Using Partial Triadic Analysis for Depicting the Temporal Evolution of Spatial Structures: Assessing Phytoplankton Structure and Succession in a Water Reservoir

Abstract

Partial triadic analysis is a multiway analysis method that is a well suited statistical tool to get a clear representation of a chronological series of matrices, one for each sample date. It allows the simultaneous principal component analyses of several matrices and permits one to find a spatial structure common to every matrix and to study its temporal stability. Partial triadic analysis begins by searching for an average table called compromise. The compromise table is then analyzed and its reproducibility by each initial table is finally investigated.

A partial triadic analysis was applied to a phytoplankton dataset that was collected in 2006 at six stations in the Marne Reservoir, located in France in the Seine catchment area. The spatial and temporal organizations of the assemblages of these different species were derived and hence the existence of some changes in water quality could be assessed since micro-organisms, especially phytoplankton species, may be considered as potential indicators of local and more global changes in aquatic ecosystems and may thus constitute an excellent biomarker of water quality. This example demonstrates the power of partial triadic analysis for depicting the temporal evolution of spatial structures.

The exposition is accessible to readers with an intermediate to advanced knowledge of statistics. Some prior exposure to principal component analysis is required for reading the article which can be viewed as a sequel to Bertrand et al. (2007). A basic knowledge of R is helpful.