Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data analysis.

We propose a method for detecting a Guttman effect in a complete disjunctive table U with Q questions. Since such an investigation is a nonsense when the Q variables are independent, we reuse a previous unpublished work about the chi-squared independence test for Burt's tables. Then, we introduce a two-steps method consisting in plugging the first singular vector from a preliminary Correspondence Analysis (CA) of U as a score x into a subsequent singly-ordered Ordinal Correspondence Analysis (OCA) of U . OCA mainly consists in completing x by a sequence of orthogonal polynomials superseding the classical factors of CA. As a consequence, in presence of a pure Guttman effect, we should in principle have that the second singular vector coincide with the polynomial of degree 2, etc. The hybrid decomposition of the Pearson chi-squared statistics (resulting from OCA) used in association with permutation tests makes possible to reveal such relationships, i.e. the presence of a Guttman effect in the structure of U , and to determine its degree - with an accuracy depending on the signal to noise ratio. The proposed method is successively tested on artificial data (more or less noisy), a well-known benchmark, and synchrotron X-ray diffraction data of soil samples.

Global production increased by spatial heterogeneity in a population dynamics model.

Spatial and temporal heterogeneity are often described as important factors having a strong impact on biodiversity. The effect of heterogeneity is in most cases analyzed by the response of biotic interactions such as competition of predation. It may also modify intrinsic population properties such as growth rate. Most of the studies are theoretic since it is often difficult to manipulate spatial heterogeneity in practice. Despite the large number of studies dealing with this topics, it is still difficult to understand how the heterogeneity affects populations dynamics. On the basis of a very simple model, this paper aims to explicitly provide a simple mechanism which can explain why spatial heterogeneity may be a favorable factor for production. We consider a two patch model and a logistic growth is assumed on each patch. A general condition on the migration rates and the local subpopulation growth rates is provided under which the total carrying capacity is higher than the sum of the local carrying capacities, which is not intuitive. As we illustrate, this result is robust under stochastic perturbations.

Fairly processing rare and common species in multivariate analysis of ecological series. Application to macrobenthic communities from Algiers harbour.

Systematic sampling of communities gives rise to large contingency tables summing up possible changes in the assemblages' structure. Such tables are generally analysed by multivariate statistical methods, which are ill-suited for simultaneously analysing rare and common species (Field et al., 1982). In order to separately process species belonging to either of these categories, we propose a statistical method to select common species in a sequence of ecological surveys. It is based on a precise definition of rarity, and depends on a rarity parameter. In this work, this parameter will be optimised so that the sub-table of common species captures the essential features of the complete table as well as possible. In this way we analysed the spatio-temporal evolution of macrobenthic communities from the Algiers harbour to study the pollution influence during a year. The examination of the communities' structuring was done through Principal Components Analysis (PCA) of the species proportions table. Environmental variables were simultaneously sampled. We show that the data structure can be explained by about 25% of the total number of present species. Two environmental gradients were brought to the fore inside the harbour, the first one representing pollution, and the second one representing hydrological instabilities. Since rare species can also convey information, the complete table was also coded according to a generalised presence/absence index and submitted to Correspondence Analysis. The results were consistent with those of PCA, but they depended on more species, and highlighted the influence of sedimentology on the assemblages composition.

Forecasting physicochemical variables by a classification tree method. Application to the Berre Lagoon (south France).

The dynamics of the "Etang de Berre", a brackish lagoon situated close to the French Mediterranean sea coast, is strongly disturbed by freshwater inputs coming from an hydroelectric power station. The system dynamics has been described as a sequence of daily typical states from a set of physicochemical variables such as temperature, salinity and dissolved oxygen rates collected over three years by an automatic sampling station. Each daily pattern summarizes the evolution, hour by hour of the physicochemical variables. This article presents results of forecasts of the states of the system subjected to the simultaneous effects of meteorological conditions and freshwater releases. We recall the main step of the classification tree method used to build up the predictive model (Classification and Regression Trees, Breiman et al., 1984) and we propose a transfer procedure in order to test the stability of the model. Results obtained on the Etang de Berre data set allow us to describe and predict the effects of the environmental variables on the system dynamics with a margin of error. The transfer procedure applied after the tree building process gives a maximum gain in prediction accuracy of about 15%.