact, if the species climatic niche is conserved from its native range to its invaded range, distribution data from the native range can be very valuable to characterize the full potential climatic niche of the species and thus the full geographical space it can invade. In this context, SDMs calibrated with distribution data from only the invasive range might under-predict the potential invasive range if the species is not at equilibrium yet [36]. However, if niche conservatism during invasions has been shown for some species [70,71], other studies revealed niche shifts during invasions [29,72,73], highlighting an inconsistent pattern of niche conservatism during invasions [74]. Accounting for native distribution data when calibrating invasive SDM may thus not improve their predictive accuracy in all cases. Here, we took advantage of having independent validation data to investigate this issue. In the case of V. v. nigrithorax, the invasive range is clearly predicted to be larger when accounting for native data (Fig 2 & S2 Fig). It is thus clear that at this time of the invasion, the climatic niche occupied by V. v. nigrithorax in its invaded range differs from the one occupied in its native range. If the native climatic niche is to be conserved, the full potential invasive range of the species might be better predicted by accounting for both invasive and native data, as the species is not at equilibrium with its environment in its invasive range yet (Fig 1). However, if the native climatic niche of V. v. nigrithorax is not to be conserved, accounting for native data when modeling its potential invasive range might lead to overprediction. Furthermore, predicting the full potential invasive range might not be as relevant as predicting the areas that are most likely to be invaded next, from a management point of view. Actually, the model predictive accuracy is slightly but significantly better when accounting for invasive data only (Fig 3). Thus, if the modeling purpose is to predict which areas the species is most likely to invade next, it is better to perform the SDMs without accounting for native data. Of course, similar studies need to be carried out for other species to know whether we can generalize such results or whether it depends on the species (as it appears to be the case for niche conservatism during invasions). Furthermore, although significant, the difference in model predictive accuracy is slight (Fig 3 & S1 Table), highlighting a very good predictive accuracy even when performing SDMs with both native and invasive data.

Conclusions

SDMs are increasingly used in ecology whether to predict the potential impact of global change or to predict the potential invasive range of introduced species. Yet, they are often criticized, especially because their predictive accuracy cannot be truly estimated due to a lack of independent validation data. Our study of the invasion of V. v. nigrithorax showed that the predicted climate suitability of independent validation points was very good. Such a result means that the spread of V. v. nigrithorax is–at least partially–climatically driven and can be accurately predicted by SDMs. In the case of V. v. nigrithorax, SDMs predictive accuracy was slightly but significantly better when models were calibrated with invasive data only, excluding native data. Although more validation studies for other cases of alien invasion are needed to generalize our results, our findings validate the use of SDMs in invasion biology.

Supporting information

Acknowledgments

This work was supported by the INVACOST project (ANR & Fondation BNP Paribas), Biodiversa Eranet (FFII), France AgriMer (Programme communautaire pour l’Apiculture, 2008–2011 and 2013–2016), the MEDDE (Ministère de l’Ecologie, du Développement Durable et de l’Energie) and the MAAF (Ministère de l’Agriculture, de l’Agroalimentaire et de la Forêt). We are most thankful all persons and organizations that provided records of hornet nests in France and in Europe (their list is available on the INPN website).