A new technique for ordering asymmetrical three-dimensional data sets in ecology.

The aim of this paper is to tackle the problem that arises from asymmetrical data cubes formed by two crossed factors fixed by the experimenter (factor A and factor B, e.g., sites and dates) and a factor which is not controlled for (the species). The entries of this cube are densities in species. We approach this kind of data by the comparison of patterns, that is to say by analyzing first the effect of factor B on the species-factor A pattern, and second the effect of factor A on the species-factor B pattern. The analysis of patterns instead of individual responses requires a correspondence analysis. We use a method we call Foucart's correspondence analysis to coordinate the correspondence analyses of several independent matrices of species x factor A (respectively B) type, corresponding to each modality of factor B (respectively A). Such coordination makes it possible to evaluate the effect of factor B (respectively A) on the species-factor A (respectively B) pattern. The results obtained by such a procedure are much more insightful than those resulting from a classical single correspondence analysis applied to the global matrix that is obtained by simply unrolling the data cube, juxtaposing for example the individual species x factor A matrices through modalities of factor B. This is because a single global correspondence analysis combines three effects of factors in a way that cannot be determined from factorial maps (factor A, factor B, and factor A x factor B interaction) whereas the applications of Foucart's correspondence analysis clearly discriminate two different issues. Using two data sets, we illustrate that this technique proves to be particularly powerful in the analyses of ecological convergence which include several distinct data sets and in the analyses of spatiotemporal variations of species distributions.

Testing sexual segregation and aggregation: old ways are best.

The study of sexual segregation has received increasing attention over the last two decades. Several hypotheses have been proposed to explain the existence of sexual segregation, such as the "predation risk hypothesis," the "forage selection hypothesis," and the "activity budget hypothesis." Testing which hypothesis drives sexual segregation is hampered, however, by the lack of consensus regarding a formal measurement of sexual segregation. By using a derivation of the well-known chi-square (here called the sexual segregation and aggregation statistic [SSAS]) instead of existent segregation coefficients, we offer a reliable way to test for temporal variation in the occurrence of sexual segregation and aggregation, even in cases where a large proportion of animals are observed alone. A randomization procedure provides a test for the null hypothesis of independence of the distributions of males and females among the groups. The usefulness of SSAS in the study of sexual segregation is demonstrated with three case studies on ungulate populations belonging to species with contrasting life histories and annual grouping patterns (isard, red deer, and roe deer). The existent segregation coefficients were unreliable since, for a given value, sexual segregation could or could not occur. Similarly, the existent segregation coefficients performed badly when males and females aggregated. The new SSAS was not prone to such limitations and allowed clear conclusions regarding whether males and females segregate, aggregate, or simply mix at random applicable to all species.

Internal correspondence analysis of codon and amino-acid usage in thermophilic bacteria.

Starting from two datasets of codon usage in coding sequences from mesophilic and thermophilic bacteria, we used internal correspondence analysis to study the variability of codon usage within and between species, and within and between amino acids. The first dataset included 18,958,458 codons from 58,482 coding sequences from completely sequenced genomes of 25 species, along with 6,793,581 dinucleotides from 21,876 intergenic spaces. The second dataset, with partially sequenced genomes, included 97,095,873 codons from 293 bacterial species. Results were consistent between the two datasets. The trend for the amino-acid composition of thermophilic proteins was found to be under the control of a pressure at the nucleic acid level, not a selection at the protein level. This effect was not present in intergenic spaces, ruling out a pressure at the DNA level. The pattern at the mRNA level was more complex than a simple purine enrichment of the sense strand of coding sequences. Outliers in the partial genome dataset introduced a note of caution about the interpretation of temperature as the direct determinant of the trend observed in thermophiles. The surprising lack of selection on the amino-acid content of thermophilic proteins suggests that the amino-acid repertoire was set up in a hot environment.

Testing for phylogenetic signal in phenotypic traits: new matrices of phylogenetic proximities.

Abouheif adapted a test for serial independence to detect a phylogenetic signal in phenotypic traits. We provide the exact analytic value of this test, revealing that it uses Moran's I statistic with a new matrix of phylogenetic proximities. We introduce then two new matrices of phylogenetic proximities highlighting their mathematical properties: matrix A which is used in Abouheif test and matrix M which is related to A and biodiversity studies. Matrix A unifies the tests developed by Abouheif, Moran and Geary. We discuss the advantages of matrices A and M over three widely used phylogenetic proximity matrices through simulations evaluating power and type-I error of tests for phylogenetic autocorrelation. We conclude that A enhances the power of Moran's test and is useful for unresolved trees. Data sets and routines are freely available in an online package and explained in an online supplementary file.

From dissimilarities among species to dissimilarities among communities: a double principal coordinate analysis.

This paper presents a new ordination method to compare several communities containing species that differ according to their taxonomic, morphological or biological features. The objective is first to find dissimilarities among communities from the knowledge about differences among their species, and second to describe these dissimilarities with regard to the feature diversity within communities. In 1986, Rao initiated a general framework for analysing the extent of the diversity. He defined a diversity coefficient called quadratic entropy and a dissimilarity coefficient and proposed a decomposition of this diversity coefficient in a way similar to ANOVA. Furthermore, Gower and Legendre (1986) built a weighted principal coordinate analysis. Using the previous context, we propose a new method called the double principal coordinate analysis (DPCoA) to analyse the relation between two kinds of data. The first contains differences among species (dissimilarity matrix); the second the species distribution among communities (abundance or presence/absence matrix). A multidimensional space assembling the species points and the community points is built. The species points define the original differences between species and the community points define the deduced differences between communities. Furthermore, this multidimensional space is linked with the diversity decomposition into between-community and within-community diversities. One looks for axes that provide a graphical ordination of the communities and project the species onto them. An illustration is proposed comparing bird communities which live in different areas under mediterranean bioclimates. Compared to some existing methods, the double principal coordinate analysis can provide a typology of communities taking account of an abundance matrix and can include dissimilarities among species. Finally, we show that such an approach generalizes some of these methods and allows us to develop new analyses.

Spatial variation in springtime food resources influences the winter body mass of roe deer fawns.

It is well established that the dynamics of mammalian populations vary in time, in relation to density and weather, and often in interaction with phenotypic differences (sex, age and social status). Habitat quality has recently been identified as another significant source of individual variability in vital rates of deer, including roe deer where spatial variations in fawn body mass were found to be only about a tenth of temporal variations. The approach used was to classify the habitat into blocks a priori, and to analyse variation in animal performance among the predefined areas. In a fine-grained approach, here we use data collected over 24 years on 1,235 roe deer fawns captured at known locations and the plant species composition sampled in 2001 at 578 sites in the Chizé forest to determine the spatial structure at a fine scale of both vegetation and winter body mass of fawns, and then to determine links between the two. Space and time played a nearly equal role in determining fawn body masses of both sexes, each accounting for about 20% of variance and without any interaction between them. The spatial distribution of fawn body mass was perennial over the 24 years considered and predicted values showed a 2 kg range according to location in the reserve, which is much greater than suggested in previous work and is enough to have strong effects on fawn survival. The spatial distribution and the range of predicted body masses were closely similar in males and females. The result of this study is therefore consistent with the view that the life history traits of roe deer are only weakly influenced by sexual selection. The occurrence of three plant species that are known to be important food items in spring/summer roe deer diets, hornbeam ( Carpinus betulus), bluebell ( Hyacinthoides sp.) and Star of Bethlehem ( Ornithogalum sp.) was positively related to winter fawn body mass. The occurrence of species known to be avoided in spring/summer roe deer diets [e.g. butcher's broom ( Ruscus aculeatus) and beech ( Fagus sylvatica)], was negatively related to fawn body mass. We conclude that the spatial variation in the body mass of fawns in winter in this forest is as important as the temporal variation, and that the distribution of plant species that are actively selected during spring and summer is an important determinant of spatial variation in winter fawn body mass. The availability of these plants is therefore likely to be a key factor in the dynamics of roe deer populations.