2.1 sPlot and GloNAF databases

We used the sPlot database, which contains vegetation plots across the globe in which composition and abundance of plant communities were recorded (www.idiv.de/splot; Bruelheide et al., 2019). To identify alien species in the plots, we matched the sPlot database with the GloNAF database (van Kleunen et al., 2019). We focused on neophytes, defined as species that were introduced after the year 1492 in the respective regions. The GloNAF database contains lists of alien species for non-overlapping regions (countries or regions within countries) across the world. We could thus match all plots from sPlot with a region of GloNAF, and label the alien species in the plots. Species that were not labelled as “alien” were labelled as “native”.

2.2 Plot selection

We selected plots that had geographic coordinates because these could be linked to a GloNAF region, and that were classified as “forest” (i.e., with a minimum tree layer cover of 25%). It could be that some of the trees in the plots were planted. Unfortunately, we did not have detailed information about the land use history of the plots. To reduce the likelihood of including plantation forests, we excluded plots with fewer than three woody species. We also excluded plots that were smaller than 100 m² because these often contain too few woody individuals for community-level analyses. The average plot size was 362 m², with a maximum of 40,000 m² (4 ha). If species had plots in their alien range on the same continent as plots in their native range (e.g., some plots for Acer negundo and Acer pseudoplatanus), then these alien plots were excluded to ensure abiotic and biotic differences between the native and alien ranges. This resulted in native and alien ranges that were on different continents for all species. In total across the species, we used 228,943 plots, of which 213,359 were in the native ranges and 15,584 in the alien ranges (Figure 1).

2.3 Focal tree species selection

In total, we included 41 species from 24 families (Supporting Information Appendix S1). We included species that are part of the global tree list of Botanic Gardens Conservation International (http://www.bgci.org/global_tree_search.php), which also includes palms and some other tree-like species. Our 41 “tree species” included 1 palm (Syagrus romanzoffiana), 1 non-woody species (Carica papaya), 7 gymnosperm trees and 32 angiosperm trees. The focal tree species that we included occurred in at least three plots in their native and at least three in their alien range, and had their native and alien ranges on different continents. A total of 15 of these species are native to Eurasia, 24 to the Americas, 1 to Africa and 1 to Oceania. More alien tree species exist, but these were not found in sufficient numbers of plots and/or have their native and alien ranges on the same continent. The 41 alien species were classified as “invasive” or “non-invasive” based on information from Rejmánek and Richardson (2013).

2.4 Species abundance

The “relative abundance” of a focal species per plot was calculated as the species’ share of the woody vegetation cover, based on canopy coverage. For all plots in sPlot, this relative cover of each species was calculated as the ratio between individual species' cover and total cover of all woody species. Across all plots, we had a total of 3,240 woody species. We excluded all non-woody species from the calculation of relative coverage, so that we could test clear hypotheses among woody species in forest ecosystems.

2.5 Functional traits

We focused on specific leaf area (SLA; cm²/g), adult tree height (H; m), oven-dried seed mass (SM; mg) and wood density (WD; g/cm³). We obtained trait information for all species in the study plots from the global trait database TRY (Kattge et al., 2011), by constructing a taxonomic backbone as described in Bruelheide et al. (2019). In sPlot, trait values for species without data in TRY were covered by gap-filling using a Bayesian hierarchical probabilistic factorization (for details see Schrodt et al., 2015), which gave similar results to non-gap-filled data (Bruelheide et al., 2019). All traits are based on species-level data; hence, we could not include intraspecific trait variation.

2.6 Dissimilarity and competitive trait differences

2.7 Human influence and climatic conditions

We used the human influence index (HII; Gallardo, Zieritz & Aldridge, 2015) as a proxy for human influence. The data were obtained from the Socioeconomic Data and Applications Center (SEDAC) via http://sedac.ciesin.columbia.edu/data/set/wildareas-v2-human-influence-index-geographic/, and had a 1-km² resolution. The proxy is based on nine variables related to human population pressure (human population density), human land use and infrastructure (built-up areas, night-time lights, land use/land cover), and human access (coastlines, roads, railroads, navigable rivers). Human influence may especially favour alien species through transport, use and planting of these species in the surrounding anthropogenic areas, which could increase propagule pressure in forests (i.e., spatial variation in how often species may arrive in the region, directly or indirectly due to human activity). Furthermore, human influence could have a positive effect on alien species through disturbance or nutrient deposition, which may increase the establishment success and growth of alien species in the surrounding region (and hence, facilitate spread to our forest plots) and/or in the plots.

As a measure of climatic conditions that the species experience, and to evaluate the climatic conditions associated with high species abundance, we used the standardized precipitation and evapotranspiration index (SPEI), which is a climatic drought index based on precipitation and temperature, at a spatial resolution of 0.5° (Vicente-Serrano, Beguería & López-Moreno, 2010). Positive values indicate humid conditions and negative values indicate dry conditions. We calculated the SPEI based on a temporal scale of 12 months, which means that the index of a specific month is based on that month and the 11 preceding months. SPEI at this time-scale is mainly related to variations in groundwater storage (Vicente-Serrano et al., 2010). Average monthly SPEI values were calculated based on average monthly rainfall and average monthly potential evapotranspiration. Potential evapotranspiration was derived from average monthly temperature and latitude, using the “Thornthwaite” function from the “SPEI” package in R (Begueria & Serrano, 2015). Monthly rainfall and temperature were obtained from CHELSA (climatologies at high resolution for the earth’s land surface areas), see further details in Bruelheide et al., 2019. Besides the original SPEI values, we also calculated the dissimilarity between local SPEI and species’ optimal SPEI. Optimal SPEI was calculated as the average SPEI at which the species occurred in its native range. This index indicates how close a species’ occurrence is to the centre of that species’ climatic niche, although this may not always be a good measure of “optimal” conditions (Dallas et al., 2017).

2.8 Statistical analyses

To test for differences in abundance between the native and alien ranges across species, we used a linear mixed-effects model including species and plot as random intercepts, using the lmer function of the lme4 package (Bates, Maechler, Bolker & Walker, 2015; Figure 2).

We formulated a two-level hierarchical linear regression model (using Bayesian inference) to test for effects of multivariate trait dissimilarity, competitive trait differences [in specific leaf area (ΔSLA), plant height (ΔH), seed mass (ΔSM) and wood density (ΔWD)], human influence index (HII) and the standardized precipitation and evapotranspiration index (SPEI) on relative abundance, and to test how these effects differ between native and alien ranges and depend on species' traits. The first level of the model describes the species-specific responses of relative abundance to the above-mentioned predictor variables, range (native versus alien range), and the two-way interactions of each predictor variable with range. We included a random effect of plot identity and incorporated interspecific variation in the intercept as well as in the slope parameters for all main effects. Additionally, we included woody species richness in the plot as a predictor of abundance because high richness (which is correlated with large plot size) decreases the average relative abundance of species and can therefore influence the effects of dissimilarity and competitive differences. We only included species richness to correct for this effect on relative abundance, and hence did not include an interaction between species richness and range. In the second level of the model, to better understand what drives the differences in these regression slopes among species, each regression slope was itself described by a normal linear regression sub-model that uses species' traits (SLA, H, SM and WD) as predictors. In other words, species-level trait values were used as predictors of the interspecific variation in regression parameters (intercept and slopes). This hierarchical model structure ensures that uncertainty in regression slopes is not neglected when estimating how they depend on species' traits (Houslay & Wilson, 2017). We did not describe interspecific variation in the interactions between range (native versus alien) and other predictors because these interaction effects on abundance (i.e., slope differences between native and alien ranges) were generally small (Figure 3). Relative abundance, the response variable, was ln-transformed to meet assumptions of normality of the model residuals, and all variables were scaled prior to analysis by subtracting the mean and dividing by the standard deviation (Schielzeth, 2010). The variance inflation factors of the variables included in the model were all <4, indicating no problem of collinearity (Zuur, Ieno & Elphick, 2010).

To analyse the hierarchical linear regression model, we applied Bayesian inference because this can accommodate the complex hierarchical structure of our model and data. Parameter estimation was done using the jags software (Plummer, 2013) and the rjags package in R (Plummer, Stukalov, et al., 2016). We set uninformative priors for all parameters; for all slopes of the fixed effects and predictors of the random slopes we set priors with mean = 0 and variance = 10³, and for the standard deviation parameters (associated with the slopes of the fixed effects and predictors of the random slopes) we set priors with a uniform distribution between 0 and 100. Samples of the parameter posterior distribution were obtained from 3 independent Markov chains using Markov chain Monte Carlo (MCMC), each running for 10,000 iterations after a burn-in phase of 1,000 iterations. We checked for convergence of the model visually by plotting the posterior sample distribution and trace plot of each parameter (Supporting Information Appendix S2), and by evaluating Gelman and Rubin’s univariate and multivariate potential scale reduction factors (Gelman & Rubin, 1992), using the gelman.diag function of the coda package in R (Plummer, Best, Cowles, & Vines, 2006). The univariate and multivariate potential scale reduction factors were all ≤1.01, indicating that the MCMC sampler converged. We found no significant phylogenetic signal in our model output (Supporting Information Appendix S3). A mathematical model description can be found in Supporting Information Appendix S4, and the R script in Supporting Information Appendix S5. All analyses were performed in R version 3.4.3 (R Core Team, 2017).

4.1 Environmental–biotic filtering drives abundance in native and alien ranges

Our finding that tree species with low trait dissimilarity to co-occurring trees are relatively more abundant is consistent with a recent global study that showed weak effects of trait dissimilarity on tree growth (Kunstler et al., 2016). However, our results sharply contrast with hypothesis 1, and with results of many studies in the invasion literature on different vegetation types, which find that local-scale species abundance is mainly determined by biotic interactions and niche differentiation (Carboni et al., 2013). Trees in forest ecosystems may experience strong environmental–biotic filtering at local spatial scales (e.g., plots < 1 ha) because the dense vegetation causes strong light limitation, which could explain our observed negative effect of trait dissimilarity on abundance (Montesinos-Navarro et al., 2018). Thus, our results contradict the idea that functionally dissimilar alien species would experience reduced competition with native species, and would become most dominant (Rundel, Dickie & Richardson, 2014). Functional dissimilarity may be important in more open ecosystems such as grasslands (Carboni et al., 2016), but our results, and the results of Kunstler et al. (2016), suggest that this is not the case for tree species in forest ecosystems.

4.2 Higher wood density, height and seed mass than co-occurring trees increase abundance in native and alien ranges

We expected, and found, that species that grow taller and have denser wood and larger seeds compared to their neighbours reach highest abundance (Figure 3, Supporting Information Appendix S8b). Species with taller adult stature than co-occurring species (i.e., positive ∆H) can access higher light conditions that allow fast growth, and contribute disproportionally to woody abundance in the plot (Slik et al., 2013), which may enhance their abundance levels. WD is a generally important trait for trees in forests, as high WD is related to shade tolerance (Ameztegui et al., 2017; Markesteijn et al., 2011). Although alien species with “acquisitive” trait values (e.g., species with low WD that grow faster in diameter and height) are usually most successful in open and disturbed ecosystems (Kleunen, Weber, et al., 2010; Tecco, Díaz, Cabido & Urcelay, 2010), more conservative trait values (e.g., higher shade tolerance and WD) may be of general importance in forests (Martin et al., 2009; van der Sande et al., 2017). The effect of ∆WD, however, tended to be stronger in the alien compared to the native range (Figure 3), suggesting a higher importance of shade tolerance, possibly because light limitation suppresses tree abundance more strongly in the alien range. The underlying reason for this may be that trees are typically younger and smaller in the alien range, and therefore suffer more light limitation than in the native range. Further research needs to demonstrate whether and why light limitation is a stronger constraint in the alien compared to the native range.

The positive effect of ∆SM in the native range is consistent with the idea that light limitation creates a strong filter, as larger seeds are associated with enhanced recruitment success in the forest understorey (Dalling & Hubbell, 2002). ∆SM did not, however, affect abundance in the alien range. There is a known trade-off between seed number and seed size, and this could suggest that seed number is more important to achieving higher abundance in the alien range than it is in the native range. This novel finding could indicate that propagule pressure not only initiates, but also sustains, invasion. Small seeds enhance invasion in open ecosystems (Taylor et al., 2016), but could also enhance abundance in forests if dispersal is a limiting factor. The balance between the importance of seed number and seed size may also depend on the time since establishment in the alien range. With longer time since arrival to a new area, abundance may be less limited by the lack of arriving seeds (i.e., seed number) and relatively more by establishment of seedlings (i.e., seed size).

4.3 Human influence is not associated with local tree abundance

We expected that tree abundance in the alien range would be highest with strong human influence in the region, as human influence may increase propagule pressure (Gallardo et al., 2015) through higher planting intensity of alien species in the surrounding region, which then disperse their seeds to nearby forests, and/or through higher disturbance and human-facilitated seed dispersal (intentional or unintentional) (Dainese et al., 2017; Hulme, 2014). We found, however, that the relationship between abundance of alien species and human influence was not significant (Figure 3). This indicates that, although propagule pressure is known to be important for enhancing regional abundance and invasiveness of woody alien species (Bucharova & van Kleunen, 2009; Feng & van Kleunen, 2016), and for local-scale abundance of life forms other than trees (Chytrý et al., 2008), human influence (at least as quantified in this study) may not predict local-scale abundance of alien tree species in forests. The lack of effect of human influence on tree abundance could be caused by a weaker relationship between human influence and propagule pressure for trees than for other life forms, because many alien tree species were first introduced in plantations that were far from built-up areas and night-time lights (which are key components of the HII). Our measure of human influence might not capture the presence of nearby plantations (and hence, seed source areas), or key aspects of human influence on secondary forests. Proximity of plantations could be a predictor of invasive alien tree species abundance, explaining the weaker role of environmental–biotic filtering and height differences in accounting for their abundance (Supporting Information Appendix S9a).

4.4 Species-specific differences in mechanisms underlying abundance

We expected that species may vary in the importance of environmental–biotic filtering, niche differentiation effects and competitive trait differences for their local abundance. Specifically, abundance of species with a conservative growth strategy (e.g., with high WD and low SLA) may be most strongly affected by environmental–biotic filtering, because strong filtering limits the abundance of other, potentially more competitive species. The abundance of acquisitive species (e.g., with low WD and high SLA), however, may mostly depend on competitive trait differences, which can confer an advantage over slower growing conservative species in high-light environments. The positive effect of SLA on the relationship between ∆SLA and abundance indicates that especially acquisitive species may indeed gain advantage from competitive trait differences (even though, on average across species, ∆SLA did not affect abundance, Figure 3). The positive effect of WD on the relationship between ∆WD and abundance indicates that especially conservative species with dense wood may gain an advantage. These results may indicate that two different strategies—being more acquisitive and being more durable than co-occurring species—can both provide competitive advantage and increase abundance (Guo et al., 2018). Alternatively, these results, and the absence of effects of SLA and WD on other trait effects (e.g., multivariate dissimilarity, ∆H, ∆SM) on abundance, may indicate that species with quite extreme values of SLA or WD may gain the strongest advantage of ∆SLA and ∆WD on abundance.

The negative effect of seed mass on the relationship between HII and abundance (Figure 4) indicates that species with small seeds experience more positive effects of human influence, possibly because smaller seeded species tend to be better adapted to human disturbances.