Co‐inertia analysis: an alternative method for studying species–environment relationships

Abstract

1. Methods used for the study of species-environment relationships can be grouped into: (i) simple indirect and direct gradient analysis and multivariate direct gradient analysis (e.g. canonical correspondence analysis), all of which search for non-symmetric patterns between environmental data sets and species data sets; and (ii) analysis of juxtaposed tables, canonical correlation analysis, and intertable ordination, which examine spedes-environment relationships by considering each data set equally. Different analytical techniques are appropriate for fulfilling different objectives. 2. We propose a method, co-inertia analysis, that can synthesize various approaches encountered in the ecological literature. Co-inertia analysis is based on the mathematically coherent Euclidean model and can be universally reproduced (i.e. independently of software) because of its numerical stability. The method performs simultaneous analysis of two tables. The optimizing criterion in co-inertia analysis is that the resulting sample scores (environmental scores and faunistic scores) are the most covariant. Such analysis is particularly suitable for the simultaneous detection of faunistic and environmental features in studies of ecosystem structure. 3. The method was demonstrated using faunistic and environmental data from Friday (Freshzvater Biology 18, 87-104, 1987). In this example, non-symmetric analyses is inappropriate because of the large number of variables (species and environmental variables) compared with the small number of samples. 4. Co-inertia analysis is an extension of the analysis of cross tables previously attempted by others. It serves as a general method to relate any kinds of data set, using any kinds of standard analysis (e.g. principal components analysis, correspondence analysis, multiple correspondence analysis) or between-class and within-class analyses.

Importance of microhabitat characteristics in the macrobenthos microdistribution of a large river reach

“…The co-inertia analysis maximized the correlation between the two structures : the habitat structure and the fauna structure (Dolédec & Chessel 1994). The optimizing criterion was that the resulting sample scores, the habitat scores for matrix H and the faunistic scores for matrix F, were the most covariant and could be compared directly on the same factorial map.…”

Structure of endemic fish assemblages in the upper Yangtze River Basin

“…In the present study, we introduced both the species distribution data set and land-cover variables into CIA and DA in the R software using the 'ade4' package (Thioulouse et al, 1997). The logic of principal component analysis was applied in both CIA and DA methods because the land-cover factors related to the distribution of species were supposed to be limiting (Dolédec and Chessel, 1994). The DA was conducted to determine which land-cover variables discriminate between the clusters previously defined by the SOM procedure.…”

The pedological heritage of the Dolomites (Northern Italy): Features, distribution and evolution of the soils, with some implications for land management

“…A coinertia analysis of these two sets of data was then carried out according to the methods described by Dolédec and Chessel (1994). A permutation test (also called MonteCarlo test, or randomization test) was used to assess the statistical significant correlation between the two data sets.…”