INTRODUCTION

Flowering plants are estimated to have diversified into an extant global flora of about 369.000 species . Most of those species have small spatial ranges and maintain low population densities, and are thus considered rare . On the other side, a few species are considered common or dominant, as they achieve high population densities and have colonized large stretches of land . Though this pattern has been recognized as early as the 19th century (Darwin, 1859), the reasons why most species are rare and a few are common or dominant are still unclear .
Plant functional traits have been successfully used to explain species occurrence patterns in relation to environmental conditions . For example, leaf morphology is correlated with climate , and chemical composition of plants is correlated with soil properties . It has also been shown that species with particular trait values increase in abundance when filtered by the environment . Surprisingly, however, a basic description of trait differences between common and rare species, irrespective of changes in environmental conditions, is still missing. A reason for this might be that rarity (or commonness) has multiple dimensions and can apply to different spatial scales. For example, while a species may be locally abundant in a certain habitat type (i.e. be common), it might have a restricted distribution globally (i.e. be rare).
Most studies relating traits to ecological parameters are focussing on aboveground traits, most likely because they are overrepresented in trait databases . Although leaf traits, plant height and seed weight are considered to capture most variation in plant form and function , inclusion of belowground traits can substantially increase predictive power for species distributions . Belowground traits, however, are usually not considered as their measurement is technically challenging and labour intensive . Moreover, belowground traits are often assumed to be correlated with aboveground trait . However, other studies show that correlations between above and belowground traits vary tremendously among clades and depend on the traits considered .
We tested if plant functional traits explain the success of species across spatial scales from local abundance in grassland plots to their worldwide distribution. To do so, we measured root traits and seed weight on 242 grassland species grown in two large common-environment experiments. In addition, we extracted aboveground and bud-bank traits from databases. We then tested how the traits relate to the abundance and occurrence in grassland plots of the German Biodiversity Exploratories , the occurrence frequency across Germany, the occurrence frequency across the European and Mediterranean region, and their global occurrence as naturalized alien species. We aimed to answer the following questions:
1) Do plant functional traits explain species success, i.e. abundance and occurrence frequency across spatial scales?
2) Do the contributions of traits to species success vary with the spatial scale considered?
3) Do above- and belowground traits contribute differently to explaining species success?