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Local neighbourhood interactions are considered a main driver for biodiversity–productivity relationships in forests. Yet, the structural responses of individual trees in species mixtures and their relation to crown complementarity remain poorly understood. Using a large‐scale forest experiment, we studied the impact of local tree species richness and structural variability on above‐ground wood volume allocation patterns and crown morphology. We applied terrestrial laser scanning to capture the three‐dimensional structure of trees and their temporal dynamics. We found that crown complementarity and crown plasticity increased with species richness. Trees growing in species‐rich neighbourhoods showed enhanced aboveground wood volume both in trunks and branches. Over time, neighbourhood diversity induced shifts in wood volume allocation in favour of branches, in particular for morphologically flexible species. Our results demonstrate that diversity‐mediated shifts in allocation pattern and crown morphology are a fundamental mechanism for crown complementarity and may be an important driver of overyielding. [ABSTRACT FROM AUTHOR]