Application of inertia methods to benthic marine ecology: Practical implications of the basic options

Abstract

The various so-called inertia methods, the aim of which is to summarize the relationships between points by a configuration of reduced dimension, may al1 be considered variants of a more general method, In this regard, the links existing between Principal Component Analysis, Principal Coordinates Analysis and the Analysis of Correspondences appear clearly. Three fundamental options (inherent in al1 inertia methods) determine the divergences among these techniques: choice of distance, choice of weights attributed to the points, choice of position of the origin. This viewpoint also shows up the relationships between the analysis of the R and Q matrices of one and the same set of data. The application of these techniques to data of the benthic bionomy of the North Gascony continental shelf illustrates the ecological implications of the three possible theoretical choices. Analysis of the differences observed at the level of the structures obtained produces an overall ecological interpretation that one method taken in isolation could not reveal. 'OKa = square of the length of the segment OK. 1 fonn of inertia is given by: c (j~, j2) = Z P (i) X (i, j11.X (i, j2).

Results of ecological monitoring of three beaches polluted by the 'Amoco Cadiz' oil spill: development of meiofauna from 1978 to 1984

“…The distance is used, and points are unequally weighted, which makes possible the symmetry between observations (= samples here) and variables (= species here). Further details are given, among others, by Chardy et al (1976). This method allows a graphic representation of the t h espace development of samples and species.…”

Spatial and temporal distribution of Amphipoda associated with mussel beds from the Bay of Santos (Brazil)

“…Owing to the nature of the original data matrix (samples X species) emphasis was placed on correspondence analysis (Hill 1974, Legendre & Legendre 1984, which associates the points of a contingency table by means of the Chi square distance. T h s ordination method is less affected than others by abundance of species, density and profile of samples, and double absences (Chardy et al 1976). To help delimit the species and sample groupings in the factorial planes, a cluster analysis was also performed.…”

The application of multivariate statistical methods to phytoplankton counts from the Hauraki Gulf, New Zealand

“…The log volumes of the 96 phytoplankton species provided the raw data for a similarity matrix, based on a chi-squared measure (Chardy et al 1976). The first 2 axes derived by eigenanalysis of -) and 2 ( ) for every month during the sampling this matrix explained only 8% of the total variance but provided a framework for plotting both species and samples from which an interesting pattern emerged.…”