CONICET | Buscador de Institutos y Recursos Humanos

A tree-ring data-set is a three-way data structure with subscripts corresponding to tree × ringvariables × time, that can be broken down into a series of matrices or ?k-tables? forming a superior structure called ?datacube?. Partial Triadic Analysis (PTA) is a robust methodology useful for datacube analysis that has proven to be a good tool for unravelling and hierarchizing the different sources of variation within tree-ring datasets. The PTA is currently used as a means of extracting dominant spatio-temporal pattern of a particular data set. In the present study, we carried out a PTA for a set of conventional ring microdensity variables in order to characterize the structure of Douglas-fir variation in three common garden experiments. In this study, Douglas-fir individuals belongs to families nested in three provenances and planted in three environmentally contrasted sites in France. The tree-ring time series corresponds to twelve successive years. We use the results of the PTA analysis in an original way: since the method is based on PCA, and because the analysis depends upon the eigen- decomposition of positive semi- definite k-matrices, it is possible to identify a subset of new orthogonal variables that capture a certain part of the variance in the original data. A series of analysis of variance were performed with some of these new orthogonal variables in order to take advantage of the PTA results and to determine the statistical significance of the sources of variation due to the provenances and sites. We found highly significant differences between provenances and sites in most cases, indicating that the individual variation is not only due to site conditions, but also reflect a genetic structuring in the tree-ring variables.