Multivariate analyses are well known and widely used to identify and understand structures of ecological communities. The ade4 package for the R statistical environment proposes a great number of multivariate methods. Its implementation follows the tradition of the French school of "Analyse des Données" and is based on the use of the duality diagram. We present the theory of the duality diagram and discuss its implementation in ade4. Classes and main functions are presented. An example is given to illustrate the ade4 philosophy.

Increasing attention is being devoted to taking landscape information into account in genetic studies. Among landscape variables, space is often considered as one of the most important. To reveal spatial patterns, a statistical method should be spatially explicit, that is, it should directly take spatial information into account as a component of the adjusted model or of the optimized criterion. In this paper we propose a new spatially explicit multivariate method, spatial principal component analysis (sPCA), to investigate the spatial pattern of genetic variability using allelic frequency data of individuals or populations. This analysis does not require data to meet Hardy-Weinberg expectations or linkage equilibrium to exist between loci. The sPCA yields scores summarizing both the genetic variability and the spatial structure among individuals (or populations). Global structures (patches, clines and intermediates) are disentangled from local ones (strong genetic differences between neighbors) and from random noise. Two statistical tests are proposed to detect the existence of both types of patterns. As an illustration, the results of principal component analysis (PCA) and sPCA are compared using simulated datasets and real georeferenced microsatellite data of Scandinavian brown bear individuals (Ursus arctos). sPCA performed better than PCA to reveal spatial genetic patterns. The proposed methodology is implemented in the adegenet package of the free software R.

HOW TO CITE TSPACE ITEMSAlways cite the published version, so the author(s) will receive recognition through services that track citation counts, e.g. Scopus. If you need to cite the page number of the TSpace version (original manuscript or accepted manuscript) because you cannot access the published version, then cite the TSpace version in addition to the published version using the permanent URI (handle) found on the record page. Abstract. Species spatial distributions are the result of population demography, behavioral traits, and species interactions in spatially heterogeneous environmental conditions. Hence the composition of species assemblages is an integrative response variable, and its variability can be explained by the complex interplay among several structuring factors. The thorough analysis of spatial variation in species assemblages may help infer processes shaping ecological communities. We suggest that ecological studies would benefit from the combined use of the classical statistical models of community composition data, such as constrained or unconstrained multivariate analyses of site-by-species abundance tables, with rapidly emerging and diversifying methods of spatial pattern analysis. Doing so allows one to deal with spatially explicit ecological models of beta diversity in a biogeographic context through the multiscale analysis of spatial patterns in original species data tables, including spatial characterization of fitted or residual variation from environmental models. We summarize here the recent progress for specifying spatial features through spatial weighting matrices and spatial eigenfunctions in order to define spatially constrained or scale-explicit multivariate analyses. Through a worked example on tropical tree communities, we also show the potential of the overall approach to identify significant residual spatial patterns that could arise from the omission of important unmeasured explanatory variables or processes. REVIEWS

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.

Multivariate analyses such as principal component analysis were among the first statistical methods employed to extract information from genetic markers. From their early applications to current innovations, these approaches have proven to be efficient for the analysis of the genetic variability in various contexts such as human genetics, conservation and adaptation studies. However, because multivariate analysis is a wide and diversified area of statistics, choosing a method appropriate to both the data and to the question being asked can be difficult. Moreover, some particularities of genetic markers need to be taken into account when using multivariate methods. As a consequence, multivariate analyses are often used as black boxes, which results in frequent mistakes in the literature. In this review, we provide a critical analysis of the application of multivariate methods to genetic markers, using a general framework that unifies all these methods for the sake of clarity. First, we focus on some common mistakes in these applications and ways to avoid these pitfalls. We then detail the most critical particularities of allele frequencies that demand adaptations of multivariate methods, and we propose solutions to the subsequent problems. Finally, we tackle several questions of interest in which multivariate analysis has a great role to play, such as the study of the typological coherence of different genetic markers, or the investigation of spatial genetic patterns.

In this paper, we introduce the concept of Ôoriginality of a species within a setÕ in order to indicate the average rarity of all the features belonging to this species. Using a phylogenetic tree of 70 species of New World terrestrial Carnivora, we suggest measuring the originality by a probability distribution. This maximizes the expected number of features shared by two species randomly drawn from the set. By using this new index, we take account of branch lengths whereas current indices of originality focus on tree topology. As a supplement to Nee and May's optimizing algorithm, we find that originality must be one of the criteria used in conservation planning.

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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.