In this review, the unique features and facts of long-term experiments are presented. Long-term experimental plots provide information of forest stand dynamics which cannot be derived from forest inventories or small temporary plots. Most comprise unthinned plots which represent the site specific maximum stand density as an unambiguous reference. By measuring the remaining as well as the removed stand, the survey of long-term experiments provides the total production at a given site, which is most relevant for examining the relationship between site conditions and stand productivity on the one hand and between stand density and productivity on the other. Thus, long-term experiments can reveal the site-specific effect of thinning and species mixing on stand structure, production and carbon sequestration. If they cover an entire rotation or even the previous and following generation on a given site, they reveal a species' long-term behaviour and any growth trends caused by environmental changes. Second, we exploit the unique data of European long-term experiments, some of which have been surveyed since 1848. We show the longterm effect of different density regimes on stand dynamics and an essential trade-off between total stand volume production and mean tree size. Long-term experiments reveal that tree species mixing can significantly increase stand density and productivity compared with monospecific stands. Thanks to surveys spanning decades or even a century, we can show the changing long-termperformance of different provenances and acceleration of stand production caused by environmental change, as well as better understand the growth dynamics of natural forests. Without long-term experiments forest science and practice would be not in a position to obtain such findings which are of the utmost relevance for science and practice. Third, we draw conclusions and show perspectives regarding the maintenance and further development of long-term experiments. It would require another 150 years to build up a comparable wealth of scientific information, practical knowledge, and teaching and training model examples. Although tempting, long-term experiments should not be sacrificed for cost-cutting measures. Given the global environmental change and the resulting challenges for sustainable management, the network of long-term experiments should rather be extended regarding experimental factors, recorded variables and inter-and transdisciplinary use for science and practice.

Abstract& Key message We studied the size-density trajectories of pure even-aged unthinned beech stands in the ranges of 625-40, 000 trees per hectare initial densities and of 12-33 years of age. A new piecewise polynomial function family was fitted to the trajectories, giving way to various applications. Initial number of stems per hectare (N 0 ) and mean girth at breast height at the onset of mortality (Cg 0 ) were parameters of the trajectory model, in addition to the parameters of the maximum size-density line. The two former parameters were tied by a linear relationship, which allowed the prediction of trajectories not considered in this study. Furthermore, the generic trajectory equation fitted the trajectories of thinned stands not used in the estimation of the parameters. & Context This paper models the size-density trajectories of pure even-aged beech stands, including the early development stage, which is not as well documented as are the later stages.& Aims The work reported in this paper concerns the development of a novel approach to size-density trajectories, considered as a mortality model to provide references to managers of beech forests. & Material and methods A 33-year-old beech spacing trial beginning at 12 years of age provided the opportunity to study the size-density trajectories of unthinned stands of this species. The beech data helped us to develop a new piecewise function to model these trajectories. The model we chose was a polynomial segment smoothly joining two linear functions. & Results The fits of this model allowed us to estimate the parameters of the size-density trajectories of all stands, which were the quadratic mean girths at mortality onset and at maximum density. A linear relationship between these characteristics allowed us to reduce the number of parameters needed to fit the trajectories and made it possible to predict a stand trajectory from any initial density not observed in the experimental stands. & Conclusion A single-parameter function family could be used to fit the size-density trajectories of beech stands. The predicted trajectories have various applications in beech silviculture and growth simulators.

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