1. Trait-based approaches have been increasingly used to understand the role of environmental and biotic filters on species assembly. However, our understanding of the relationships between traits and community assembly processes remain limited. Indeed, various assembly processes may lead to similar functional patterns, and the effects of a given process may vary with the considered traits. Especially, competition can result in trait divergence or convergence depending on whether the trait is related to niche differences or to species’ competitive abilities. 2. In this study, we used a process-based forest gap-model to explore the effect of environmental and biotic assembly processes on the functional diversity of tree communities along a productivity gradient of 11 sites across central Europe. In a simulation experiment, we (i) disentangled the effects of environmental and biotic filtering on community structure, and (ii) tested whether competition resulted in trait divergence or convergence. 3. Our results confirmed the expected decrease in species richness with decreasing site fertility. We detected environmental filtering for traits related to both species environmental requirements and species competitive ability, highlighting that environmental trait filtering can affect all aspects of tree life-history strategies. 4. We observed convergence of traits related to growth and light capture resulting from competition for light, suggesting that tree species assembly is mainly driven by differences in competitive abilities. Additionally, the observed trait convergence was stronger in more productive sites than in less fertile ones, reflecting the impact of environmental conditions on competitive interactions. 5. Synthesis. Our study shows that process-based forest models can help to test whether functional traits composition reveal the signature of community assembly processes. This process-based approach challenges the classical view on the links between traits and mechanisms driving community assembly.