ABSTRACT Aim? The drivers of species assembly, by limiting the possible range of functional trait values, can lead to either convergent or divergent distributions of traits in realized assemblages. Here, to evaluate the strengths of these species assembly drivers, we partition trait variance across global, regional and community scales. We then test the hypothesis that, from global to community scales, the outcome of co-occurring trait convergence and divergence is highly variable across biomes and communities. Location? Global: nine biomes ranging from subarctic highland to tropical rain forest. Methods? We analysed functional trait diversity at progressively finer spatial scales using a global, balanced, hierarchically structured dataset from 9 biomes, 58 communities and 652 species. Analyses were based on two key leaf traits (foliar nitrogen content and specific leaf area) that are known to drive biogeochemical cycling. Results? While 35% of the global variance in these traits was between biomes, only 15% was between communities within biomes and as much as 50% occurred within communities. Despite this relatively high within-community variance in trait values, we found that trait convergence dominated over divergence at both global and regional scales through comparisons of functional trait diversity in regional and community assemblages against random (null) models of species assembly. Main conclusions? We demonstrate that the convergence of traits occurring from global to regional assemblages can be twice as strong as that from regional to community assemblages, and argue that large differences in the nature and strength of abiotic and biotic drivers of dominant species assembly can, at least partly, explain the variable outcome of simultaneous trait convergence and divergence across sites. Ultimately, these findings stress the urgent need to extend species assembly research to address those scales where trait variance is the highest, i.e. between biomes and within communities.