This paper is a short summary of the main classes defined in the ade4 package for one table analysis methods (e.g., principal component analysis). Other papers will detail the classes defined in ade4 for twotables coupling methods (such as canonical correspondence analysis, redundancy analysis, and coinertia analysis), for methods dealing with K-tables analysis (i.e., three-ways tables), and for graphical methods. This package is a complete rewrite of the ADE4 software (Thioulouse et al. (1997), http://pbil.univlyon1.fr/ADE-4/) for the R environment. It contains Data Analysis functions to analyse Ecological and Environmental data in the framework of Euclidean Exploratory methods, hence the name ade4 (i.e., 4 is not a version number but means that there are four E in the acronym). The ade4 package is available in CRAN, but it can also be used directly online, thanks to the Rweb system (http://pbil.univ-lyon1.fr/Rweb/). This possibility is being used to provide multivariate analysis services in the field of bioinformatics, particularly for sequence and genome structure analysis at the PBIL (http://pbil.univ-lyon1.fr/). An example of these services is the automated analysis of the codon usage of a set of DNA sequences by correspondence analysis (http://pbil.univ-lyon1.fr/ mva/coa.php).

http://pbil.univ-lyon1.fr/JTHome/Biblio/ade4-Rnews.pdf

The ade4 package - I : One-table methods

SUMMARY

1
This paper focuses on the premise that the habitat provides the templet upon which evolution forges characteristic species traits. Alternative hypotheses are that there are historic and phylogenetic constraints on the match between organism and environment.

2
In our analysis of river systems, as one dimension of the templet we choose temporal heterogeneity and assume some relationship between this and the frequency of disturbance. The second dimension is spatial heterogeneity in the physicochemical environment and we pay particular attention to the way such variation can ameliorate the influence of disturbances through the provision of refugia.

3
We derive predictions about the traits of species, including size, generation time, reproductive tactics, body form, mobility and potential for regeneration, that are likely to occur in particular regions of the two-dimensional templet. We also present predictions about community-level characteristics such as number of species per resource category and total species richness. The general predictions are intended to apply to a wide range of plants, micro-organisms and animals, provided the measurements have been made at a scale appropriate to them.

4
Hypotheses can be tested by comparing traits predicted for particular habitats, whose spatial and temporal heterogeneity have been quantified, with those actually observed. If the fit turns out to be good, we will be able to conclude that the habitat templet approach offers a sound framework within which to pose questions in river ecology.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1365-2427.1994.tb01740.x

Species traits in relation to a habitat templet for river systems

This paper addresses the question of studying the joint structure of three data tablesR,L andQ. In our motivating ecological example, the central tableL is a sites-by-species table that contains the number of organisms of a set of species that occurs at a set of sites. At the margins ofL are the sites-by-environment data tableR and the species-by-trait data table Q. For relating the biological traits of organisms to the characteristics of the environment in which they live, we propose a statistical technique calledRLQ analysis (R-mode linked toQ-mode), which consists in the general singular value decomposition of the triplet (R
 t
 D
 I
 LD
 J
 Q,D
 q
 ,D
 p
 ) whereD
 I
 ,D
 J
 ,D
 q
 ,D
 p
 are diagonal weight matrices, which are chosen in relation to the type of data that is being analyzed (quantitative, qualitative, etc.). In the special case where the central table is analysed by correspondence analysis,RLQ maximizes the covariance between linear combinations of columns ofR andQ. An example in bird ecology illustrates the potential of this method for community ecologists.

Matching species traits to environmental variables: a new three-table ordination method

Ecological studies often require studying the common structure of a pair of data tables. Co-inertia analysis is a multivariate method for coupling two tables. It is often neglected by ecologists who prefer the widely used methods of redundancy analysis and canonical correspondence analysis. We present the co-inertia criterion for measuring the adequacy between two data sets. Co-inertia analysis is based on this criterion as are canonical correspondence analysis or canonical correlation analysis, but the latter two have additional constraints. Co-inertia analysis is very flexible and allows many possibilities for coupling. Co-inertia analysis is suitable for quantitative and/or qualitative or fuzzy environmental variables. Moreover, various weighting of sites and various transformations and/or centering of species data are available for this method. Hence, more ecological considerations can be taken into account in the statistical procedures. Moreover, the principle of this method is very general and can be easily extended to the case of distance matrices or to the case of more than two tables. Simulated ecological data are used to compare the co-inertia approach with other available methods.

Co-inertia analysis and the linking of ecological data tables

Functional diversity is at the heart of current research in the field of conservation biology. Most of the indices that measure diversity depend on variables that have various statistical types (e.g. circular, fuzzy, ordinal) and that go through a matrix of distances among species. We show how to compute such distances from a generalization of Gower's distance, which is dedicated to the treatment of mixed data. We prove Gower's distance can be extended to include new types of data. The impact of this generalization is illustrated on a real data set containing 80 plant species and 13 various traits. Gower's distance allows an efficient treatment of missing data and the inclusion of variable weights. An evaluation of the real contribution of each variable to the mixed distance is proposed. We conclude that such a generalized index will be crucial for analyzing functional diversity at small and large scales.

/pdf/on-the-challenge-of-treating-various-types-of-variables-47dnie5m10.pdf

On the challenge of treating various types of variables: application for improving the measurement of functional diversity

SUMMARY
1We present an unconventional procedure (fuzzy coding) to structure biological and environmental information, which uses positive scores to describe the affinity of a species for different modalities (i.e. categories) of a given variable. Fuzzy coding is essential for the synthesis of long-term ecological data because it enables analysis of diverse kinds of biological information derived from a variety of sources (e.g. samples, literature).
2A fuzzy coded table can be processed by correspondence analysis. An example using aquatic beetles illustrates the properties of such a fuzzy correspondence analysis. Fuzzy coded tables were used in all articles of this issue to examine relationships between spatial-temporal habitat variability and species traits, which were obtained from a long-term study of the Upper Rhone River, France.
3Fuzzy correspondence analysis can be programmed with the equations given in this paper or can be performed using ADE (Environmental Data Analysis) software that has been adapted to analyse such long-term ecological data. On Macintosh AppleTM computers, ADE performs simple linear ordination, more recently developed methods (e.g. principal component analysis with respect to instrumental variables, canonical correspondence analysis, co-inertia analysis, local and spatial analyses), and provides a graphical display of results of these and other types of analysis (e.g. biplot, mapping, modelling curves).
4ADE consists of a program library that exploits the potential of the HyperCardTM interface. ADE in an open system, which offers the user a variety of facilities to create a specific sequence of programs. The mathematical background of ADE is supported by the algebraic model known as ‘duality diagram’.

A fuzzy coding approach for the analysis of long‐term ecological data

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A fuzzy coding approach for the analysis of long‐term ecological data