Genetic analyses reveal complex introduction histories for the invasive tree Acacia dealbata Link around the world

To compare genetic diversity and structure between Acacia dealbata populations sampled across the species’ native range in Australia and from its non‐native ranges in Chile, Madagascar, New Zealand, Portugal, La Réunion island, South Africa and the United States, and to investigate the most likely introduction scenarios to non‐native ranges.

to south-western Australia (i.e. Australian Capital Territory, New South Wales, Victoria and eastern Tasmania), has been introduced to many parts of the world for multiple purposes (e.g. forestry, horticulture, perfume production, railway fuel, shade and shelter) (Kull et al., 2008;Lorenzo et al., 2010;Poynton, 2009;Richardson & Rejmánek, 2011). For example, according to the Global Biodiversity Information Facility (GBIF), A. dealbata is currently present in 29 countries and islands outside Australia (GBIF Secretariat, 2019). In many of these areas, the species has escaped cultivation and is now considered an aggressive invasive species Richardson & Rejmánek, 2011). In these regions, dense mono-specific populations of A. dealbata replace or radically alter native vegetation and change soil characteristics through the release of allelopathic compounds and the fixation of atmospheric nitrogen (Poynton, 2009;Lorenzo, Pereira, & Rodríguez-Echeverría, 2013).
Acacia dealbata has a short generation time and can reach reproductive maturity at four to five years of age (Stelling, 1998). The species also has generalist pollination requirements and seed-dispersal syndromes (Carr, 2001). Based on morphology and environmental requirements, it was previously thought that A. dealbata consisted of two subspecies (Kodela & Tindale, 2001). However, recent studies based on a combination of ecological niche modelling, DNA sequencing analyses and microsatellite genotyping questioned this taxonomic division (Hirsch et al., 2017(Hirsch et al., , 2018. Instead, across the species' native range, two geographically structured genetic lineages, corresponding roughly to Australian mainland populations and Tasmanian populations, have been described (Hirsch et al., 2018). In our latest work, we compared the genetic makeup of these native lineages to invasive populations from South Africa where the species was introduced in the mid-19th century (Hirsch et al., 2019;Poynton, 2009). Surprisingly, South African populations were genetically distinct from native populations, and modelling approaches indicated that these populations originated from an unknown or "ghost" source (Hirsch et al., 2019). To gain a more comprehensive understanding of the species' introduction history around the world, this study aims to compare the two native lineages of A. dealbata with invasive populations from Chile, Madagascar, New Zealand, Portugal, La Réunion and the United States-countries that represent some of the species most prominent invasive ranges (Lorenzo et al., 2010;. Historical records documenting the introduction histories of A. dealbata to these countries are largely lacking, in particular with regard to the origin of invasive populations. In Europe, A. dealbata was first introduced in 1816 for horticultural and floricultural purposes and is now considered a highly invasive species in south-western parts of the continent (Adair, 2008;Cavanagh, 2006;Martins et al., 2016). In Portugal, the first record of the species is from 1850, when it was introduced for the cut-flower, tannin and timber industries (Alves, 1858;Martins et al., 2016).
Although the species already established invasive populations during the 19th century, it was only in 1999 that it was officially listed as

K E Y W O R D S
Australian acacias, biological invasions, Fabaceae, genetic diversity, genetic structure, introduction history, microsatellite markers, tree invasions, wattles invasive (Marchante et al., 2005;Martins et al., 2016). Acacia dealbata now occurs throughout Portugal (Marchante et al., 2005), and it is considered one of the top 20 target species for biological control programs in Europe (Sheppard et al., 2006). Acacia dealbata is also considered invasive on the two western Indian Ocean islands of Madagascar and La Réunion, where it was introduced in 1898 and 1841, respectively (Kull et al., 2008. In La Réunion, the species was primarily introduced to control soil erosion, while in Madagascar, its main uses were afforestation, railway fuel and shading (Kull et al., 2008). Around the mid 1900s, aircraft were used to disseminate A. dealbata seed over large parts of Madagascar; by the end of the 1960s, the species occurred over more than 30,000 ha (Chauvet, 1968;Roche, 1956). Although A. dealbata is clearly invasive, some policymakers in Madagascar downplay this status and laud its value for reforestation (Kull et al., 2007(Kull et al., , 2008. In Chile, after being introduced in 1869, the wider dissemination of A. dealbata started in the early 1900s for erosion control and as a source of fuel wood (Fuentes et al., 2014;Kull et al., 2011). The species currently has vast invasive populations along rivers, roads and in disturbed habitats across central Chile from Valparaiso to Los Lagos (including Juan Fernandez Island and Easter Island (Langdon et al., 2019)). In the Bío-Bío region alone, it is estimated that the species may cover as much as 100,000 ha (Fuentes-Ramírez et al., 2010). Another country where A. dealbata is listed as invasive species is New Zealand (CABI, 2020). According the New Zealand Conservation Network (http://www.nzpcn.org.nz), the species became naturalized in the country in 1870, although the date of introduction remains unknown. The species is valued for its attractive flowers, coppicing ability, quality timber and shelter, and is still available for sale in New Zealand (e.g. https://www.south ernwo ods.co.nz/shop/ acaci a-dealb ata/). Unlike many regions around the globe, growth trials in New Zealand used seed material of A. dealbata sourced from Tasmania, mainland Australia and from non-native ranges of the species, such as India (Shelbourne et al., 2000). In the United States, A. dealbata occurs almost exclusively in California (USDA & NRCS, 2020) and is not considered invasive (CABI, 2020). It was one of the first Australian acacias to be introduced to California in the early 1850s, and subsequent introductions are thought to have occurred (Butterfield, 1938). The species did not fare well in California, and many individuals died within a few years after their introduction (M. Rejmánek, pers. comm.;Hastings & Heintz, 1976).
By comparing the genetic characteristics (i.e. genetic diversity and structure) of A. dealbata populations collected across the native range and introduced ranges discussed above, and by applying stateof-the-art genetic modelling, our study aims to shed more light on the historical movement of the species and its global biogeography.
Such information may benefit ongoing initiatives to develop effective management options for the species (e.g. biological control) and improve biosecurity strategies.

| Sampling, DNA extraction and genotyping
In addition to available data for native A. dealbata populations (Hirsch et al., 2018) and invasive South African populations (Hirsch et al., 2019), we also generated microsatellite genotyping data for non-native populations in Chile, Madagascar, New Zealand, Portugal, La Réunion and the United States of America (USA) (Figure 1; Table 1). In each country, fresh healthy leaves were sampled from 20 randomly chosen individuals per population. Care was taken to sample individuals across the distribution of each population (i.e. sampling of only one part of a population was avoided) and the minimum distance between sampled individuals was 5 m. The collected plant material was dehydrated and stored on silica gel until DNA extraction. DNA extractions were carried out using the cetyltrimethylammonium bromide (CTAB) F I G U R E 1 Regions where Acacia dealbata samples were collected for this study. Red circles indicate exact sampling locations (see Table 1) and numbers in parentheses give the number of individual populations sampled in each country/region TA B L E 1 Population information and genetic diversity measures for Acacia dealbata populations included in this study. Lat  Hirsch et al. (2018). Genetic diversity measures for native and South African populations were previously published by Hirsch et al. (2019) and are shown here for the sake of comparison.  method (Doyle & Doyle, 1990) with some modifications (see Hirsch et al., 2018Hirsch et al., , 2019. All DNA extractions were diluted to a concentration of 100 ng/μl. Ten nuclear microsatellites loci were amplified using a set-up of two multiplex PCRs (for PCR conditions and further details see Hirsch et al., 2018Hirsch et al., , 2019 (48)  . The same scenarios were tested for the invasion history of South Africa populations by Hirsch et al. (2019). A change of colour along the scenario pathways represents a founding event of a new population for which potential bottleneck effects were considered. In cases where populations merge in the scenario (highlighted with an asterisk), admixture rates were implemented in the scenario code (for details see Table S2, Appendix S2). NAT0 = overarching native population; NAT1 = Tasmanian populations and Australian mainland populations AUS_1, AUS_2 and AUS_3; NAT2 = Australian mainland populations (except AUS_1, AUS_2 and AUS_3); INV = populations from corresponding non-native range; G1, G2 = two unsampled ("ghost") populations.

SD
Further details on the model parameters (i.e. tsplitNAT1, tsplitNAT2, etc.) are provided in Table S2, Appendix S2. The non-native range names underneath the diagrams indicate for which non-native populations the corresponding scenario was the most likely one ( Figure S6, Appendix S1)

F I G U R E 3
Comparison of the genetic diversity measures between the native (white) and non-native (grey) ranges of Acacia dealbata. (a) allelic richness, (b) observed heterozygosity and (c) expected heterozygosity. Native populations were grouped into two genetic lineages according to Hirsch et al. (2018) (NAT1 = Tasmanian populations and southern most mainland population; NAT2 = main Australian mainland population). Boxplots are combined with beeswarm plots (black points) to displays the distribution of individual measurements. Range abbreviations correspond to the "range IDs" in Table 1 representing 42 native and 50 non-native populations (Table 1). It is worth noting that the microsatellite data reported in our previous studies (Hirsch et al., 2018(Hirsch et al., , 2019 and the new data of this study were generated and scored at the same time.

| Dataset characteristics and genetic diversity
Our genotype dataset was initially checked for the presence of scor-  (Kim & Sappington, 2013).
Therefore, for more detailed estimates of null allele frequencies at each locus and population, the expected maximization method as implemented in the software FreeNA (Chapuis & Estoup, 2007) was also applied. FreeNA was also used to calculate uncorrected and corrected (i.e. excluding null alleles; so-called ENA method as described in Chapuis & Estoup, 2007) pairwise F ST values (Weir, 1996). For all loci, allele frequency departures from HWE expectations were F I G U R E 4 Genetic structure results for the native and non-native populations of Acacia dealbata. (a) STRUCTURE bar plots. The delta K method following Evanno et al. (2005) revealed K = 2 as optimal genetic structure but also showed a strong signal for K = 4. Range abbreviations above and numbers underneath the bar plots refer to the population ID's and range information provided in Table 1. (b) Principal coordinates analysis for the native and non-native populations of A. dealbata. The analysis was based on genetic distances (following Cavalli-Sforza and Edwards 1967) between populations and the first three axes explained 14.9%, 10.4% and 8.7% of the variation, respectively. Populations are indicated with different colours and symbols according to their geographic origin (see plot legend). The numbers within the symbols refer to the population IDs (without prefix "TAS," "AUS," etc.) provided in Table 1. Numbers for La Réunion and the USA are highlighted in bold for better readability tested using the packages adegenet version 2.1.1 (Jombart, 2008) and pegas version 0.11 (Paradis, 2010)

| Genetic structure and variation
For the complete dataset (i.e. including all native and non-native populations), and for each non-native range separately, Bayesian assignment tests as implemented in STRUCTURE version 2.3.4 (Pritchard et al., 2000) were performed to investigate the genetic structure among populations of A. dealbata. The sub-datasets for native range and the South African range were previously analysed using the same approach (Hirsch et al., 2018(Hirsch et al., , 2019, and these analyses were therefore not repeated in this study. For each dataset, a range of possible genetic clusters (K values; individual non-native ranges using a Mantel tests (Mantel, 1967). This was previously done for native and South African populations (Hirsch et al., 2018(Hirsch et al., , 2019

| Inferring the introduction histories of Acacia dealbata
To test different introduction scenarios to each of the different non- Before running all simulations, the performance of prior estimates was tested for each dataset following the recommendations by Bertorelle et al. (2010). For the final analysis of each non-native range dataset, 1 × 10 6 datasets were simulated for each scenario using the high-performance computation cluster at Stellenbosch University's Central Analytical Facilities' (http://www.sun.ac.za/hpc). The prior distributions of parameters and parameter rules applied for these analyses are specified in Table S2, Appendix S2. As an initial step, these prior settings were optimized in preliminary DIY ABC runs as recommended by Bertorelle et al. (2010). For each simulation, we used information from the primary literature to infer the time of introduction of A. dealbata (i.e. residence time) to corresponding non-native ranges (see Introduction section for details) and the species' minimum generation time of four to five years (Stelling, 1998). This provided us with the maximum number of generations within each non-native range (Table S2, Appendix S2). For each ABC analysis, we applied a generalized stepwise mutation model and the following summary statistics were used: mean number of alleles, mean genetic diversity (Nei, 1987) 10,000 datasets per scenario). The median of the absolute deviation (RMedAD) and the median relative bias (MedRB) on 500 test datasets for the most likely scenario were calculated to assess the precision of parameter estimations .
For the scenario with the highest posterior probability in each ABC analysis (see Results), we estimated type I errors (i.e. false negatives) and type II errors (i.e. false positives) by using the "confidence in scenario choice" function implemented in DIYABC and following the protocol described by Cornuet et al. (2010). For these calculations, a set of 100 independent datasets and logistic regression approaches were used. For the most likely scenarios, we also applied the "model checking" option of the DIYABC software to test the ability (i.e. adequacy) of these scenarios to simulate datasets similar to the observed datasets . For this approach, 1,000 datasets were simulated from the parameter posterior distributions of the corresponding scenario and different summary statistics as for previous steps were used to avoid overestimating the fit of a scenario .

| Dataset characteristics and genetic diversity
We found no evidence for scoring errors due to band stuttering in our genotype dataset. All loci were polymorphic and the number of alleles per locus ranged between 5 and 17 (mean: 9.2). All loci were also characterized by significant departures from HWE expectations ( Figure S1, Appendix S1). However, there was no consistent pattern of significant HWE departure for a specific locus across all populations. Overall, allele frequency departure from HWE was due to a bias towards an excess of heterozygous genotypes (data not shown).
We detected a low average null allele frequency of 0.023 in our dataset but did not find a significant difference between ENA-  Figure 3). South African populations also had much lower allelic richness than native populations (Hirsch et al., 2019; Table 1, Figure 3).
Populations from all other non-native ranges had similar, or even slightly higher, genetic diversity measures compared to native populations (Table 1, Figure 3). In all cases, inbreeding coefficients were very low or showed no evidence of inbreeding (Table 1).
We found evidence for clones in the majority (i.e. 80.4%) of the 92 investigated A. dealbata populations (Table 1). Native populations had a mean PD of 0.70, while the mean PD varied between 0.58 and 0.92 in non-native populations (Table 1). We did not find any significant differences in PD or MLG between the native range and non-native ranges (Kruskal-Wallis chi-squared = 10.85, p = .15 and Kruskal-Wallis chi-squared = 12.49, p = .09, respectively). We also found allelic richness, regardless if calculated with the full dataset (Table 1) or the clone-corrected dataset (Table S3, Appendix S1), to be significantly and positively correlation with MLG (Spearman's rho = 0.59, p < .001 and Spearman's rho = 0.36, p < .001, respectively). Overall, the presence of clones did not influence the overall genetic diversity results ( Figure S2 and Table S3, Appendix S1) and we therefore report all further results on the full dataset.

| Genetic structure
The STRUCTURE analysis of the complete dataset (i.e. all native and non-native populations) revealed the highest delta K values for K = 2 (delta K = 65.9) and K = 4 (delta K = 42.3) ( Figure S3, Appendix S1).  (Figure 4b). A similar lack of association was observed for two New Zealand populations, while the remaining three populations from this country clustered with Tasmanian populations (Figure 4b).
When considering the separate STRUCTURE analyses for each of the non-native ranges, we identified two genetic clusters in New Zealand (delta K = 8.8), in Portugal (delta K = 25.4), in La Réunion (delta K = 196.2), and in the United States (delta K = 20.4) ( Figures S3 and   S4, Appendix S1). Within Chile and Madagascar, three genetic clusters were identified (delta K = 23.0 and 39.3, respectively) ( Figures S3 and   S4, Appendix S1). However, for Chile, Madagascar, Portugal and the United States, the graphical representation of these groups ( Figure S4, Appendix S1), as well as significantly lower pairwise F ST values between pairs of populations within each non-native range compared to native populations ( Figure S5 and Table S4, Appendix S1), rather suggest a lack of biologically meaningful genetic structure in these ranges. In contrast, pairwise F ST values between pairs of populations within New Zealand and La Réunion were significantly higher than those between native populations ( Figure S5 and Table S4, Appendix S1). However, in the case of New Zealand, the extremely low delta K value (i.e. 8.8; Figure S3, Appendix S1) provides only very weak support for two genetic structures. The lack of genetic structure in Chile was further supported by the fact that raw model probabilities from the K = 1 STRUCTURE runs did not differ significantly from those for the K = 3 (i.e. the optimal K found in this non-native range) (Wilcoxon rank sum test; W = 241.5, p = .260). For all other non-native ranges, the probabilities of their optimal K were significantly higher than those for K = 1 (in all cases: W = 400, p < .001). Further, no evidence for IBD was found within any of the non-native ranges (Table S5, Appendix S1).

| Introduction histories
The DIYABC results showed that scenario 4 had the highest probability for Chile (p = .403; 95% CI = 0.391-0.414) and Madagascar (p = .456; 95% CI = 0.429-0.483), and scenario 3 for the United States (p = .325; 95% CI = 0.313-0.337). However, the low probability levels in both these cases, as well as the high similarity to probabilities of the other scenarios tested ( Figure S6, Appendix S1), indicate a lack of power in these models. Consequently, all further discussion around the introduction history of A. dealbata in these ranges does not rely on DIYABC results (see Discussion section below).
Further, these two non-native ranges also had high probabilities for scenario 1 (p = .456, 95% CI = 0.449-0.4630 and p = .3486, 95% CI = 0.333-0.365, respectively) ( Figure S6, Appendix S1). This scenario also implies and further strengthens the likelihood of a direct Tasmanian origin, but not involving multiple introductions (Figure 2). However, in contrast to La Réunion, confidence intervals for these two scenarios in New Zealand did not overlap which points to a higher likelihood for the multiple introduction scenario than for the single introduction scenario.  (Table S6, Appendix S1). In these two cases, the high Type I error was mainly due to the fact that scenario 1 was "mis-identified" as the scenario with the highest probability (i.e. for New Zealand in 69 out of 100 cases and for La Réunion in 76 out of 100 cases).
For each non-native range, however, results of the adequacy tests via the model checking function in DIYABC showed no significant deviation between observed and simulated summary statistics for the corresponding most likely introduction scenario. This indicates that the posterior distributions of these scenarios are well corroborated by the observed data and they sufficiently explain the "real" observed data (Table S7, Appendix S1).
According to our STRUCTURE analyses that included only populations from La Réunion (i.e. identification of two genetic clusters), we also ran DIYABC models for each cluster separately. Although the quality of the parameter performance was not affected by these models, they produced no meaningful outcomes (i.e. nearly all posterior probabilities for the tested scenarios had similar and low values). We therefore considered only the DIYABC model for which the non-native populations were pooled.

| D ISCUSS I ON
Our results show that the global history of A. dealbata introductions and invasions is complex and that the native sources of many invasive populations around the globe remain unknown, despite our comprehensive sampling in Australia.
While our ABC modelling approach did not clearly support a specific introduction scenario for Chile and Madagascar, our Bayesian assignment analyses suggest that these populations exhibit patterns consistent with admixture between different sources following multiple introductions. Such a geographic reshuffling of genetic diversity is generally considered as being beneficial for maintaining high diversity levels and can contribute to a lack of clear genetic structure (Cristescu, 2015;Smith et al., 2020), as was evident in both ranges. Admixture between previously isolated populations can have an important influence on the invasion success of a species (Dlugosch et al., 2015). High genetic diversity can help the introduced species to overcome negative effects of genetic bottlenecks and to decrease its sensitivity to genetic drift (Lavergne & Molofsky, 2007). Genetic admixture can also create novel genotypes which may promote rapid adaptation to novel environmental conditions or is often characterized by increased performance (Lavergne & Molofsky, 2007). Such increased performance is also known as "heterosis" (i.e. hybrid vigour) which is the phenotypic superiority that is often evident for first generation hybrid genotypes compared to their parental genotypes (Ellstrand & Schierenbeck, 2000;Li et al., 2017). A recent study by Li et al. (2017) showed that heterosis effects due to admixture can persist beyond the first generation in invasive plants. We also detected instances of clonality in populations from both the native and non-native ranges of A. dealbata. Whether these clones represent individual trees or coppicing stems from the same individual remains unknown. However, since we sampled trees at least 5m apart, it is likely these represent different individuals.
Our ABC models showed that a direct origin, after multiple introductions, from only one of the two native lineages (i.e. Tasmania) seemed to be the most likely for A. dealbata populations in New Zealand and La Réunion. Populations in these two regions, however, show differences in genetic diversity and structure. New Zealand populations had similar genetic diversity levels to native and other non-native ranges and showed no clear genetic structure. We assume that high propagule pressure due to the multiple introductions helped to maintain high levels of genetic diversity in this range (Thompson et al., 2016). As discussed above, such a boost of genetic diversity can be beneficial for the invasion success of an introduced species by providing sufficient genetic variation to overcome founder effects and to cope with environmental conditions in the new range (Dlugosch et al., 2015;Lavergne & Molofsky, 2007). Moreover, although genetic structure had weak support in New Zealand, the STRUCTURE analysis indicated gene flow between putative genetic clusters ( Figure S4, Appendix S1) which is likely to sustain the genetic diversity in this range. In contrast, populations from La Réunion have very low genetic diversity (even lower than South African populations; see Hirsch et al., 2019) and showed genetic structure. Such extremely low genetic diversity levels are likely due to very low propagule pressure (number and size of introduction events) and genetic drift (Thompson et al., 2016;Ward et al., 2008) Lamarque et al., 2013;Peperkorn et al., 2005).
The ABC analysis also showed that populations of A. dealbata in Portugal originated from an unknown "ghost" population. Although not sufficiently supported by our DIYABC models, multivariate ordination (PCoA) indicated that such unknown origin scenario is also likely for the majority of populations from the United States. This is similar to the results found by Hirsch et al. (2019) for the South African populations of A. dealbata. While this finding might suggest insufficient sampling of populations in the native range, we think that this is unlikely given our very comprehensive sampling in Australia (Hirsch et al., 2019). However, we cannot exclude the possibility that the "ghost" population might represent a native source population that has gone extinct at the time of our sampling.
Including material from herbarium samples in future genetic studies would help to assess the likelihood of this being the case (Besnard et al., 2018). Another explanation for a "ghost" population could be that the unknown source represents an unsampled population from another non-native range that was not included in this study (e.g.
Italy, France). Such a phenomenon is called a "bridgehead effect" in which a particular invasive population serves as source for introductions into other areas (Lombaert et al., 2010). The unknown population, however, might also represent a cultivated source as was shown for A. saligna in several parts of its non-native range (Thompson et al., 2012(Thompson et al., , 2015. Further studies on the global invasion history of A. dealbata should sample invasive populations from other parts of the world and should also include samples from herbarium specimens and commercially distributed seed lots. Some of our results should be interpreted with caution. For instance, for La Réunion and the United States, the small number of populations (i.e. three in each case) may bias the outcomes of the genetic analyses and modelling. Future studies on the genetic characteristics of non-native populations from these ranges should include more populations to allow for more generalizable conclusions. An increased sampling might also help to achieve better supported models in the ABC approach for Chile, Madagascar and the United States, as this would not only increase the power of the overall dataset but would also allow to define additional potential introduction scenarios in more detail.
Another aspect shown by our results is that, specifically in the case of populations from La Réunion, discrepancies can occur between ABC approaches and more traditional genetic methods (i.e. STRUCTURE and PCoA). To elucidate, if only the traditional methods had been considered in drawing conclusions about the introduction history, the interpretation would most likely have been that these populations originated from an unknown source (Figure 4). The ABC approach, however, predicted a Tasmanian origin for the populations in La Réunion. Similar inconsistencies between these different methodologies were observed by Mallez et al. (2018). As far as we know, the study by Mallez et al. (2018) is the only study before ours where such different outcomes were observed. Reasons for such discrepancies remain to be determined. However, as discussed by Mallez et al. (2018), a potential explanation could be that very low genetic diversity levels bias the reliability of traditional genetic approaches.
In invasive populations, low genetic diversity is usually the result of strong genetic drift following founder events. In contrast to traditional methods, the ABC approach is able to take the stochasticity and therefore random consequences of genetic drift, into account; it is therefore a more reliable approach for drawing conclusions about introduction histories Mallez et al., 2018).
Our results have several implications for the management of invasive populations of A. dealbata. Although there are important benefits to be gained from transferring insights on, and lessons from, management strategies for invasive species between regions Wilson et al., 2011), the clear differences in the introduction histories for different parts of the non-native range must be considered. This applies especially for the evaluation of biological control agents which should ideally be highly co-evolved and locally adapted to achieve the best results (Müller-Schärer et al., 2004). In cases like New Zealand and La Réunion, where invasive populations originated directly from one of the native clusters (i.e. Tasmania), the search for co-evolved control agents could be restricted to these source areas. For the other investigated ranges where non-native populations originated from admixture or even from unknown source areas, the selection of biological control agents will be more challenging. Further, to improve management strategies in ranges for which our approach revealed a "ghost" population as source of introduction, further studies are needed to determine the identity of the unknown source(s). For example, if a "ghost" population resembles a bridgehead population from another non-native range, it would be important to focus management (i.e. vigilance) against the corresponding source populations (Lombaert et al., 2010). If the unknown source resembles cultivated populations, management should focus on preventing the further (commercial) distribution of seed material or other propagative material from such sources. In general, care needs also to be taken when applying niche-model approaches to predict the species potential ranges. Such approaches are likely to produce inaccurate outcomes when models do not consider detailed information on the origins of invasive populations (Thompson et al., 2012).

| CON CLUS ION
Our study shows that globally invasive A. dealbata populations have complex and contrasting introduction histories which need to be taken in account for when planning management approaches. While our data comprised a comprehensive global sample set, intensified sampling is still required to unravel the introduction histories for some ranges in more detail. Consequently, it is also important to recognize that current programs aiming to import and breed new genetic material of A.
dealbata should be halted until we can fully understand how that new genetic material could affect the invasiveness of the species.
We also showed that it is important to combine traditional genetic methodologies with newly developed approaches. They can be complementary, although in some cases traditional genetic tools can be misleading.

ACK N OWLED G EM ENTS
We thank the following people for their assistance with collect- Africa", a Subcommittee B Grant from Stellenbosch University (to JLR) and CONICYT PIA AFB170008 (to AP).

CO N FLI C T O F I NTE R E S T
The authors declare that there is no conflict of interest regarding the publication of this article.

PEER R E V I E W
The peer review history for this article is available at https://publo ns.com/publo n/10.1111/ddi.13186.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data used in this study are available from the authors upon request.