Stéphane Dray

VARIATION PARTITIONING OF SPECIES DATA MATRICES: ESTIMATION AND COMPARISON OF FRACTIONS

Establishing relationships between species distributions and environmental characteristics is a major goal in the search for forces driving species distributions. Canonical ordinations such as redundancy analysis and canonical correspondence analysis are invaluable tools for modeling communities through environmental predictors. They provide the means for conducting direct explanatory analysis in which the association among species can be studied according to their common and unique relationships with the environmental variables and other sets of predictors of interest, such as spatial variables. Variation partitioning can then be used to test and determine the likelihood of these sets of predictors in explaining patterns in community structure. Although variation partitioning in canonical analysis is routinely used in ecological analysis, no effort has been reported in the literature to consider appropriate estimators so that comparisons between fractions or, eventually, between different canonical models are meaningful. In this paper, we show that variation partitioning as currently applied in canonical analysis is biased. We present appropriate unbiased estimators. In addition, we outline a statistical test to compare fractions in canonical analysis. The question addressed by the test is whether two fractions of variation are significantly different from each other. Such assessment provides an important step toward attaining an understanding of the factors patterning community structure. The test is shown to have correct Type I. error rates and good power for both redundancy analysis and canonical correspondence analysis.

CO‐INERTIA ANALYSIS AND THE LINKING OF ECOLOGICAL DATA TABLES

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.

The global spectrum of plant form and function

Earth is home to a remarkable diversity of plant forms and life histories, yet comparatively few essential trait combinations have proved evolutionarily viable in today’s terrestrial biosphere. By analysing worldwide variation in six major traits critical to growth, survival and reproduction within the largest sample of vascular plant species ever compiled, we found that occupancy of six-dimensional trait space is strongly concentrated, indicating coordination and trade-offs. Three-quarters of trait variation is captured in a two-dimensional global spectrum of plant form and function. One major dimension within this plane reflects the size of whole plants and their parts; the other represents the leaf economics spectrum, which balances leaf construction costs against growth potential. The global plant trait spectrum provides a backdrop for elucidating constraints on evolution, for functionally qualifying species and ecosystems, and for improving models that predict future vegetation based on continuous variation in plant form and function.

TESTING THE SPECIES TRAITS-ENVIRONMENT RELATIONSHIPS: THE FOURTH-CORNER PROBLEM REVISITED

Functional ecology aims at determining the relationships between species traits and environmental variables in order to better understand biological processes in ecosystems. From a methodological point of view, this biological objective calls for a method linking three data matrix tables: a table L with abundance or presence-absence values for species at a series of sites, a table R with variables describing the environmental conditions of the sites, and a table Q containing traits (e.g., morphological or behavioral attributes) of the species. Ten years ago, the fourth-corner method was proposed to measure and test the relationships between species traits and environmental variables using tables R, L, and Q simultaneously. In practice, this method is rarely used. The major reasons for this lack of interest are the restriction of the original method and program to presence-absence data in L and to the analysis of a single trait and a single environmental variable at a time. Moreover, ecologists often have problems in choosing a permutation model among the four originally proposed. In this paper, we revisit the fourth-corner method and propose improvements to the original approach. First, we present an extension to measure the link between species traits and environmental variables when the ecological community is described by abundance data. A new multivariate fourth-corner statistic is also proposed. Then, using numerical simulations, we discuss and evaluate the existing testing procedures. A new two-step testing procedure is presented. We hope that these elements will help ecologists use the best possible methodology to analyze this type of ecological problem.

Community ecology in the age of multivariate multiscale spatial analysis

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.

adephylo: new tools for investigating the phylogenetic signal in biological traits

SUMMARY adephylo is a package for the R software dedicated to the analysis of comparative evolutionary data. Phylogenetic comparative methods initially aimed at accounting for or removing the effects of phylogenetic signal in the analysis of biological traits. However, recent approaches have shown that considerable information can be gathered from the study of the phylogenetic signal. In particular, close examination of phylogenetic structures can unveil interesting evolutionary patterns. For this purpose, we developed the package adephylo that provides tools for quantifying and describing the phylogenetic structures of biological traits. adephylo implements tests of phylogenetic signal, phylogenetic distances and proximities, and novel methods for describing further univariate and multivariate phylogenetic structures. These tools open up new perspectives in the analysis of evolutionary comparative data. AVAILABILITY The stable version is available from CRAN: http:/cran.r-project.org/web/packages/adephylo/. The development version is hosted by R-Forge: http://r-forge.r-project.org/projects/adephylo/. Both versions can be installed directly from R. adephylo is distributed under the GNU General Public Licence (> or =2).

Combining the fourth‐corner and the RLQ methods for assessing trait responses to environmental variation

Assessing trait responses to environmental gradients requires the simultaneous analysis of the information contained in three tables: L (species distribution across samples), R (environmental characteristics of samples), and Q (species traits). Among the available methods, the so-called fourth-corner and RLQ methods are two appealing alternatives that provide a direct way to test and estimate trait-nvironment relationships. Both methods are based on the analysis of the fourth-corner matrix, which crosses traits and environmental variables weighted by species abundances. However, they differ greatly in their outputs: RLQ is a multivariate technique that provides ordination scores to summarize the joint structure among the three tables, whereas the fourth-corner method mainly tests for individual trait-environment relationships (i.e., one trait and one environmental variable at a time). Here, we illustrate how the complementarity between these two methods can be exploited to promote new ecological knowledge and to improve the study of trait-environment relationships. After a short description of each method, we apply them to real ecological data to present their different outputs and provide hints about the gain resulting from their combined use.

Responding to spatial and temporal variations in predation risk: space use of a game species in a changing landscape of fear

Predators generate a “landscape of fear” within which prey can minimize the risk of predation by selecting low-risk areas. Depending on the spatial structure of this “landscape”, i.e., whether it is coarse- or fine-grained, prey may respond to increased risk by shifting their home ranges or by fine-scale redistributions within these ranges, respectively. We studied how wild boar (Sus scrofa L., 1758) responded to temporal changes in risk in hunted areas (risky habitat) surrounding a nature reserve (refuge habitat). Animals with home ranges “in contact” with the reserve during the low-risk season were the only ones to shift toward the refuge when the risk increased. These shifts occurred at two temporal scales in response to the increased risk during the daytime and during the hunting season. Whereas animals not influenced by the reserve found food and shelter in forest during the hunting season, shifts to the refuge area were detrimental to the rather scarce forest areas in the reserve. This confirms that...

Assessing the effects of spatial contingency and environmental filtering on metacommunity phylogenetics

Patterns in biodiversity and species coexistence are the result of multiple interacting processes including evolutionary history, trait variation, species interactions, dispersal, environmental variation, and landscape heterogeneity. Exploring patterns of biodiversity across space is perhaps the best integrative method (in contrast to the scarcity of temporal data) to interpret the influence of these multiple and interactive effects in determining community assembly, but it is still underdeveloped. Two emerging fields, metacommunity ecology and community phylogenetics, have been making relevant, though rather independent, progress toward understanding how communities are assembled in space. Our main goals were twofold. First, we described a heuristical framework to merge these two fields into “metacommunity phylogenetics.” The main goal of this framework is to provide a way to think about how niche properties of species arranged across the environment and different spatial scales influence the process of ...

Improved testing of species traits--environment relationships in the fourth-corner problem.

The fourth-corner problem entails estimation and statistical testing of the relationship between species traits and environmental variables from the analysis of three data tables. In a 2008 paper, S. Dray and P. Legendre proposed and evaluated five permutation methods for statistical significance testing, including a new two-step testing procedure. However, none of these attained the correct type I error in all cases of interest. We solve this problem by showing that a small modification of their two-step procedure controls the type I error in all cases. The modification consists of adjusting the significance level from mean square root of alpha to alpha or, equivalently, of reporting the maximum of the individual P. values as the final one. The test is also applicable to the three-table ordination method RLQ.