In Europe, concerns regarding the provision of ecosystem services from forests, such as biodiversity, has led to a widespread conversion from even-aged to close-to-nature forest management. These concerns have also led to a demand for quantifying stand structure, dynamics, and species diversity in order to evaluate ecosystem status and devise management action. In this study, species distribution, species association, and size diversity in a semi-natural, unmanaged beech forest in Denmark were analyzed using spatial indices including uniform angle index, mingling index, and differentiation index and spatial functions including pair correlation function, bivariate pair correlation function, mark variogram, and the Wiegand scheme. To analyze the spatial patterns of tree species, two plots, one in a less disturbed part of the forest and the other in a more recently disturbed part, was selected. Based on the spatial functions, all species showed a clustered pattern as a result of forest dynamics. Fagus sylvatica L. was segregated from other species and was more likely to form pure groups. In contrast, Ulmus glabra L.-Fraxinus excelsior L. and Ulmus glabra L.-Acer psedoplatanous L. showed positive association. All species in the less disturbed part of the forest showed positive spatial correlation of tree diameters, probably as a result of gap-phase dynamics. However, a lack of spatial correlation of tree diameters was observed for beech and elm trees in the more recently disturbed part of the forest. Our results indicated that spatial functions using stem-mapped data provide more reliable results and additional insights into the stand structure than neighborhood based indices. The study findings can be used to align forest management practices with goals of protecting biodiversity in managed forest.