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Individual tree architecture and the composition of tree species play a vital role for many ecosystem functions and services provided by a forest, such as timber value, habitat diversity, and ecosystem resilience. However, knowledge is limited when it comes to understanding how tree architecture changes in response to competition. Using 3D-laser scanning data from the German Biodiversity Exploratories, we investigated the detailed three-dimensional architecture of 24 beech (Fagus sylvatica L.) trees that grew under different levels of competition pressure. We created detailed quantitative structure models (QSMs) for all study trees to describe their branching architecture. Furthermore, structural complexity and architectural self-similarity were measured using the box-dimension approach from fractal analysis. Relating these measures to the strength of competition, the trees are exposed to reveal strong responses for a wide range of tree architectural measures indicating that competition strongly changes the branching architecture of trees. The strongest response to competition (rho = −0.78) was observed for a new measure introduced here, the intercept of the regression used to determine the box-dimension. This measure was discovered as an integrating descriptor of the size of the complexity-bearing part of the tree, namely the crown, and proven to be even more sensitive to competition than the box-dimension itself. Future studies may use fractal analysis to investigate and quantify the response of tree individuals to competition. [ABSTRACT FROM AUTHOR]