Introduction

Biological invasions have long been precipitated by expanding transport and global trade (Mack et al. 2000) and have become a major component of global change (Liebhold et al. 1995; Vitousek et al. 1997). Once established in new locations, the impacts of invasive species can be severe. Invasive species cause public health issues, threaten endangered species, challenge biodiversity in their invaded ranges, and cause loss to agriculture, forest, society, and other segments of economy (Pimentel et al. 2005). Management, including preventing introductions and early detection, becomes important to minimize the impacts of invasive species. In 2009, a new invasive insect, kudzu bug, Megacopta cribraria (F.) (Hemiptera: Heteroptera: Plataspidae), was first reported in the U.S. in Georgia (Suiter et al. 2010). Kudzu bug is named after the Asian kudzu vine (Pueraria montana (Lour.) Merr.), which is in the pea family (Fabaceae), because it primarily feeds on kudzu. However, kudzu bug was reported to occur on 33 plant species and to feed on at least 9 plant species in the U.S. (Gardner et al. 2013). Kudzu bug was first described by Fabricius (1798) and is native to Asia (Eger et al. 2010). Kudzu bug is the only known species in the family Plataspidae to occur in the Americas (Ruberson et al. 2013). Since its invasion, kudzu bug has spread quickly throughout the southeastern U.S. By the end of 2016, kudzu bug had been confirmed in 13 states (EDDMapS 2017).

In its native range, kudzu bug is one of the main pests of soybean (Li et al. 2001; Wu et al. 2006). Since the invasion of kudzu bug in the U.S., researchers have studied its biology, host range, and presence, as well as its effects on soybean, kudzu and human residential areas in the U.S. (Eger et al. 2010; Gardner et al. 2013; Ruberson et al. 2013; Zhang et al. 2012). Research indicated that high kudzu bug densities can reduce soybean yield by as much as 59.6% (Seiter et al. 2012). In addition to potential economic losses, kudzu bug is also a nuisance in urban areas. Kudzu bugs aggregate in great numbers on homes and structures in spring, and they may also move to buildings to overwinter (Ruberson et al. 2013; Suiter et al. 2010). As strong fliers, kudzu bugs also become a concern in open areas (Ruberson et al. 2013). Kudzu bugs can be a human health concern in urban areas, where their direct contact with humans can induce rashes on skin (Ruberson et al. 2013). As commercial trading has increased and cross-border labor cooperation has long been developed among countries in North and South America (Kay 2005), it has become a considerable concern that others countries might be susceptible to invasion of kudzu bug (Gardner et al. 2013).

Modeling and predicting invasion processes of pest species are essential for early prediction and warning (Sutherst 2003) and are increasingly used for detection and control of invasion outbreaks (Václavík and Meentemeyer 2009). Invasive pest modeling is critical to manage, mitigate or prevent the infestation of invasive pest species (Gallien et al. 2010). The ecological niche-based methods have widely been used to model the potential geographic distribution of invasive species. Hutchinson (1957) described the ecological niche as a multi-dimensional environmental space where both abiotic and biotic factors permit positive growth of species. The ecological niche can be furthered described as fundamental niche (FN) and realized niche (RN). FN delineates the abiotic environmental conditions that allow an organism to survive, while RN describes the set of conditions actually occupied by a species after interacting with other species (Hutchinson 1957). Compared to RN, FN only considers abiotic factors and is easily to measure, thus FN or a subset of FN has been increasingly used to model species’ geographic extent (Guisan and Zimmermann 2000; Soberón and Peterson 2005). Niche-based distribution models construct relations between the occurrences of species with various environmental features (Randin et al. 2006).

To model the potential invasion of a species in the invaded range, the classical approach uses the distribution data from the native range and then projects the model into the invaded range (Peterson 2003). One underlying assumption of this approach is that the species will conserve its niche when it invades a new geospatial range (Wiens and Graham 2005). Niche conservatism refers to the tendency of species to retain their ancestral ecological traits (Wiens and Graham 2005). However, this assumption can sometimes be incorrect (Broennimann et al. 2007), and makes the classical approach insufficient to predict potential biological invasion. For some species, niche shift may occur as with the invasions resulting in the change of habitat preference in the new range (Broennimann et al. 2007; Randin et al. 2006). This change is called evolutionary niche shift and had been evidenced in published research (Broennimann et al. 2007; Guisan et al. 2014; Randin et al. 2006). However, Soberón and Peterson (2011) suggested that in some cases the “niche shift” is more likely a result of environmental heterogeneity between two geospatial ranges, namely non-evolutionary niche shift, than a real niche shift of the given species. Here we use the term environmental space shift instead of niche shift to represent both types of niche shift. Once the environmental space shift exists, the distribution models trained with native occurrence data may have limited ability to predict the potential invasion in the new range as the native environmental conditions may fail to express the true habitat requirement in the new range. Broennimann and Guisan (2008) and Jiménez-Valverde et al. (2011) suggested that the potential distribution model for invasive species could be developed using occurrence data from both the native and the invaded ranges when the occupied environmental space differs between the two ranges. Thus, testing the conservatism of environmental niche is crucial for determining whether occurrence data in native range or in both native and invaded ranges should be used to predict the potential invasion.

It is not known if kudzu bug conserves its environmental space in the U.S., leading to lack of adequate research to predict the invasion risk of kudzu bug in North and South Americas. Whereas the climatic preference of kudzu bug is also not fully understood (Gardner et al. 2013; Zhang et al. 2012), knowledge on the climatic preference of this pest species could contribute to its early warning and detection as well as provide information on pest ecology. To address these gaps, we examined if the invaded populations of kudzu bug in the U.S. occupied the same environmental space as the native populations in Asia. We also calculated the stability, expansion, and unfilling of occupied environmental space in the U.S. to better understand the niche dynamics of kudzu bug in the new range. Niche stability and expansion (1- niche stability) measure the proportion of occupied environmental space in the invaded range that is overlapping and non-overlapping, respectively, with that in the native range. Whereas the niche unfilling is the proportion of occupied environmental space in the native range, which is available but has not been occupied in the invaded range. We then considered two commonly used niche-based methods to model the potential invasion of kudzu bug in North and South America. Finally, we analyzed the variable importance and climatic preference of kudzu bug for its value of providing information for management of kudzu bug, as well as its value to increase knowledge on kudzu bug ecology.

Methods

Species point occurrence data

We collected kudzu bug occurrence data in both the native range in Asia and the invaded range in the U.S. In total, we used 319 points as occurrence data. All the occurrence data are available on request. Readers are referred to Zhu et al. (2012) for detailed information on data acquisition in the native range. After deleting redundant records, we retained 164 points as occurrence data in Asia. Occurrence data of kudzu bug in the invaded range in the U.S. were acquired from the Early Detection and Distribution Mapping System (EDDMapS 2017). The EDDMapS dataset contained the date and location of confirmed occurrences of kudzu bug since 2009 (Gardner et al. 2013). Excluding repeated records, we retained 155 points as the occurrence data in the invaded range. These occurrence data were distributed throughout the southeastern U.S.

Environmental variables

We used ‘bioclimatic’ variables from WorldClim (Hijmans et al. 2005) and elevation from the Hydro-1K digital elevation model dataset (USGS 1996). The spatial range of variables includes Asia, North and South America. We selected 12 bioclimatic variables (6 temperature-related variables and 6 precipitation-related variables; Table 1) rather than all 19 bioclimatic variables based on two principles: (1) we chose variables that are important to kudzu bug based on its biology, as research suggested that temperature and humidity both impact kudzu bug (Shi et al. 2014; Wang et al. 1996), and (2) we deleted variables that have very strong correlation (r > 0.8) with the remaining variables across the whole study area. These 12 bioclimatic variables plus elevation provided 13 variables for our models, and all variables had the same resolution of 30 arc-second (approximately 1 km).

Table 1 Full name and brief name of 12 bioclimatic variables selected for use in our models; T temperature, P precipitation
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Test of environmental space difference

Several methods had been used to test the niche conservatism (Guisan et al. 2014), and researchers suggested that quantifying niche changes by directly comparing the environmental attributes while considering the available environmental space between two spatial ranges is a most appropriate method (Broennimann et al. 2012; Guisan et al. 2014). We therefore used the method proposed by Broennimann et al. (2012) to test the equivalence and similarity of environmental spaces occupied by native and invaded kudzu bug populations. This method takes the available environmental space in different ranges into account by applying kernel smooth function to correct occurrence densities with available environmental densities. The niche equivalency and similarity was then tested on the niche overlap along using the D metric (Broennimann et al. 2012; Warren et al. 2008), which was first proposed by Schoener (1968). Using the method proposed by Broennimann et al. (2012), the D-metric can be expressed as:

$$D = 1 - \frac{1}{2}\left( {\mathop \sum \limits_{ij} \left| {Z_{1ij} - Z_{2ij} } \right|} \right),$$

where \(Z_{1ij}\) and \(Z_{2ij}\) represent the occupancy of entity 1 and entity 2 at given environmental conditions, respectively. The D value varies from 0 to 1, with 0 indicating no niche overlap and 1 indicating niche identical. To test the niche equivalency, all occurrences in both spatial ranges are first pooled together, and then randomly split into two datasets, this procedure can be repeated n times (n = 1000 in this research). The number of occurrences in the two new datasets keeps the same as the number in the original datasets (Warren et al. 2008). For each repetition, the simulated niche overlap D is calculated. With enough repetition, the derived D values can be used to construct a robust null distribution of D value, based on which the niche equivalency can be accepted if the observed D value falls in the density of 95% of the simulated D values. Although niche similarity test is different from niche equivalency test, niche similarity test also used the randomization procedures to construct null distribution of D values. Interested readers are referred to Broennimann et al. (2012) for detailed description on the niche similarity test.

To test the shift of environmental space of kudzu bug between native and invaded populations, we only included Asia and the U.S. as the study area. A principal component analysis (PCA) was conducted on the occurrences and the available environmental conditions to ensure the native and invaded ranges were represented equally. We uniformly extracted 500 pixels from both ranges (totally 1000 pixels) to represent the available environmental conditions. The first two axes of PCA were then used to calculate the overlap of environmental spaces between the native and invaded populations. The available environmental spaces and the occupied environmental space by native and invaded populations were also visualized on the first two axes of PCA. The “ecospat” package in R (Di Cola et al. 2017) was used to test the equivalency and similarity of occupied environmental space by native and invaded populations. Niche expansion, stability, and unfilling were also calculated using “ecospat” package.

Model development

To predict the invasion risk of kudzu bug, we consider North and South America as study area for reasons stated earlier. We considered two commonly used niche-based methods, Genetic Algorithm for Rule-Set Production (GARP) (Stockwell and Peters 1999) and Maximum Entropy Model (Maxent) (Phillips et al. 2006) for this purpose. GARP and Maxent models were chosen because prior research demonstrated their better performances when compared with many other models (Hernandez et al. 2006; Tsoar et al. 2007). Both models only require occurrence data and use pseudo-absence data during the construction of models by extracting random points from the geospatial extent of input environmental variables. Occurrence data from both native and invaded ranges were used to train the model. We first compiled both the occurrence data in Asia and the U.S. (totally 319 occurrence), and then randomly extracted 70% of occurrences (n = 223) as training data and used the remaining 30% (n = 96) as an extrinsic testing data. We repeated this random splitting 10 times to generate 10 sets of training and testing data. Thus, GARP and Maxent models were run and evaluated ten times and with each time an individual set of training and testing data were used. We then averaged the output models of 10 runs as the final model for GARP and Maxent.

GARP

The GARP modeling system is a genetic algorithm that produces sets of rules that delineate ecological niches of species (Stockwell and Peters 1999). GARP models were developed using the “best subsets” procedure in OpenModeller (Muñoz et al. 2011). In this procedure, the GARP model was run 100 times on an individual training dataset (out of 10 data splits; see previous section) and the training dataset was further split internally into 70% intrinsic training data and 30% intrinsic testing. This internal split of the data is necessary to select 10 best models (of the 100 obtained) and generate a GARP prediction. This procedure was conducted for the 10 random splits of training and testing datasets. We maintained other default parameters. The output GARP predictions were then evaluated by using the remaining extrinsic testing data.

Maxent

Maxent modeling system predicts species’ geographic distribution by fitting variable data with a probability distribution. This probability distribution is generated using training data and has the maximum entropy by subjecting to constraints representing the unknown information (Phillips et al. 2006). Maxent models were implemented using the Maxent program (Phillips et al. 2006) with the default parameters. All 10 models (based on the 10 random splits of occurrence datasets; see above) were then evaluated by using the remaining extrinsic testing data. We used the logistic output as the model output type. The Maxent logistic output is an estimate of suitability of one area to the target species (Phillips and Dudík 2008). The logistic output of the Maxent model varies from 0 to 1, to better visualize the output model we multiplied the final average model by 100 to provide the same scale of values as GARP.

Model evaluation statistics

Three methods were used to evaluate the models: the area under the receiver operating characteristic curve (AUC) (Fielding and Bell 1997), omission rate (OR), and true skill statistic (TSS) (Allouche et al. 2006). The overall AUC, OR, and TSS were calculated to evaluate and compare the performance of two models, and the three measures for the native and invaded ranges were also calculated. To compare the performance of the GARP and Maxent models, the one-tailed Wilcoxon signed-rank test was used to compare the measures of two models.

AUC is a generally accepted and threshold-independent measurement of model performance (Fielding and Bell 1997). The value of AUC varies from 0 to 1, with AUC ≥ 0.9 considered as good performance (Swets 1988). TSS takes both omission and commission errors into account by adding sensitivity and specificity and subtracting 1. TSS varies from − 1 and + 1, where 1 indicates perfect model performance and values of zero or less indicate poor performance. “ROCR” package (Sing et al. 2005) in R software was used to calculate AUC and TSS. The AUC and TSS were calculated for all the 10 models of each algorithm. OR is a threshold-dependent measurement. To convert the suitability model to binary presence/non-presence model, we carefully selected the threshold for GARP and Maxent model. As GARP usually predicts a large or even overly extensive area of potential distribution (Peterson et al. 2007), we set the threshold for GARP to 50% of the best subset models, which means only places predicted by at least half of the best models are considered as potential distribution area. To ensure that the OR of GARP and Maxent is comparable, we used the “equalized predicted area” method proposed by Phillips et al. (2006) to set the threshold of Maxent. The threshold was set for each Maxent model to give the Maxent binary model the same number of pixels predicted as potential distribution area as the GARP binary model.

Variable importance and climatic preference

To determine the climatic preference of kudzu bug, we first selected the most important variables for the construction of both GARP and Maxent models. We then analyzed the co-occurrence of predicted invasion risk and the values of important variables. To determine the most important variables, the jackknife test was used. The Maxent program (Phillips et al. 2006) internally conducted the jackknife test and evaluation on the variable contribution. The jackknife test on the GARP model was run externally by generating 13 models that used one variable in isolation and 13 models that excluded one variable in turn. Analysis of the response of the predicted invasion risk values to important variables was only conducted for the Maxent model.

Results

Environmental space shift

Based on the PCA on both the available and occupied environment in two ranges, the first two PCs explained 64.69% of the total variance. According to the first two PCs, the total overlap of occupied environmental space between the native and invaded populations is 0.196. The statistical test suggested that the two populations did not occupy an equivalent environmental space, as the observed D value fell outside of the 95% confidence interval of simulated values (Fig. 1c). The test on the similarity of environmental space indicated that the occupied environmental space by native populations was similar with the invaded populations (P value = 0.069, Fig. 1d). However, the same test on invaded populations suggested a difference indicating the occupied environmental space by invaded populations was not similar with native populations (P value = 0.047, Fig. 1e). The niche expansion, stability, and unfilling were 0.044, 0.956, and 0.670, respectively, indicating the dissimilarities of occupied environmental spaces were mainly caused by niche unfilling of kudzu bug in the U.S. Thus, the low overlap of occupied environmental space (0.196) was also mostly resulted from the niche unfilling of kudzu bug in the invaded range.

Fig. 1
figure 1

Analysis on environmental space shift of kudzu bug between native and invaded populations. a Environmental occupancy of kudzu bugs in native and invaded ranges, the dashed orange and blue contour lines represent the 95% of the available environmental space in the U.S. and Asia respectively, while the solid ones represent the 100% of the available environmental space. The orange and blue gradients indicate occupied environmental spaces in the U.S. and Asia, respectively, while the grey to black gradients indicate overlap of occupied environmental spaces (the darker gradients indicating higher density of overlap). b Correlation circle of the first two principal components (PCs), which totally explain 64.69% of the variable variance. c–e Observed environmental space overlap (bars with red diamond) and simulated niche overlaps (grey bars) on test of environmental space equivalency (c), environmental space similarity of Asia to U.S. (d), and environmental space similarity of U.S. to Asia (e) of two populations

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Model evaluation and comparison

Maxent had a continuous output with values varying from 0 to 100, and higher values represented a higher invasion risk. The output of GARP “best subset” procedure was categorical with values varying from 0 to 100. Ten runs of the Maxent model returned 10 AUCs varying from 0.96 to 0.97, and the AUCs of 10 GARP models varied from 0.91 to 0.93. GARP and Maxent both had mean AUCs higher than 0.9 indicating that both models had good performance. Maxent had significant higher AUC than GARP based on the one-tailed Wilcoxon signed-rank test (P value = 0.001, Table 2). The TSS had the same pattern indicating that Maxent had better performance than GARP (P value = 0.001, Table 2). As TSS showed the same pattern with AUC, we therefore only used AUC and OR for model comparison hereafter.

Table 2 Comparison of AUC and OR of GARP and Maxent models
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Using 50% of best subset models as the threshold rule, the percent area predicted by 10 GARP models varied from 18.47 to 21.90%. The threshold value of 10 Maxent models varied from 0.93 to 1.83 when predicting the same area as GARP. The P value for the Wilcoxon signed-rank test on OR was 0.005 (Table 2), indicating that the Maxent models had a significantly lower OR than the GARP models (P value = 0.005, Table 2). This outcome was consistent with the AUC result, suggesting that the Maxent models performed better than the GARP models. The final binary GARP and Maxent models predicted 20.96% of the total study area as potential distribution area for the kudzu bug.

Invasion risk

The GARP and Maxent model pixels with higher values suggest regions with more suitable environment for the species and, thus, at a higher risk of invasion. GARP and Maxent models both predicted high suitability values for most of the observed occurrence points (Figs. 2, 3). The suitability value of occurrence points from the Maxent model varied between 1.71 and 79.61 (mean = 57.165), while the suitability value from the GARP model varied between 28 and 100 (mean = 97.490). Despite the distinct difference of suitability values predicted by two models, both models had high agreement in terms of relative invasion risk (Fig. 3). In the Americas, high invasion risk was predicted in the eastern U.S., most regions in the Central America, and the central region in South America (Fig. 3a, b). High agreement was also observed in binary models (Figs. 2, 3): both models indicated similar regions that will be or already were infested by kudzu bug; however, differences in the two binary models were also observed. Part of Greenland was predicted as potential distribution area by Maxent model but not by GARP model (Fig. 3c, d). The situation was reversed in northern Brazil where the GARP model classified potential suitable area while the Maxent model classified the same type of area as unsuitable area (Fig. 3c, d).

Fig. 2
figure 2

a–b Predicted suitability maps of kudzu bug in native range in Asia. The higher the value is, the more suitable the area is c–d, binary predictions of the suitability maps in Asia. Occurrences, which were used to develop and evaluate models, were shown as green dots

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Fig. 3
figure 3

a–b Predicted invasion risk model of kudzu bug in North and South America. The higher the value is, the more risky that the region would be infested by kudzu bug. c-d, Binary predictions of suitability maps in North and South America. Occurrence of kudzu bug in U.S., which were used to develop and evaluate models, were shown as green dots. Regions that were covered by green dots in c-d were all predicted as suitable places

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Variable importance and climatic preference

GARP and Maxent yielded similar rankings of variable importance (Fig. 4). Both models ranked annual mean precipitation (Annual P, BIO12), mean temperature of the coldest quarter (BIO11), precipitation of the warmest quarter (BIO18), annual mean temperature (BIO1) and mean annual temperature range (BIO7) as five of the six most important variables. The models also ranked elevation, mean diurnal temperature range (BIO2), and precipitation seasonality (BIO15) as the three least important variables. However, differences also were observed for specific rankings of these five variables. The GARP model ranked precipitation of the wettest quarter (BIO16) as the fourth important variable, while Maxent ranked it as the seventh most important variable. Analysis of variable contribution to the Maxent models generated similar results with the jackknife tests: BIO12, BIO11, BIO1, BIO8 and BIO7 are five of the most important variables, contributing 28.4, 19.8, 16.2, 12.7 and 11.7% to the model, respectively. Cumulatively, the five most important variables contributed 88.8% to the Maxent models.

Fig. 4
figure 4

Jackknife test of AUC for the Maxent and GARP models (P, T and Max are abbreviations for Precipitation, Temperature, and Maximum, respectively)

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Response curves for the five most important variables in Maxent were generated to examine the climatic preference of kudzu bug. For annual mean precipitation (Fig. 5a), high suitability (> 0.5) were limited between 1000 and 1700 mm and the highest suitability was predicted at 1300 mm. For mean temperature of the coldest quarter (Fig. 5b), annual mean temperature (Fig. 5d), and mean annual temperature range (Fig. 5e), the high probabilities of occurrence were predicted from 0 to 12 °C, 12 to 20 °C, and 28 to 35 °C, respectively, and the highest probabilities occurred at 6, 15, and 32 °C, respectively. The response curve of the suitability to precipitation of the warmest quarter is different from the former four variables (Fig. 5c). The high suitability occurred at the range of 330–375 mm and values greater than 440 mm, and the highest suitability occurred at 750 mm.

Fig. 5
figure 5

Response curve of the predicted suitability value by Maxent model to five most important variables (a—annual mean precipitation, b—mean temperature of coldest quarter, c—precipitation of warmest quarter, d—annual mean temperature, and e—temperature annual range) (red curves indicate mean response and the blue margins reflect ± 1 Standard Deviation over 10 runs)

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Discussion

Environmental space shift

The niche equivalency test indicated that the native and invaded populations of kudzu bug do not inhabit in identical environmental conditions. However, this does not indicate a niche shift. Niche change had been proved rare among multiple groups of species (Petitpierre et al. 2012; Strubbe et al. 2013). Based on two independent studies with different groups of species, Petitpierre et al. (2012) and Strubbe et al. (2013) concluded that niche difference is more likely caused by niche unfilling than real niche change due to niche expansion. In this research, we also observed little proportion of niche expansion (4.44%) and high niche stability (95.56%). However, the niche unfilling in the U.S. is as high as 67%, indicating that kudzu bugs have not been reported in 67% of the environmental space, which is occupied by native populations and available in the U.S. This suggests that the invasion of kudzu bug is far from equilibrium and more places could be further infested in the U.S. Based on the available environmental space in native and invaded ranges, the environmental heterogeneity also exists. The study area in Asia has more available environmental conditions than the U.S. Although the niche expansion in the U.S. is only 4.44%, the inequivalent environmental spaces occupied by native and invaded species and environmental heterogeneity between two ranges both prove the effectiveness of using occurrence information from the native and invaded ranges for predicting the potential invasion.

Significant difference of model performance between native and invaded ranges

Attention should be given to the significant difference on performance of GARP and Maxent models between the invaded and native ranges. Both AUC and OR indicated that the Maxent and GARP models had significantly different performance between native and invaded ranges (Table 3). The difference of model performance in native and invaded regions may result from the intrinsic characteristics of models and the features of occurrence data. We noticed that occurrence data in the invaded range had a dense distribution in the southeastern U.S. (Fig. 3c), while occurrence data in the native range was scattered around a much larger region in Asia (Fig. 2c). As the Maxent model is based on a fitted probability distribution (Phillips et al. 2006), environmental conditions that were more frequent in our dataset are taken as the better potential environment by Maxent. Whereas GARP model delineates the potential distribution area of species by setting a series of rules, thus is less impacted by the sampling density. As a result, GARP did not constantly show better performance in the U.S. where the sampling density is higher confirming that GARP is less sensitive to the sampling bias (Costa et al. 2010). The significant difference of model performance or sample density between the native and invaded ranges was also observed in similar research conducted by Broennimann and Guisan (2008) and Sobek-Swant et al. (2012). We therefore suggest attention should be given to the difference in sample density between the native and invaded ranges, as the difference may introduce a sampling bias in the models.

Table 3 Comparison of AUC and OR of GARP and Maxent models obtained for native and invaded training ranges
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Selection of threshold for GARP and Maxent

The choice of threshold for the GARP and Maxent models is crucial for converting models into binary prediction. The GARP model tends to predict overly extensive areas of potential distribution, whereas the Maxent model tends to be too conservative. Choosing 50% of the best subset models as the threshold for GARP coincides with the observation by Phillips et al. (2006) that for GARP models, areas predicted by 5–10 out of the 10 best-subset models were appropriate to be classified as the species’ potential distribution area. We selected the Maxent threshold value to match the percent area predicted as potential distribution to that of binary GARP models. By using this method, the potential distribution model generated by GARP was in high agreement with that generated by Maxent. This result further confirmed that the Maxent model resembles the GARP model when lower levels of predictions were used as threshold (Peterson et al. 2007). We realize that the fixed value 50 is not the optimal method to convert suitability maps into binary prediction maps. Both Liu et al. (2005) and Jiménez-Valverde and Lobo (2007) concluded that the fixed threshold was the worst criteria of converting suitability maps into binary prediction maps, while the sensitivity–specificity based thresholds were most accurate. However, in this research, as the omission rate, which is derived from confusion matrix, was used to compare the performance of GARP and Maxent, using a threshold derived from confusion matrix would make the comparison bias towards GARP model. We recommend readers to select the most appropriate threshold method based on research objectives.

Invasion risk and climate preference of kudzu bug

Regions with high invasion risk include most states in eastern U.S., most countries in Central America, and countries in central South America. Currently kudzu bug is only present in the southeastern U.S. in Americas. However, climate conditions (including temperature and precipitation) of Central America and a large proportion of South America are similar with the conditions of south Asia, where most of the occurrences in native range were distributed (Hijmans et al. 2005). This similarity explains why high invasion risk were predicted in those regions and suggests that kudzu bug can successfully establish there once it has been accidently introduced. Although kudzu bug is the only member found in America in the family of Plataspidae, a close relative of kudzu bug, Coptosoma xanthogramma (White), had been found in Hawaii in 1965, and established as a pest of legumes (Beardsley and Fluker 1967). This confirms that kudzu bug can establish in tropical climate regions, where part of Central and South America are located. However, soybean is an important crop in Central and South American countries including Mexico, Brazil, and Argentina, thus to avoid potential economic losses of soybean by kudzu bug, we recommend serious quarantine in these regions to prevent the entry of kudzu bug. In the U.S., the high proportion of niche unfilling suggests that more places could be further infested. Meanwhile, a majority of the soybean production is distributed in upper Midwest, where most of the regions have not been infested by kudzu bug. Therefore, early detection is also highly recommend in the upper Midwest of the U.S.

Kudzu bugs generally inhabit warm (annual mean temperature around 15 °C) and humid (annual mean precipitation around 1300 mm) regions. This finding coincides with the description of the climatic preference of kudzu bug in native range in Asia (Wang et al. 1996). It had been conjectured that low winter temperature (below − 14 °C) might kill some bugs in Georgia (Gardner and Olson 2016). Our finding confirmed this conjecture: kudzu bug had low possibility (< 30%) of occurrence in regions with mean temperature of the coldest quarter around 0 °C, whereas the possibility decreases to almost 0 (around 3%) when the mean winter temperature reached − 10 °C. We realize that the occurrence of the main host plant, kudzu, which is not included in this research, may have played an important role in determining the invasion of kudzu bug. Further study is underway to analyze how the density of host plant (including soybean and kudzu) impact the spread of kudzu bug.

Based on the current distribution of kudzu bug in the U.S., our study suggests that the environmental conditions where kudzu bugs inhabit are not the same between native and invaded ranges. The effectiveness of using occurrence data from both native and invaded ranges to predict potential biological invasion was therefore confirmed. In addition, we suggest careful examination of the difference of sample density between native range and invaded range to avoid sample bias for similar research. Kudzu bug generally inhabits warm and humid places. Management, including quarantine and prevention measures, are suggested for these regions to avoid invasion and outbreak of kudzu bug. Regions with suitable climatic conditions for kudzu bug could be managed to change the microenvironment to avoid severe damage from kudzu bug.