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Aim s : Ecological theories predict that assembly processes are driven by two deterministic forces: environmental filtering and limiting similarity. Their relative importance under different environmental conditions is still not completely obvious. Therefore, in this paper the predictions of the stress–dominance hypothesis (SDH) are tested in several sites. Location: Kiskunság in Hungary, and Deliblato Sands in Serbia, Central Europe. Methods: We studied a productivity gradient from open sand grasslands to meadows. The cover of species was estimated visually in plots with a size of 2 m × 2 m, resulting in 344 vegetation plots. Four trait values (height, seed mass, specific leaf area, and leaf size) were collected from field measurements and databases. The weighted median of interspecies distances in traits (a robust alternative to Rao's quadratic entropy) was used to determine functional diversity. The convergence and divergence of each trait in communities were evaluated by randomization tests, and effect sizes were calculated for each plot. We used hierarchical general additive models (HGAM) to determine whether the trend of effect sizes along the productivity gradient is the same in different sites. Results: The HGAM approach indicated that trait variations follow global trends but are influenced by site‐specific effects. The exception is seed mass, whose variation did not have any trend. Both environmental filtering and limiting similarity exist in the communities, and mainly a shift from trait convergence to a divergence pattern along the productivity gradient was observed. Conclusion: The results are mainly congruent with theoretical expectations, but the results from the different sites did not lead to the same conclusion. Although traits follow a global trend, the site effect is not negligible. Critical evaluation of SDH using trait convergence/divergence patterns for exploring rules of community assembly points out the weaknesses of this hypothesis. Therefore, alternative ways of studying trait patterns should be found to better understand community organization. [ABSTRACT FROM AUTHOR]