Dissecting the Space-Time Structure of Tree-Ring Datasets Using the Partial Triadic Analysis

Abstract

Tree-ring datasets are used in a variety of circumstances, including archeology, climatology, forest ecology, and wood technology. These data are based on microdensity profiles and consist of a set of tree-ring descriptors, such as ring width or early/latewood density, measured for a set of individual trees. Because successive rings correspond to successive years, the resulting dataset is a ring variables × trees × time datacube. Multivariate statistical analyses, such as principal component analysis, have been widely used for extracting worthwhile information from ring datasets, but they typically address two-way matrices, such as ring variables × trees or ring variables × time. Here, we explore the potential of the partial triadic analysis (PTA), a multivariate method dedicated to the analysis of three-way datasets, to apprehend the space-time structure of tree-ring datasets. We analyzed a set of 11 tree-ring descriptors measured in 149 georeferenced individuals of European larch (Larix decidua Miller) during the period of 1967–2007. The processing of densitometry profiles led to a set of ring descriptors for each tree and for each year from 1967–2007. The resulting three-way data table was subjected to two distinct analyses in order to explore i) the temporal evolution of spatial structures and ii) the spatial structure of temporal dynamics. We report the presence of a spatial structure common to the different years, highlighting the inter-individual variability of the ring descriptors at the stand scale. We found a temporal trajectory common to the trees that could be separated into a high and low frequency signal, corresponding to inter-annual variations possibly related to defoliation events and a long-term trend possibly related to climate change. We conclude that PTA is a powerful tool to unravel and hierarchize the different sources of variation within tree-ring datasets.

A Methodological Approach for Spatiotemporally Analyzing Water-Polluting Effluents in Agricultural Landscapes Using Partial Triadic Analysis

“…In combination with these assessment techniques, simultaneous analyses of the spatial and temporal variability in longitudinal data can be achieved with PTA. When repeated measurements are performed within a spatial structure, PTA allows for depicting of temporal variability of the multivariable spatial structure and/or the spatial structure of the temporal trajectories (Rossi et al 2014). This multivariate analysis was initially developed by Escoufier (1973) and was later integrated into the statistical method of ACT‐STATIS (Analyse Conjointe de Tableaux–Structuration des Tableaux à Trois Indices de la Statistique) by L'Hermier des Plantes (1976).…”

“…Partial triadic analysis can be viewed as a particular simplified case of Tucker three‐mode factor analysis (Tucker, 1966). The first example was given by Jaffrenou (1978) and was later developed by Thioulouse and Chessel (1987), Thioulouse et al (2004), Kroonenberg (1989), Dolédec (1988), Lavit (1988), Centofanti et al (1989), Kiers (1991), Rossi (2003), Jiménez et al (2006), Decaëns et al (2009), Mendes et al (2010), Marques et al (2011), and Rossi et al (2014).…”

Community ecology in 3D: Tensor decomposition reveals spatio-temporal dynamics of large ecological communities

“…One way to keep the full information in 3D data sets is the extension of multivariate analysis to k-tables (such as STATIS [ 6 ]) and the simultaneous analysis of a sequence of paired ecological tables [ 7 – 9 ]. While the extension to k-tables is a clear improvement, which has found numerous applications among ecologists to study spatio-temporal patterns [ 10 , 11 ], the k-table approach considers one of the dimensions (often time or space) only as a repetition, restricting the results by the a-priori choice of the repetitive dimension and impeding the study of the interaction between time and space. Recently, other approaches have been developed to extend species distribution models to full communities, like the joint dynamic species distribution model [ 12 , 13 ] and the hierarchical modelling of species communities [ 14 ].…”

The spatiotemporal pattern of earthworm community in the grass savannas of Lamto (Ivory Coast)

“…A complementary step (referred to as the intra-structure analysis) examines the discrepancies between the observed pattern recorded at each sampling occasions and the model common to all dates. Readers are referred to Rossi (2003a) and Rossi et al (2014) for a presentation of the PTA.…”