Analysing the effect of stand density and site conditions on structure and growth of oak species using Nelder trials along an environmental gradient: experimental design, evaluation methods, and results

Background: Most current approaches in forest science and practice require information about structure and growth of individual trees rather than - or in addition to - sum and mean values of growth and yield at forest stand level as provided by classic experimental designs. By inventing the wheel design, Nelder provided the possibility to turn to the individual tree as basic information unit. Such trials provide valuable insights into the dependency of growth on stand density at particular sites. Methods: Here, we present an extension of the original design and evaluation by Nelder. (i) We established Nelder wheels along an environmental gradient through Europe in atlantic climate in Belgium and Germany, Mediterranean climate in Italy, continental climate in Hungary as well as on high land climate in Mexico. Such disjunct Nelder wheels along an environmental gradient can be regarded and analysed as a two- factor design with the factors of site condition and stand density. (ii) We present an advanced statistical approach to evaluate density dependent growth dynamics of trees planted in form of the Nelder design, which considers spatio-temporal autocorrelation. (iii) We prove the usefulness of the methods in improving ecological theory concerning density related productivity, trade-offs between facilitation and competition, and allometric relations between size variables. Results: First evaluations based on remeasured Nelder wheels in oak (Quercus robur L.) show a size growth differentiation during the first observation period. In particular, height growth is accelerated under higher competition indicating facilitation effects. We detect furthermore a high variability in allometric relations. Conclusions: The proposed design, methods, and results are discussed regarding their impact on forest practice, model building, and ecological theory. We conclude that the extended Nelder approach is highly efficient in providing currently lacking individual tree level information.