Robin Pouteau
email: robin.pouteau@ird.fr

Wilfried Thuiller
email: wilfried.thuiller@univ-grenoble-alpes.fr

Carsten Hobohm
email: hobohm@uni-flensburg.de

Caroline Brunel
email: caroline.brunel@ird.fr

Barry J Conn
email: barry.conn@sydney.edu.au

Wayne Dawson
email: wayne.dawson@durham.ac.uk

Michele De
email: michele.dechoum@ufsc.br

Sá Dechoum

Aleksandr L Ebel

Franz Essl
email: franz.essl@univie.ac.at

Ori Fragman-Sapir

Alexandr L Ebel

Trevor Fristoe
email: trevor.fristoe@uni-konstanz.de

Nejc Jogan
email: jernej.jogan@bf.uni-lj.si

Holger Kreft
email: hkreft@uni-goettingen.de

Bernd Lenzner
email: bernd.lenzner@univie.ac.at

Carsten Meyer
email: carsten.meyer@idiv.de

Jan Pergl
email: jan.pergl@ibot.cas.cz

Petr Pyšek
email: pysek@ibot.cas.cz

Alla Verkhozina

Patrick Weigelt
email: patrick.weigelt@forst.uni-goettingen.de

Qiang Yang
email: qiang.yang@uni-konstanz.de

Elena Zykova
email: elena.yu.zykova@gmail.com

Svetlana Aćić

Emiliano Agrillo
email: emiliano.agrillo@isprambiente.it

Fabio Attorre
email: fabio.attorre@uniroma1.it

Ariel Bergamini
email: ariel.bergamini@wsl.ch

Christian Berg
email: christian.berg@uni-graz.at

Erwin Bergmeier
email: erwin.bergmeier@bio.uni-goettingen.de

Idoia Biurrun
email: idoia.biurrun@ehu.es

Steffen Boch
email: steffen.boch@wsl.ch

Gianmaria Bonari
email: gianmaria.bonari@unibz.it

Zoltán Botta-Dukát
email: botta-dukat.zoltan@okologia.mta.hu

Helge Bruelheide
email: helge.bruelheide@botanik.uni-halle.de

Juan Antonio Campos
email: juanan.campos@ehu.eus

Andraž Čarni
email: carni@zrc-sazu.si

Laura Casella
email: laura.casella@isprambiente.it

Maria Laura Carranza
email: carranza@unimol.it

Milan Chytrý
email: chytry@sci.muni.cz

Renata Ćušterevska
email: renatapmf@yahoo.com

Michele De Sanctis
email: michele.desanctis@uniroma1.it

Jürgen Dengler
email: dr.juergen.dengler@gmail.com

Panayotis Dimopoulos
email: pdimopoulos@upatras.gr

Rasmus Ejrnaes
email: rasmus@bios.au.dk

Jörg Ewald
email: joerg.ewald@hswt.de

Federico Fernández-González
email: federico.fdez@uclm.es

Rosario G Gavilán
email: rgavilan@ucm.es

Jean-Claude Gegout
email: jean-claude.gegout@agroparistech.fr

Rense Haveman
email: rense.haveman@wur.nl

Maike Isermann
email: maike.isermann@uni-bremen.de

Ute Jandt
email: ute.jandt@botanik.uni-halle.de

Florian Jansen
email: florian.jansen@uni-rostock.de

Borja Jiménez-Alfaro
email: jimenezalfaro.borja@gmail.com

Ali Kavgacı
email: alikavgaci1977@yahoo.com

Larisa Khanina
email: khanina.larisa@gmail.com

Ilona Knollová

Anna Kuzemko

Maria Lebedeva
email: lebedevamv@mail.ru

Jonathan Lenoir
email: jonathan.lenoir@u-picardie.fr

Tatiana Lysenko

Corrado Marcenò
email: marcenocorrado@libero.it

Jesper Vasiliy Martynenko

Erenskjold Moeslund

Ricarda Pätsch

Remigiusz Pielech

Valerijus Rašomavičius

Iris De Ronde

Eszter Ruprecht

Solvita Rūsiņa

Pavel Shirokikh

Jozef Šibík

Urban Šilc

Angela Stanisci

Zvjezdana Stančić

Jens-Christian Svenning

Grzegorz Swacha

Pavel Dan Turtureanu

Milan Valachovič

Kiril Vassilev

Sergey Yamalov

Mark Van Kleunen

Alexandr L Ebel

Bioinvasions

Ori Fragman
email: ofragman@013.net

Zoltán Botta

Martin Luther

Giuliano Fanelli
email: giuliano.fanelli@gmail.com

• Komarov

Climate and socio-economic factors explain differences between observed and expected naturalization patterns of European

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Species that maintain self-sustaining populations outside their native range independently of direct human intervention (i.e., naturalized species; [START_REF] Richardson | Naturalization and invasion of alien plants: concepts and definitions[END_REF][START_REF] Blackburn | A proposed unified framework for biological invasions[END_REF] pose a serious concern to native biodiversity and ecosystem functioning and services worldwide (IPBES, 2019). Their number has increased substantially over the last few centuries and does not show any indication of saturation [START_REF] Seebens | No saturation in the accumulation of alien species worldwide[END_REF]. Regions differ considerably in their richness of naturalized species of vascular plants, and species vary considerably in their extent of naturalization [START_REF] Pyšek | Naturalized alien flora of the world: species diversity, taxonomic and phylogenetic patterns, geographic distribution and global hotspots of plant invasion[END_REF][START_REF] Essl | Drivers of the relative richness of naturalized and invasive plant species on Earth[END_REF]. Part of this variation may result from regional differences in the size of the potential naturalized alien pool and the size of the range potentially available for naturalized species. Little is known about the relationship of the observed and potential richness of naturalized plant species (i.e. the maximum numbers of alien species that these regions could host given species' environmental tolerances; [START_REF] Stohlgren | The myth of plant species saturation[END_REF].

The actual distribution of naturalized alien plant species results from the number of introductions by humans (intentional or not) followed by the interplay of factors that determine the environmental space available for a species and factors that prevent or promote the extent to which an equilibrium with an environmental space is reached.

Environmental suitability (e.g., climate, habitat) determines the potential (expected) distribution range by filtering the subset of introduced species that can maintain populations over long periods by successfully reproducing, i.e., naturalized species [START_REF] Richardson | Naturalization of introduced plants: ecological drivers of biogeographical patterns[END_REF]. Human activities can further influence the observed distribution range of species by altering environmental conditions and dispersal processes that dictate opportunities for introductions. For instance, human transport, trade and increasing urban development tend to broaden observed ranges, while, conversely, biosecurity responses can contain this expansion [START_REF] Hulme | Trade, transport and trouble: managing invasive species pathways in an era of globalization[END_REF]).

An increasing body of literature is investigating what proportions of species' potential alien ranges are actually occupied [START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF][START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF][START_REF] Strubbe | Niche conservatism among nonnative vertebrates in Europe and North America[END_REF][START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF][START_REF] Liu | Most invasive species largely conserve their climatic niche[END_REF]. Indeed, most alien species are occupying only a subset of the niche corresponding to suitable environments that are occupied in their native range ('niche filling').

Certain alien species are also able to colonize new environments that are not occupied in their native range ('niche expansion'). Patterns of niche filling and niche expansion vary highly depending on the type of organisms. For instance, the average niche filling was found to be 80% for vascular plants considered invasive (i.e., spreading into areas away from sites of introduction; [START_REF] Richardson | Naturalization and invasion of alien plants: concepts and definitions[END_REF], 37% for invasive insects and 20% for invasive birds, whereas the average niche expansion was 26% for birds, 20% for insects and 5% for plants [START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF][START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF][START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF]. Niche changes during invasions appear to be primarily driven by introduction history (e.g., propagule pressure and colonization processes) in birds, and by human disturbance in insects [START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF]. However, little is known about what causes possible differences between observed and expected ranges in naturalized plants.

Much of the research effort has been devoted to understanding the socio-economic drivers of the number of naturalized alien plant species [START_REF] Pyšek | Disentangling the role of environmental and human pressures on biological invasions across Europe[END_REF][START_REF] Van Kleunen | Global exchange and accumulation of non-native plants[END_REF][START_REF] Dawson | Global hotspots and correlates of alien species richness across taxonomic groups[END_REF][START_REF] Essl | Drivers of the relative richness of naturalized and invasive plant species on Earth[END_REF], some of them focusing on the subset of invasive species [START_REF] Essl | Macroecology of global bryophyte invasions at different invasion stages[END_REF][START_REF] Bellard | Major drivers of invasion risks throughout the world[END_REF]. However, studies dealing with alien species richness always face the challenge of disentangling the specific role of socio-economic drivers from that of large-scale biogeographical factors also known to influence species richness, irrespective of species origin (e.g., latitudinal gradient, resource availability). Moreover, while it is recognized that environmental matching between native and alien ranges largely controls naturalization [START_REF] Richardson | Naturalization of introduced plants: ecological drivers of biogeographical patterns[END_REF][START_REF] Feng | Introduction history, climatic suitability, native range size, species traits and their interactions explain establishment of Chinese woody species in Europe[END_REF], focusing on alien species richness does not allow accounting for species-specific environmental requirements. Hence, determining the expected distributional range of naturalized species should be an important step in understanding the influence of socioeconomic factors on observed patterns of naturalization [START_REF] Xu | Human activities have opposing effects on distributions of narrow-ranged and widespread plant species in China[END_REF].

Another advantage of analyzing species composition is that it allows for the identification of the species that explain the pattern of naturalized species richness and their characteristics.

Many other studies have attempted to determine which species' performance or natural distribution traits are associated with naturalization success by comparing naturalized and non-naturalized plant species (e.g., [START_REF] Pyšek | Traits associated with invasiveness in alien plants: where do we stand?[END_REF][START_REF] Van Kleunen | A meta-analysis of trait differences between invasive and non-invasive plant species[END_REF][START_REF] Pyšek | Naturalization of central European plants in North America: species traits, habitats, propagule pressure, residence time[END_REF]. Conclusions from these studies delivered little consensus and often appear to be context-and species-dependent. This might partly be because these studies only investigated trait differences of native versus alien or non-invasive versus invasive species (i.e., a binary variable), or tested for relationships between traits and the observed naturalized range without considering the potential range. Therefore, we believe we can gain additional insight into the drivers of naturalization patterns by searching for traits that explain the extent to which species fill or expand beyond their suitable alien range (i.e., a continuous variable that accounts for the potential range).

Europe is the second-most important donor continent of naturalized alien plant species, after Asia. However, the European flora is by far the most successful in naturalizing. Of the ~14,200 vascular plant species native (i.e. both endemic and non-endemic) to Europe, 3,383 have become naturalized somewhere in the world; this is three times more than expected by chance (van [START_REF] Van Kleunen | Global exchange and accumulation of non-native plants[END_REF]. Furthermore, five of the 10 globally most widely naturalized species are native to Europe [START_REF] Pyšek | Naturalized alien flora of the world: species diversity, taxonomic and phylogenetic patterns, geographic distribution and global hotspots of plant invasion[END_REF]. The European flora is therefore suitable for studying drivers of differences between observed and expected naturalized ranges.

Current knowledge of which region-and plant-related characteristics influence the extent to which species fill their expected naturalized ranges is poor and relies only on the search of the socio-economic drivers of niche/range filling of a few invasive alien species (usually < 50; e.g., [START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF][START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF][START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF][START_REF] Strubbe | Niche conservatism among nonnative vertebrates in Europe and North America[END_REF]. However, the drivers of niche/range filling have never been explored for naturalized species (a much broader group of species than invasives; Richardon et al., 2000); yet the processes driving the ability to survive and reproduce are likely to differ from the processes driving the spread and impact of invasive species (e.g., [START_REF] Abellán | Climate matching drives spread rate but not establishment success in recent unintentional bird introductions[END_REF]. Moreover, the drivers of the difference between observed and expected naturalized regional floras (and not between observed and expected distributions of a few individual species) have never been explored.

In this study, we focused on 1,485 plant species endemic to Europe, an unprecedented number for this type of study, which allowed us to analyse in more detail what explains variation in the differences between observed and expected values. We determined both their current observed distribution in 931 non-European regions using the 'Global Naturalized Alien Flora' database (GloNAF; van Kleunen et al., 2019) and their expected distribution using biogeoclimatic ensemble species distribution models (SDMs). We also explored which socio-economic factors explain why some regions have a recorded naturalized flora of European origin close to their expected naturalized flora, while other regions have not.

Finally, we examined whether species distribution patterns, economic uses and functional traits explain why some species fill a larger portion of their expected range than others do.

Materials and methods

Expected naturalized ranges

Species selection

Many plant species native to Europe are also native to other continents such as Asia and Africa, for which there is usually a lower density (temporal and spatial) of species occurrence records [START_REF] Meyer | Multidimensional biases, gaps and uncertainties in global plant occurrence information[END_REF]. Therefore, we focused on vascular plant species whose native range is restricted to Europe (European endemics), as this allows us to better capture the full realized niche of the species in their native range. The physiography of the European continent was defined as bordered by the Arctic Ocean to the north (Iceland and Norwegian Islands were included, Greenland was excluded), the Atlantic Ocean to the west (the British and Irish Isles were included and the Macaronesian archipelagos were excluded), the Ural Mountains, the Ural River, and the Caspian Sea to the east, and the Caucasus and the Mediterranean Sea to the south (Mediterranean islands were included, Anatolia was excluded).

The database 'Endemic vascular plants in Europe' (EvaplantE; Hobohm 2014), which comprises a list of > 6,200 endemic taxa, was used as a baseline for species selection.

Scientific names were standardized based on a working list of all plant species (The Plant List; TPL; http://www.theplantlist.org/ version 12-10-2018). This taxonomic standardization was done with the R package 'Taxonstand' [START_REF] Cayuela | Taxonstand: taxonomic standardization of plant species names v.2.1. R Foundation for Statistical Computing[END_REF]. Standardized infraspecific taxa were excluded from the list, resulting in 4,965 species (Figure 1).

Compilation of species occurrence records

To comprehensively describe the distribution of the species in Europe (which in addition to the native range might for some species also include part of their alien range), we combined occurrence records from six sources (see Supporting Information Appendix S1 for details and references): the 'Global Biodiversity Information Facility' (GBIF), the 'European Vegetation Archive' (EVA; [START_REF] Chytrý | European Vegetation Archive (EVA): an integrated database of European vegetation plots[END_REF], the 'EU-Forest' dataset, the 'Atlas Florae Europaeae', the 'Plant Functional Diversity of Grasslands' network (DIVGRASS) and the digital atlas of the German flora.

When several occurrence records from these different sources were duplicated on the same cell, only one occurrence record per species was kept to avoid pseudoreplication. Cell size was set to 0.42° × 0.42° (~50 km × 50 km at the equator) to approach the resolution of the source of occurrence records having the coarsest resolution (Atlas Florae Europaeae). Using a higher resolution (i.e., a smaller cell size) would have required to downscale this source of occurrence records, which typically introduces spatial biases and uncertainty in the model predictions (Bonbi & D'Amen, 2012). Moreover, this resolution appeared to be a good compromise to account for the fact that the selected environmental variables (climate, land use and soil type) determine invasion potential at different scales (10,000 to 200 km, 2,000 to 10 km, and 10 km to 10 m, respectively; [START_REF] Milbau | A hierarchical framework for integrating invasibility experiments incorporating different factors and spatial scales[END_REF]. Species with fewer than 10 deduplicated occurrence records were not further considered since the resulting SDM might be inaccurate. The final dataset comprised 135,189 occurrence records for a total of 1,485 European plant species, belonging to 327 genera and 67 families (Table S1), i.e. on average 91 occurrence records per species with a maximum of 1,382 occurrence records for Achillea ptarmica (Asteraceae). We had enough occurrence records to build an SDM (i.e., 10 occurrences) for 272 European species among the 407 already naturalized species and for 1,213 species currently not known to be naturalized anywhere.

Environmental predictors of expected ranges

We defined six environmental variables to model and project species expected ranges. These variables were related to climate, land use, and soil physico-chemical properties, which are commonly recognized to shape the distribution of plants [START_REF] Gurevitch | The ecology of plants, 2 nd edition[END_REF].

Annual mean temperature (°C), annual precipitation (mm) and precipitation seasonality (yearly coefficient of variation) representing the period 1979-2013 were provided at a 30 arcsec resolution by the CHELSA climate database [START_REF] Karger | Climatologies at high resolution for the earth's land surface areas[END_REF]. Worldwide correlations between these variables and the others described below did not exceed the threshold of |r| = 0.70 (Supporting Information Appendix Figure S1) beyond which collinearity begins to severely distort model estimations and subsequent predictions [START_REF] Dormann | Collinearity: A review of methods to deal with it and a simulation study evaluating their performance[END_REF]. However, these variables reflecting trends in average climate conditions were significantly correlated with climate extremes to which plants are recognized to be highly responsive [START_REF] Zimmermann | Climatic extremes improve predictions of spatial patterns of tree species[END_REF]. The percentage of each grid cell with primary land cover based on the Harmonized Global Land Use models was also used [START_REF] Chini | Harmonized Global Land Use for Years 1500 -2100, V1. Data set[END_REF].

Organic carbon content (g per kg) and pH in the first 15 cm of soil were extracted at a 1 km resolution from the global gridded soil information database SoilGrids [START_REF] Hengl | SoilGrids1km -Global Soil Information Based on Automated Mapping[END_REF].

Environmental variables were aggregated (using the mean value) to the resolution of 0.42° × 0.42°.

Species distribution modelling

Comparing the realized niche within the native versus alien ranges can lead to three cases:

1) in the alien range, the species uses a similar or smaller realized niche than in the native range, e.g., because of new competitors, herbivores or pathogens, or dispersal limitation; 2) the species occupies a realized niche very different from the one in the native area but within the species initial fundamental niche, e.g., because of new biotic interactions, multiple sites of introduction, niche differentiation or different environmental conditions; or 3) the realized niche extends outside of the species initial fundamental niche, e.g., because of rapid niche evolution, enemy-release or new positive interactions (see [START_REF] Gallien | Predicting potential distributions of invasive species: where to go from here?[END_REF] for further details). As options 2 and 3 remain impossible to predict for a large number of species, we only considered option 1 in this study.

The expected distribution of the 1,485 European plant species was modelled by statistically relating the environmental predictors to the distribution data in Europe. Six species distribution modelling (SDM) methods including generalized additive models, generalized linear models, generalized boosting trees, maximum entropy, multivariate adaptive regression splines and random forest were used. All of these methods require presence and absence or pseudo-absence/background data (a random subset of the available environmental conditions in the area, i.e., Europe in our case), whose selection can significantly affect predictions if not made adequately. Consequently, we performed a preliminary analysis to identify the most appropriate set of pseudo-absences for each SDM method (Appendix S2). The predictive performance of SDM in Europe was assessed by measuring the area under the receiver operating characteristic (ROC) curve (AUC) and the true skill statistics (TSS; [START_REF] Allouche | Assessing the accuracy of species distribution models: prevalence, kappa and the true skill statistic (TSS)[END_REF]. AUC values can range from 0 to 1, an AUC of 1 indicating a perfect fit, an AUC of 0.5 meaning that predictions from SDM do not differ from random, and an AUC of 0 meaning the SDM is always incorrect. TSS ranges from -1 to 1, where 1 indicates perfect agreement and 0 indicates a random prediction.

To combine the predictive capability of the six SDMs, their projections were subsequently aggregated into an average or consensus projection. To ensure the quality of the ensemble SDM, we only kept the projections for which the accuracy estimated by AUC and TSS were higher than 0.8 and 0.6, respectively, and assembled the selected SDMs using a committeeaverage approach with each SDM was weighted proportional to its TSS evaluation.

Probability maps obtained from the ensemble forecasting projections were then transformed into binary suitable/non-suitable maps using the threshold maximizing the TSS to ensure the most accurate predictions, since it is based on both sensitivity and specificity. The entire species distribution modelling workflow was performed within the 'biomod2' R platform [START_REF] Thuiller | BIOMODa platform for ensemble forecasting of species distributions[END_REF].

Recorded naturalized ranges

The current observed naturalized range of the European flora was obtained through the GloNAF database version 1.2, a recently compiled database of ~14,000 naturalized alien plant species covering 1,029 regions worldwide, corresponding to administrative regions such as countries, states and provinces, and also including 381 islands (van Kleunen et al., 2019). The size of a region ranged from 0.03 km² (Tauna islet of the Gambier archipelago, French Polynesia) to 2,486,952 km² (the Republic of the Sudan plus South Sudan). A total of 407 European endemic species were found as naturalized in at least one of the non-European GloNAF regions.

We explored various definitions of suitability by analyzing what proportion of a region should be suitable for a species to become naturalized in this region. The following definitions were used: at least one suitable cell, 1%, 5%, 20%, 50%, or 100% suitable cells, respectively. For each region, species were classified into: true positives (TP), i.e., species that are both observed and predicted as being successfully naturalized in the region; false positives (FP), i.e., species that have not become naturalized, but are predicted as successfully naturalized; false negatives (FN), i.e., species that are observed as successfully naturalized but not predicted to be naturalized; and true negatives (TN), i.e., species that are neither predicted nor observed to be naturalized in the region. Then, the predicted naturalized species pool was compared to the observed naturalized pool by calculating: 1) the naturalization debt in the broad sense hereafter referred to as 'naturalization debt' (FP/(TP+FP)), i.e., the proportion of predicted naturalizations that are not yet observed either because species are not yet introduced to the focal area (introduction debt) or because they were introduced, but are not naturalized yet (naturalization debt in the strict sense, i.e., sensu [START_REF] Rouget | Invasion debtquantifying future biological invasions[END_REF], which can take several decades or centuries for some taxa; 2) the assemblage sensitivity (TP/(TP+FN)), i.e., the proportion of observed naturalizations that are correctly predicted ; 3) the negative predictive value (TN/(TN+FN)), i.e., the proportion of species that were not predicted to be naturalized and have not become naturalized in the region.

Socio-economic drivers of naturalization patterns

Seven factors were extracted to explain naturalization debt, assemblage sensitivity and the negative predictive value (Table 1). These factors were selected because they provided insights into introduction pathways, human pressures and inventory effort: airport density ('Airports'), seaport density ('Seaports'), number of international treaties relevant to invasive alien species ('Treaties'), human population density ('Population'), proportion of croplands ('Cropland'), human development index ('Development') and species inventory effort ('Inventory'; for details, see Appendix S3). These socio-economic factors were independent of the surface area of the regions. They were available for 526 non-European regions including 17 islands or archipelagos and 509 mainland areas. Regional factors were tested for multicollinearity by computing a correlation matrix based on Pearson's r. Crosscorrelations did not exceed r = 0.51 (between airport and seaport density), which is below the threshold of 0.70 (Figure S3; [START_REF] Dormann | Collinearity: A review of methods to deal with it and a simulation study evaluating their performance[END_REF].

Identification of the drivers of naturalization patterns was based on boosted regression trees (BRTs), a machine-learning method that combines a large number of relatively simple tree models to optimize predictive performance [START_REF] Elith | A working guide to boosted regression trees[END_REF]. The quality of BRT fits was controlled with the coefficient of determination of the regression between estimated and observed values (r 2 ) and the standard error (se). Results were interpreted by looking at the relative influence of the seven regional socio-economic factors to the predictive models (calculated based on the number of times a factor is selected in the model, weighted by its improvement to the overall model) and by considering the partial dependence of the predictions on each factor after accounting for the average effect of the other factors.

Plant features explaining naturalization patterns

To assess which species-level features affect naturalization success, we first compared European species recorded as naturalized outside Europe ('naturalized') and those not recorded as naturalized outside Europe ('non-naturalized'). Eight features including two distributional indices, the economic use of the species and four functional traits were selected: 1) species prevalence in Europe measured as the number of 0.42° × 0.42° cells occupied; 2) the surface area of the species' expected range outside Europe. These distributional indices were used because more widespread species are usually hypothesized to have a greater potential to spread and a higher invasion success [START_REF] Gallien | Global predictors of alien plant establishment success: combining niche and trait proxies[END_REF]; 3) whether the species is used as an ornamental plant or 4) has other economic relevance (e.g., food plant, medicines, materials) according to the World Economic Plants (WEP) database [START_REF] Wiersema | World Economic Plants : A Standard Reference[END_REF]) since the ornamental and economic relevance of a species is thought to be a key predictor of its probability to be introduced and its naturalization success (van Kleunen et al., 2018, 2020); 5) the growth form (i.e., graminoid, non-graminoid herb, shrub or tree), a major determinant of invasiveness [START_REF] Pyšek | Traits associated with invasiveness in alien plants: where do we stand?[END_REF]; 6) mean specific leaf area (SLA), i.e., the ratio of leaf area to leaf dry mass (expressed in m -²•g); 7) mean plant height (in m); and 8) mean seed mass (in g). These last three functional traits represent key axes of plant ecological strategies following the leaf-height-seed (LHS) scheme of [START_REF] Westoby | A leaf-height-seed (LHS) plant ecology strategy scheme[END_REF]. Correlation between LHS traits was |r| < 0.27. Functional traits were extracted from the TRY database [START_REF] Kattge | TRY plant trait databaseenhanced coverage and open access[END_REF]. Linear mixed-effect models (LMMs) were fitted using a phylogenetic generalized least square approach (PGLS) to compare features of naturalized and non-naturalized species while controlling for between-species phylogenetic distances (for details on the phylogeny used, see Appendix S4). As we did not have data on all features for each species (see Figure 6), we ran separate LMMs for each of the eight features. LMMs were performed using the gls() function of the R package 'nlme' [START_REF] Pinheiro | nlme: Linear and Nonlinear Mixed Effects Models[END_REF].

We used LMMs accounting for phylogeny to test whether plant-feature values explain: 1) the relative extent of range filling, i.e., the proportion of suitable regions where a species has become naturalized; and 2) the relative extent of range expansion, i.e., the proportion of unsuitable regions where a species has nevertheless become naturalized. The indices of range filling and expansion that we used are similar to the indices used by Petitpierre et al.

(2012). However, we calculated them in the geographical space instead of in the environmental space because occurrence data on naturalized plants are not evenly comprehensive across regions (which would have been needed to offer a reliable fit of the niches), and when an alien species is reported, we do not always know whether or not it reproduces in the wild (Figure 1).

Results

Socio-economic drivers of naturalization patterns

European endemic vascular plant species have naturalized in 319 non-European regions.

The naturalization debt (i.e., the proportion of species which are not yet naturalized in a particular region but likely to become so, if introduced, given their environmental envelope) ranged from 95 to 100% (mean = 99%) among the 931 non-European regions according to the threshold of one pixel and from 71 to 100% (mean = 99% as well) according to the threshold of 100% of suitable cells (Figure 2). This means that less than 5% and less than 29% of species for which a region is suitable according to the lowest and highest thresholds, respectively, have actually been recorded there. When restricting the analysis to 272 European species already naturalized outside of Europe, the naturalization debt decreased but remained relatively high with values in the range 81-100% (mean = 96%) with the former threshold and 52-100% (95%) with the latter threshold.

The proportion of observed naturalizations that are correctly predicted based on environmental matching (sensitivity) ranged from 0 to 100% for all thresholds and both species sets. However, the average value of sensitivity was two percentage points lower for the full set of species (19-64%) than for the subset of already naturalized species (21-66%).

The average proportion of unsuccessful naturalizations in unsuitable environments (negative predictive value) was between 98.8% and 100% (mean = 99.9%) with the lowest threshold, and between 97.0% and 100% (mean = 99.7%) with the highest threshold for the full set of species. When considering already naturalized species only, the negative predictive value decreased substantially to the range 80.0-100% (mean = 99.4%) in the former case and 83.4-100% (mean = 98.8%) in the latter case. The threshold of 1% of suitable cells offered the best solution for maximizing sensitivity while still having a high negative predictive value when comparing observed and expected naturalized floras. Therefore, we used predictions from this threshold in the subsequent analyses.

Naturalization debt was lower in more developed regions (human development index > 0.7) (Figures 3 and4) with moist and cool climates, including coastal North America, Japan, temperate Australia and New Zealand (Figure 5). Sensitivity increased progressively with the level of development and inventory effort (Figures 3 and4), and reached maximum values in North-East America, the South American Atlantic Forest and the southern Andes, Turkey, the East-Central African mountains, South Africa, Japan, temperate Australia and New Zealand (Figure 5). The negative predictive value was lower in more developed regions (human development index > 0.7), with more treaties relevant to biological invasions (number of treaties > 20; Figures 3 and4), including regions in North America, the southern tip of South America and Africa, most of northern Asia excluding Mongolia, temperate Australia and New Zealand (Figure 5).

Plant features explaining naturalization patterns

Compared to plant species that are currently not known to be naturalized somewhere else [START_REF] Abellán | Climate matching drives spread rate but not establishment success in recent unintentional bird introductions[END_REF]213), those that are naturalized (272) tend to be more widespread in Europe, to have a wider expected range outside Europe, and to have an ornamental or other economic use (Figure 6). There was no significant difference in functional traits between naturalized and non-naturalized species.

On average, species were found to be naturalized in 4.2% of their potentially suitable regions outside Europe (Figure S4). Thirty of the species occupied less than 0.1% of suitable regions and 31 species occupied more than 10% of suitable regions. The species with the most complete range filling was Syringa vulgaris (Oleaceae), native to the Balkan Peninsula and Romania, being currently naturalized in 70% of its suitable regions (Table S2). The average range expansion into regions estimated to be unsuitable was 0.4%. 118 species (43%) exhibited range expansion above 0.1%, but only one species had a range expansion above 10%: Verbascum virgatum (Scrophulariaceae), native to south-western Europe and southern England, and currently naturalized in 10.5% of the regions that were predicted to be unsuitable for it. We found that species performing best at filling their expected range have an ornamental or other economic relevance, a higher SLA, and a narrower expected range than species with a less complete range filling (Table 2). Furthermore, species observed as naturalized beyond their expected range tend to have an ornamental or other economic use and to be less widespread in their native range than species with no range expansion (Table 2).

Discussion

The global geographic pattern of richness in naturalized plant species from Europe is nonrandom as supported by our results, originating from a complex interplay of at least four mechanisms: 1) environmental matching between the native range of individual species and their expected alien range, which largely controls unsuccessful naturalization; 2) the alteration of the environment in the alien ranges by socio-economic activities (after accounting for sampling effort); 3) introduction pressure associated with the economic use of the species; and 4) differences in functional traits (e.g., SLA), which cause some species to more completely fill their expected alien ranges than others.

Accounting for environmental matching to decipher patterns of naturalization

We modelled environmental tolerance of species and then the influence of extrinsic socioeconomic drivers (Figure 1), instead of both together as done in previous studies [START_REF] Essl | Macroecology of global bryophyte invasions at different invasion stages[END_REF][START_REF] Dawson | Global hotspots and correlates of alien species richness across taxonomic groups[END_REF]. This allowed us to separate the effect of environmental matching in explaining the global pattern of richness in naturalized plant species from Europe. We elucidated that the environment alone is able to correctly predict up to two thirds of successful naturalizations (i.e., sensitivity) and 99.9% of unsuccessful naturalizations (i.e., negative predictive value), depending on the method used to compare local expected distributions with regional observed distributions ('upscaling method'; Figure 2). Based on a similar approach, Bellard et al. (2013) showed that even the so-called "world's 100 worst invasive alien species" have a quite restricted expected range, covering mainly Europe and the areas along the Atlantic coast of North America. Thus, it clearly appears that knowing the available suitable environmental space of species is critical to assess the factors that determine their naturalization success.

Our approach indicated that non-European regions are currently occupied by less than 5% of the endemic European plants for which the area, or parts of it, would be suitable (Figure 2). Therefore, all regions have an enormous naturalization debt. This debt suggests that many endemic European plants have not been introduced outside of Europe yet or that they still have not overcome the biotic barriers provided by herbivores, pathogens and native competitors or the lack of important mutualists. Nevertheless, the large environmentally SDMs are increasingly used as a basis to implement biosecurity policies, e.g., by drawing up watch lists or lists of undesirable species (e.g., [START_REF] Padayachee | Prioritising potential incursions for contingency planning: pathways, species, and sites in Durban (eThekwini), South Africa as an example[END_REF]. As biosecurity measures are usually taken at a regional scale while SDMs predict expected distributions at smaller scales, it is critical to determine which portion of a region should be suitable for an alien species to become naturalized, and hence, of concern. Our retrospective approach comparing SDM outputs with the current naturalized flora from Europe in 931 non-European regions showed that a threshold in the order of 1% of a focal region offers a good trade-off between maximizing correctly predicted successful and unsuccessful naturalizations (Figure 2). Nevertheless, it may be preferable to choose a lower threshold with the precautionary principle, and this threshold might change when using a different spatial resolution.

Socio-economic drivers explaining differences from expected patterns of naturalization

Our results revealed that naturalization debt mostly decreases with the level of development (Figures 3 and4), which means that a higher proportion of species with the ability to become naturalized are observed as such in more developed regions. In these regions, the distribution of naturalized species is typically closer to an equilibrium with the environment. Surprisingly, unlike other studies [START_REF] Dawson | Global hotspots and correlates of alien species richness across taxonomic groups[END_REF][START_REF] Tingley | Integrating transport pressure data and species distribution models to estimate invasion risk for alien stowaways[END_REF], proxies of international transport (i.e., density of airports and seaports in our study) did not explain naturalization debt (Figures 3 and4). Nevertheless, we found that regions with the lowest naturalization debt are all either coastal or island regions (coastal North America, Algeria, Japan, temperate Australia and New Zealand; Figure 5). As a result, although naturalization debt seems little influenced by the density of seaports, it is likely that the volume of maritime traffic, or at least the presence of seaports, does play a significant role by increasing the rates of species introductions. One might argue that this pattern also reflects that coastal regions are usually more strongly developed than more inland regions as a consequence of the increasing demand for infrastructures to sustain residential, commercial and tourist activities (Figure S2), which offers more opportunities for introduction and naturalization of alien plants in coastal regions [START_REF] Gallardo | The importance of the human footprint in shaping the global distribution of terrestrial, freshwater and marine invaders[END_REF]. We found that naturalization debt was higher for the full set of 1,485 European species (either already naturalized or not yet naturalized) than for the subset of 272 species already naturalized, which are more likely to have overcome dispersal barriers (Figure 2). This suggests that introduction pathways influence naturalization debt although, unfortunately, it remains difficult to assess by how much.

This result is in line with

In addition to the influence of development and potentially of introduction pathways on naturalized range filling, sensitivity was also found to be affected by the magnitude of inventory effort (Figures 3 and4). Specifically, regions with the highest quality record of native plant richness also tend to have more records of alien plants. This is also corroborated by [START_REF] Dawson | Global hotspots and correlates of alien species richness across taxonomic groups[END_REF], and indicates that the geographic coverage of reported plant naturalizations remains unevenly exhaustive across regions so that our findings might be significantly influenced by biases in recording effort. In contrast, the negative predictive value decreased in regions with more treaties relevant to invasive alien species (Figures 3 and4). This most likely does not indicate that treaties promote invasions, but that it is more likely that a region adopts a treaty when it has many invasive species. The effectiveness of these relatively recent treaties in preventing new invasions can only be assessed in the future.

Unexpectedly, human population density and the proportion of cropland had a relatively low contribution in explaining the global pattern of naturalization. Contrary to this, high human population densities are thought to influence the likelihood of an introduced species becoming naturalized and spreading through human impacts on the environment [START_REF] Essl | Socioeconomic legacy yields and invasion debt[END_REF][START_REF] Pyšek | Disentangling the role of environmental and human pressures on biological invasions across Europe[END_REF]. Similarly, intensive agriculture (associated with historical sowing or planting of now naturalized species and associated weed-seed contaminants) is largely recognized to be a major cause of new introductions of naturalized and invasive species [START_REF] Bellard | Major drivers of invasion risks throughout the world[END_REF][START_REF] Perrings | How to manage biological invasions under globalization[END_REF][START_REF] Seebens | Global trade will accelerate plant invasions in emerging economies under climate change[END_REF]. A potential explanation for the low contributions of population density and the proportion of cropland in driving patterns of naturalization could be its redundancy with the proportion of primary land cover used as environmental variable in SDMs since urbanization and agriculture are largely responsible for land conversion [START_REF] Chini | Harmonized Global Land Use for Years 1500 -2100, V1. Data set[END_REF]. Although this redundancy makes it difficult to isolate the effect of human population density and agriculture, we believe the introduction of primary land cover in SDMs was critical in this study to distinguish plants that are drivers and passengers of human-induced disturbances (MacDougall & Turkington, 2005). Another possible cause for the low contribution of agriculture is the ancient human colonization history of Europeans who used to transport cultivated plants across continents while other regions only recently opened up to international movements of plants (di Castri, 1989). In this perspective, most of the plants used in agriculture and associated weeds endemic to Europe with the potential to become naturalized might have already largely spread worldwide [START_REF] Monnet | Historical legacies and ecological determinants of grass naturalizations worldwide[END_REF].

Plant features explaining differences from expected patterns of naturalization

The average score of alien geographic range filling of naturalized plants from Europe was 4.2%. This might appear to be very low compared to percentages of environmental niche filling reported in other studies [START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF][START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF][START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF][START_REF] Strubbe | Niche conservatism among nonnative vertebrates in Europe and North America[END_REF][START_REF] Liu | Most invasive species largely conserve their climatic niche[END_REF]. However, it should be noted that it is easier to fill a niche than to fill all locations that have that niche. None of our species had a range filling above the commonly used threshold of 90%. Similarly, no invasive birds showed more than 90% of their native niche filled in the invasive range [START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF]. However, no less than 52% of invasive plants [START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF], 32% of 22 insects [START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF] and 10% of vertebrates [START_REF] Strubbe | Niche conservatism among nonnative vertebrates in Europe and North America[END_REF] had a niche filling above 90%. Moreover, only one naturalized plant species from Europe out of 272 had a range expansion above the commonly used threshold of 10%, while it was the case for the niche expansion of 55% of invasive insects [START_REF] Hill | A global assessment of climatic niche shifts and human influence in insect invasions[END_REF], 29% of birds [START_REF] Strubbe | Niche conservatism in non-native birds in Europe: niche unfilling rather than niche expansion[END_REF], 17% of vertebrates [START_REF] Strubbe | Niche conservatism among nonnative vertebrates in Europe and North America[END_REF] and 14% of invasive plants [START_REF] Petitpierre | Climatic niche shifts are rare among terrestrial plant invaders[END_REF].

We found that SLA was positively correlated with range filling of naturalized plants from Europe (Table 2). According to the LHS scheme of [START_REF] Westoby | A leaf-height-seed (LHS) plant ecology strategy scheme[END_REF], SLA is a proxy for rapid growth and an acquisitive resource-use strategy, which would be typical of resource-rich and/or disturbed environments, both of which have become more common in the last centuries due to human activities. In the competitor/stress-tolerator/ruderal (CSR) framework of the universal adaptive strategy theory [START_REF] Grime | Evidence for the existence of three primary strategies in plants and its relevance to ecological and evolutionary theory[END_REF], rapid growth is a key characteristic of strong competitors, suggesting that strong competitors for light and nutrients are also filling their naturalized ranges faster. Indeed, [START_REF] Guo | The role of adaptive strategies in plant naturalization[END_REF] recently showed that species with high scores on the competitor axis were more likely to naturalize. Thus, it seems very consistent that having a high SLA represents a key strategy in regions subject to intensive development associated with rapid, deep and widespread anthropogenic perturbations. SLA should therefore also indicate potential for faster expansion towards the equilibrium range in alien regions. This corroborates previous results showing that SLA is higher for naturalized and invasive species compared to non-naturalized or native species (van Kleunen et al., 2010; [START_REF] Pyšek | Traits associated with invasiveness in alien plants: where do we stand?[END_REF][START_REF] Pyšek | Naturalization of central European plants in North America: species traits, habitats, propagule pressure, residence time[END_REF].

Interestingly, seed mass was not significantly related to range filling (Table 2). This trait can have contrasting effects on patterns of naturalization since large seeds have greater nutrient reserves, which increases the chances to become naturalized, but small seeds are beneficial for long-distance dispersal and therefore favour spread [START_REF] Crawley | Comparative ecology of the native and alien floras of the British Isles[END_REF][START_REF] Moodley | Different traits determine introduction, naturalization and invasion success in woody plants: Proteaceae as a test case[END_REF]. This suggests that it is not a species' dispersal ability or the ability to settle in new regions that mainly drive naturalization but the ability to be transported by humans for aesthetic or economic values. Our results showed that species used by humans are indeed more frequently naturalized (Figure 6), and perform better at filling (e.g., Syringa vulgaris) and expanding (e.g., Verbascum virgatum) their potential range than species not used by humans (Table 2). Ornamental horticulture, agriculture and forestry are recognized as major pathways of alien plant introduction. For instance, it has been estimated that at least 75% and 93%, respectively, of the naturalized alien plants worldwide are grown in domestic and botanical gardens (van Kleunen et al., 2018), and plants with a known economic importance are 18 times more likely to be naturalized somewhere in the world (van Kleunen et al., 2020).

Possible reasons include: economic importance increases the number of releases and/or the number of individuals released (i.e., propagule pressure), while human selection favours traits related to invasiveness (e.g., ease to grow and reproduce, early and long flowering period, low susceptibility to insect pests or pathogens). Moreover, we found that the same set of distributional features explains whether or not species are naturalized and the extent of naturalized range filling and geographic expansion of species range (range filling and expansion were significantly correlated; r = 0.61, P-value < 0.001), but in opposite directions. Indeed, naturalized species tend to be more widespread in their native range and to have wider expected alien ranges than non-naturalized species, i.e., they are typically generalist species [START_REF] Gallien | Global predictors of alien plant establishment success: combining niche and trait proxies[END_REF]. In contrast, naturalized species with the most complete range filling and broadest range extension tend to have more limited expected alien ranges and to be less widespread in their native range, respectively. This result needs to be interpreted with caution since it can simply arise from a numerical artefact as it may be easier to fill a small expected range than a large one. Another possible cause could be that SDMs tend to be more accurate for specialist species than for generalists [START_REF] Connor | Effects of grain size and niche breadth on species distribution modeling[END_REF]. Furthermore, range filling depends on opportunities to disperse, so species with a wider expected alien range may basically have less chance to fill it. Finally, more narrowly distributed endemics can surprisingly have a greater range expansion if their observed distribution in the native range results from biogeographical (e.g., the Mediterranean Basin, the Alps in Europe) or from biological interactions rather than from climatic barriers. In that case SDMs would fail to fit their fundamental climatic envelope due to niche truncation [START_REF] Bush | Truncation of thermal tolerance niches among Australian plants[END_REF]. It could also be that their current distribution is matching their climatic niche, but that this distribution is not correctly reflected in data sources, maybe because they mostly inhabit under-sampled regions. Consequently, the projected expected alien ranges may underestimate the true potential ranges.

Conclusions

Our findings indicate that the environment largely controls the expected naturalized range of European plants. We demonstrated that increased anthropogenic disturbance associated with human development as well as increased probability of introductions associated with international exchange primarily explain the extent to which species spread within their expected naturalized range. We showed that plants selected for ornamental and other economic purposes perform better at filling and expanding their range, most likely because of increased introduction pressure and a preference for cultivating plants with traits that also make them more likely to naturalize. We revealed that species with functional traits indicative of rapid growth and acquisitive resource use tend to fill their range more completely than species with slower responses. These findings give a new overall picture of the drivers of naturalization that can help plan future studies on the macroecology of alien species as well as in designing future biosecurity plans. As harmful invasive species emerge from the pool of naturalized species, the analysis of which species could naturalize is a first step in identifying species that could ultimately become invasive in a region. Naturalization debt refers to the proportion of predicted naturalizations that are not yet observed, sensitivity to the proportion of correctly predicted successful naturalizations and negative predictive value to the proportion of correctly predicted unsuccessful naturalizations.

A region was considered suitable if it contained at least one suitable pixel, 1% suitable cells, 5%, 20%, 50%, and 100%. are not yet observed, sensitivity to the proportion of correctly predicted successful naturalizations and negative predictive value to the proportion of correctly predicted unsuccessful naturalizations. Socio-economic factors are sorted by mean relative influence over the three metrics. These results are for the upscaling method '1 %' i.e., a region was considered suitable for a species if it contained at least 1% suitable cells. between the most contributing regional socio-economic factors and differences between observed and expected European naturalized floras. Naturalization debt refers to the proportion of predicted naturalizations that are not yet observed, sensitivity to the proportion of correctly predicted successful naturalizations and negative predictive value to the proportion of correctly predicted unsuccessful naturalizations. Black dots represent empirical data points. These results are for the upscaling method '1 %' i.e., a region was considered suitable for a species if it contained at least 1% suitable cells. predictive value to the proportion of correctly predicted unsuccessful naturalizations. These results are for the upscaling method '1 %' i.e., a region was considered suitable for a species if it contained at least 1% suitable cells.

  suitable ranges outside of Europe confirm that European plants have a considerable potential of naturalization outside their native range (van Kleunen et al., 2015; Pyšek et al., 2017), once they have overcome dispersal barriers and biotic resistance. Our results therefore indicate that it is unlikely that the number of new naturalizations will soon have reached its peak.

  [START_REF] Pyšek | Disentangling the role of environmental and human pressures on biological invasions across Europe[END_REF] and[START_REF] Dawson | Global hotspots and correlates of alien species richness across taxonomic groups[END_REF], who found that human impact (represented by proxies like wealth and per capita GDP, respectively) play a leading role in driving the global patterns of animal and plant naturalizations. One explanation is that economic wealth is often associated with alien species introductions and with profound alteration of natural habitats, which benefit alien species establishment and growth[START_REF] Macdougall | Are invasive species the drivers or passengers of change in degraded ecosystems[END_REF][START_REF] Seebens | Global trade will accelerate plant invasions in emerging economies under climate change[END_REF].

Figure 1

 1 Figure 1 Workflow of this study used to determine which features of both plants and recipient

Figure 2

 2 Figure 2 Comparison of predicted and observed naturalized floras in 931 non-European

Figure 3

 3 Figure 3 Relative influence of seven socio-economic factors in explaining differences

Figure 4

 4 Figure 4 Joint partial dependence plots of interactions fitted by boosted regression trees

Figure 5

 5 Figure 5 Global maps of the differences between observed and expected European

Figure 6

 6 Figure 6 Difference in distributional, economic and functional features between European

Acknowledgements

Robin Pouteau was supported by the National Natural Science Foundation of China (grant number 31901176) and Taizhou University (2018YQ001). Carsten Meyer acknowledges funding by the Volkswagen Foundation through a Freigeist Fellowship (A118199), and additional support by iDiv, funded by the German Research Foundation (DFG-FZT 118, 202548816). Petr Pyšek and Jan Pergl were supported by the Czech Science Foundation (EXPRO grant 19-28807X) and the Czech Academy of Sciences (long-term research development project RVO 67985939). Idoia Biurrun and Juan Antonio Campos were supported by the Basque Government (IT936-16). Gianmaria Bonari, Milan Chytrý, Ilona Knollová, Anna Kuzemko and Corrado Marcenò were supported by the Czech Science Foundation (19-28491X). Rosario G. Gavilán was supported by Madrid Government project REMEDINAL (P2018/EMT-4338). Jens-Christian Svenning considers this work a contribution to his VILLUM Investigator project "Biodiversity Dynamics in a Changing World" funded by VILLUM FONDEN (16549). Mark van Kleunen was supported by the German Research Foundation DFG (264740629). We appreciate the helpful comments by three anonymous referees and the Handling Editor, Melodie A. McGeoch.

Data availability statement

The data used to build the species distribution models (occurrence records and environmental variables) came from openly accessible repositories cited in the manuscript


Loic Kessous

GESTURAL CONTROL OF SINGING VOICE, A MUSICAL INSTRUMENT

This paper describes research and experiments concerning digital musical instruments based on gestural control of singing voice synthesis. The purpose is to choose and use a two-handed control, a synthesis model and an adequate mapping strategy to allow an expressive pitch control and the articulation of the vowels. A visual feedback is provided to help the performer. By using different models, different aspects of synthetic singing voice as naturalness, expressiveness and vocal identity are explored in relation with gestural control. Several controllers have been tested to achieve a choice of controllers for the musical functionalities needed in this instrument.

INTRODUCTION

Today the composer can not only write notes, nuances and instrumental techniques, but also timbres and spectral evolutions. The performer can play, interpret, and possibly improvise the sound itself. One musical esthetic choice can be to not privilege pitch instead of spectral consideration or inversely but to find a way to have an optimized control for their cohabitation. A vowel singing voice synthesizer is a typical example of such a configuration: controlling the pitch precisely, modulating it expressively and modifying spectrum characteristics to articulate the vowels. Expressive gestural control of Singing voice synthesis is a challenge in itself but can also be a model for other digital musical instruments dealing with spectrum manipulation and expressive melodic phrasing.

SINGING VOICE SYNTHESIS

Since the beginning of voice synthesis some distinctions between singing voice synthesis and speech synthesis has been done. One of the more evident characterizations of the singing voice is the use of vibrato. Sound examples from the beginning of voice synthesis, like the Voder's demonstration, or Max Mathews's synthesis of "bicycle for two" [START_REF] Mathews | Bicycle built for two[END_REF] illustrate it evidently. A very popular synthesis method for voice is the source-filter method. The source models the vocal cords vibration and the air's flow turbulences. The filter models the vocal tract's resonances. The filter induces a formant structure to the spectrum, which is changing from a vowel to another. Sundberg has suggested the presence of a supplementary formant, "the singer formant". A lot of implementation structures are possible for voice synthesis. Choosing a particular one is a very discussed subject. One can use a high order filter, a bank filter (in cascade, parallel or lattice form), FOF or FM [START_REF] Mathews | Current Directions in Computer Music Research[END_REF] and many others. When filters are used one can use also different implementations for the voiced source. One can use a sawtooth signal, a Dirac pulse train, a glottal signal model (LF, R++ [START_REF] Veldhuis | A computationnally efficient alternative for the liejencrants-Fant model and its perceptual evaluation[END_REF] ) or a Physical model of glottis (mass string model). I will not try to define which of this implementation is better than another; I think it depends more on the musical application than in the intrinsic characteristics. Different implementations are presented here to explore different aspects of real-time control of singing voice. In particular, I am trying to link gesture to aspects like expressiveness, naturalness and "vocalness".

EXPRESSIVENESS, NATURALNESS AND

"VOCALNESS"

Concept and definition

Expressiveness is the capacity to express something. It can be an emotion, a sentiment, a message and probably many others things. Design of digital instrument must allow enough flexibility and precision to allow performers to introduce nuances in their play with the most possible precision. We need the best time and data precision to have an expressive control, and particularly for continuous control. This is depending on the choice or design of controllers, the choice or implementation of communication tools and protocols between controllers and computer (even if there is other hardware possibilities) and also, and that is maybe the most important one, choice and implementation of a mapping strategy. One can also use the term 'expressiveness' to suggest the ability of an instrument to be used to play different styles of music. That can mean different tone scales, tempered or not, microtonal or just scales, but also different styles, different ways to articulate the whole phrase in term of time, energy or spectrum. In this case expressiveness is correlated with the capacity for an instrument to allow the performer to adapt his/her play to a context.

Naturalness is the attribute which quantifies the possibility of a voice heard to be a human real voice or a synthesized voice. One can also evaluate if the voice is near from a analyzed voice.

'Vocalness' can be defined as a signature of the voice, a vocal identification factor, which let us say if what we heard is a voice (natural or synthetic) or not. A Theremin has an expressiveness near to the expressiveness of the voice but we can perceive a difference related to the absence of formant and maybe more precisely formant articulation (a dynamic process). This signature is also present in the framework of audio effects. A wah-wah pedal, connected to a guitar, makes it sing by using a filter (depending of the implementation it can be just one filter, two or three filters modulated in one dimension of articulation). A simple model using only three filters can be perceived as a singing voice but will not if the articulation is not properly done, in this case one will perceive three filter changing of center frequency instead of a vowel articulation. It sometimes sounds like a diphonic singer and shows the importance of the interaction between sound perception and gestural control.

Experimenting different aspects with different synthesis models

The first model is made of a sawtooth signal filtered by three second-order filters in cascade. This implementation illustrates the robustness of the vocalness in term of vowel perception; three formants are enough to identify product of spectral response of filters as vowels. It also shows the importance of continuous control of pitch in singing voice and the importance to access by gesture to a precise and fine control, not obligatory by separating drastically the generic note (as a MIDINOTE message generated by a keyboard) and the pitch modulation (as the PITCHBEND message generated by a pitch wheel). A precise continuous pitch control is essential to reproduce singing voice expressiveness.

The second model is made of 5 FOFs. I chose to use FOFs principally because the Max/MSP CHANT Library provides externals to link by rules fundamental frequency and formant frequencies. The choice was also done to use easily the dictionary of 5 formants values for soprano singer. Another Max external allows the emulation of a vocal effort. As it reproduces and adds transformation to real voice spectrum analysis this implementation is, in a first step, the best candidate to have a natural singing voice.

The third model is made of a R++ glottal source model connected to a filter bank. With this model I can connect gesture to open quotient, asymmetry coefficient, and release time of the glottal pulse, which have spectral implications and are expressive control parameters. With this implementation we can focus separately on expressiveness factors related to the glottal source and to the vocal tract. Actually, an interaction between the vocal tract and the glottal source should be taken in consideration but can be taken apart in a first time.

DESIGN OF A MUSICAL INSTRUMENT

Mapping strategies

With acoustical instruments, designers try to find the best compromise between the abilities of human body and the physical constraints due to acoustic sound generation. The gestures used on acoustical instruments strongly depend on the physical properties of the instrument. Digital musical instruments don't have physical constraints due to the sound generation: the designers of such instruments are free to choose the gestures they want and to choose the way they want to link these gestures to the sound. This link, usually called the mapping, represents an important field of research in computer music [START_REF] Hunt | Mapping performance parameters to synthesis engine[END_REF]. Although a mapping strategy should be considered as a whole, I will first consider the articulation parameters, the pitch and the loudness as completely separable variables. The model of mapping used is a three layer based on considerations related to perception [START_REF] Arfib | Strategies of mapping between gesture parameters and synthesis model parameters using perceptual spaces[END_REF].

Mapping Strategy for pitch control

To control the pitch in a large register, a circular and incremental strategy is used. To allow control within one oc-tave and from one to the other, we divide the tablet's active space into 12 sectors (12 equal angular parts where each part corresponds to a semitone of the chromatic scale). One can find here a metaphor also used in the literature to describe pitch perception. The transition between two sectors is continuous but not mandatory linear. The user can specify the power of transition (figure 1). This facilitates gestures such as portamento or vibrato because tuning control is more powerful on limits of the angular sectors, according to the transition power set by the user. Using a non-linear transition helps for vibrato and others pitch modulation gestures. The pitch control is continuous and circular, turning clockwise changes pitch from low to high. Crossing the origin in the positive direction allows controlling the pitch in the higher octave. Inversely, crossing the origin in the negative direction allows controlling the pitch in the lower octave. This possibility is only active when the middle button of the joystick is pressed; this prevents to have a non-desired octave jump. The user can also go from a note to its lower or higher octave by pressing the stylus lateral button up or down. One can also use the left and right joystick buttons located under the thumb. The first mapping step is to define, in which of the twelve angular parts is the pen. Then we look if it is more or less centered on it. Finally we need to know how many turns have been made around the center of the tablet. I have tried to respect the natural relation between distal-to-proximal consideration and precision needed. This pitch control strategy allows, for example, to make a glissando with a large range and to finish his gesture with a vibrato. This is not so easy, actually quasi-impossible, with a keyboard and a pitch modulation wheel but that's a musical gesture currently used by singers (and also other instruments). Jitter of fundamental frequency can also be controlled, for example by using the rotation axis of the joystick. One can also map jittering amplitude with the inverse of the force pressure applied on the stylus, related to the catch intensity of the stylus. This can be measured with a FSR pressure sensor fixed on the stylus.

Mapping Strategy for articulation control

When one wants to articulate between two vowels, the most evident way to do is to change the formant frequencies from a vowel to another. In some case one can observe that the "road" used can sound non-natural. A natural way is to articulate by acting on two dimensions related to tongue hump position and degree of constriction of the vocal tract [START_REF] Flanagan | Speech Analysis, Synthesis, and Perception[END_REF]. This is done by using a 2 dimensional navigation by the way of an interpolator where lists of parameters associated to vowels are adequately positioned in the interpolation plan.

Figure 5. Vowel articulation by using 'weighted' interpolation

The first step is to choose key vowels and to position them in the interpolation plan, the second step is to define the rule of interpolation, which can change radically the expressiveness when gestural control is used, the last step is to connect sensors or peripherals to the dimensions of the interpolator. General formulae for interpolation between two lists of parameters must express a resulting list in function of the others and the weights associated to each Figure 6. Pitch control Visual feedback for the Voicer of them. Using a lot of vowels don't seem to be very important but a neutral vowel at the center of the space seems to be useful.

VISUAL FEEDBACK

In digital musical instrument the Sensory Feedback channels are generally broken. Sensory feedbacks, haptic or visual, enhance the capacity of regulation and the emotional immersion of the performer. Haptic feedback is probably fundamental but requires a complete study and an adequate technology. I chose to focus here on the relation between sound and visual feedback and their implication in information affluence considerations. I hope Visual feedback can help, first for beginners and later for more expert users at the level of the cognitive processes.

Pitch control visual feedback

A visual feedback is provided for the pitch control part of the Voicer. 12 angular sectors appear in different blue intensities to be seen individually. The sector pointed by the stylus is lighted by a red component; the red intensity depends on the pressure; so, it is linked with loudness. The radius of the disc (made by all the sectors) depends on the number of turns done; so, it is linked to the octave played. The goal is to transmit to the user the most of pertinent information with the less of perception 'bandwidth' usage.

Vowel articulation visual feedback

In order to not introduce an important asymmetry in the visual feedback compared to the asymmetry in the gestural control, the articulation of vowels should also represented. One could suggest to use two screens or to separate the screen in two parts. In this case we could have one visual feedback for the pitch control and loudness and another for vowel articulation.

I have experiment to replace the circle by an ellipse and to map the 2 radius of the ellipse to vowel articulation but it is not conclusive because of the confusion with the variation of the radius due to octave representation. However, an adequate common representation could be interesting, particularly if it could reflect linkage in the sound domain.

CHOICE OF CONTROLLERS

Currently, we are studying the use of different types of controllers to achieve control functionalities needed in the design of this instrument. These controllers are a touch screen, a tactile surface, a graphic tablet, and a pen-based touch screen. The touch screen is used with a glove equipped with FSR pressure sensors at the extremities of fingers to allow, as the others peripherals used for the preferred hand, the use of the pressure applied. The first involved consideration is the catch of an object or not. This consideration implies two sub-considerations: to catch an object (here, a stylus) for pointing and to use the fingers in cooperation to manipulate it precisely (in particular, using the thumb-index pliers).

A tactile screen or a tactile surface allows pointing with whichever finger, in a monophonic implementation, or a polyphonic one, if the surface is a multi-point sensing device.

Direct or indirect interaction

Another consideration is the direct or indirect relation between manipulation and visualization. The visual feedback can be projected on the screen front of the user, or one can use a pen-based touch screen. Making a choice between these two controllers is a part of more general problem, which is the realization of a specific task, induced by the mapping strategy, based on efficiency, functionality and sensory considerations.

With a touch screen, or a pen-based touch screen, the visual feedback and the gesture have the same localization. For the others controllers the user can't look simultaneously at the visual feedback and at his own gestures.

Other considerations

Although these peripherals are different, they are used for the same functionalities. I have experimented here the Figure 8. Visual feedback with direct interaction using a stylus, and a tactile screen with a data glove with finger pressure sensors way to do the adequate choice of a peripheral for a specific function and more precisely for a specific musical function. A tactile screen doesn't seem to provide a precise enough position sensing but has the advantage to allow the use of all the fingers and to provide a common localization for gestures and visual feedback. A common localization tablet is stimulant but leads to a problem due to an asymmetry of visual feedback, which tends to focus the attention of the user to pitch control instead of providing a good compromise between pitch control and vowel articulation. The use of a tablet for the non-preferred hand seems to be inadequate because of the lack of proprioceptive feedback and the absence of spring-loaded return to a neutral position. Using symmetric functionalities is also in contradiction of models of asymmetric bimanual motor behavior [START_REF] Guiard | Asymmetric division of labor in human skilled bimanual action: The kinematic chain as a model[END_REF].

Figure 9. 'tablet+tablet' version of the Voicer

My first conclusion is to note the fact that as some of this controllers can be used as expressive musical controllers. They can fit to the functionalities needs for pitch control strategy used in this singing voice instrument. My second conclusion is to note that none of them is really perfectly adequate for this task but experimenting with them has provided good indication to build a specific controller including eventually an haptic feedback.

COMPOSITION, INTERPRETATION AND IMPROVISATION: TOOLS FOR EVALUATION

The better evaluation of a new musical instrument is to make music with it. I would like this kind of new instrument could preserve the possibility to improvise in many musical contexts as the voice or a violin, two very expressive musical instrument, can play indifferently different musical scales or music styles. In "phrasing" music: there is usually a level where one can hear entities named phrases, and in this sense interpretation would be inside a phrase, while improvisation would be at the level of the construction of phrases and their connections. Moreover one could say that interpretation is an "In-time" process, while improvisation needs an "Out-of-time" (figure 10).

Figure 10. implications of composition, interpretation and improvisation in music

At the beginning of the learning process of a musical instrument, a tonality can sometimes be privileged. This is particularly true for autodidact musicians. For example, E major is intensively used in guitar blues musical works from pioneers of the Delta blues. Composition contributes evidently to the evolution of a musical instrument but can also have some implications in the evaluation and the modification of its design. I have written a musical work named "d'ici et d'ailleurs" which version evolve continuously in parallel to the evolution of this singing voice instrument (named the Voicer).

The three movements of this musical work are in the same tonality but each of them is in a particular mode (see figure 11). Other secondary modes are also used inside each movement. Playing different modes based on the same tonality is a easiest way to evaluate the pitch control than playing different tonality. However, I have also used the Voicer in another tonality in a musical works of Daniel Arfib named 'route 729'. Different parts of this musical work offer a diversity of styles from rhythmic to arrhythmic, and from elementary sound object manipulation (glottal impulse at sub-audio frequencies with delay lines and others digital audio effects). As this a composition by itself this musical work is also a tool for improving the design of the instrument and specially the mapping used.

The Voicer has been used in several concerts and situations. First interpreted with a acoustic band composed of a guitar, a darbouka and a flute, it has been played in a second configuration with a electric band composed of a guitar, a bass, an electronic (or acoustic) saxophone and a drummer, in a third configuration with a an electronic percussion with a gesture controlled processing and a tape, and finally with a fourth configuration composed of a digital piano, an bass, an electric saxophone and a tape. Along this performance the musical work 'D'ici et d'ailleurs' has been rearranged and modified according to the evolution of the instrument, the context, and of course, my time of practice.

FUTURE AND RELATED WORKS

The work presented here is a part of a more general work on bimanual digital musical instruments. Three others bimanual instruments have been created including the Scangloves [START_REF] Kessous | The Scangloves: a video-music instrument based on Scanned Synthesis[END_REF], a granular scrubber-sampler controller and a guitar inspired controller. One of the goals of these realizations is to explore manual and bimanual mapping strategies for specific musical purpose. Elements of this work can also have implications to vocal-related digital audio effects and to their gestural control, a first example of this has been presented in [START_REF] Arfib | Gestural Strategies for Specific Filtering Processes[END_REF]. Another interest of digital instrument is the interaction with the computer and the possibility to use algorithmic but gesture controlled accompaniment as it has been used sometimes used in performance with a special version Voicer. Most of expressive features for secondary voices should then be specified by rules instead of being driven directly by gesture and suggest the necessity of a more extensive work on this point. A more powerful version of this instrument can probably be made by extending and improving concepts used in the work presented here and by extracting the better of the controller configurations experimented. I hope this instrument to be a tool for analysis of expressiveness and other aspects of voice as one can use 'Analysis by synthesis' of sound.

CONCLUSION

This work has provided a musically usable expressive instrument based on singing voice synthesis. It has also pointed on the importance of the relation between perception, mapping strategy and design or choice of controllers to make an effective musical instrument. Using alternate controllers and not controllers which imitates acoustic instruments can fit better to functionalities needed but, as they can not benefit from previous experiences of design, one should take care of sensory perception and motor behavior.

Figure 1 .

 1 Figure 1. 'Joystick+Tablet' version of the Voicer

Figure 2 .

 2 Figure 2. A three layer mapping chain digital instrument design

Figure 3 .

 3 Figure 3. Mapping used for pitch control

Figure 4 .

 4 Figure 4. Vowel articulation by using 'surfacic' interpolation

Figure 7 .

 7 Figure 7. Pitch and articulation control 'combined' Visual feedback

Figure 11 .

 11 Figure 11. The three modes used in the musical musical work 'D'ici et d'ailleurs'


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