Spatial ordination of vegetation data using a generalization of Wartenberg's multivariate spatial correlation

Question: Are there spatial structures in the composition of plant communities? Methods: Identification and measurement of spatial structures is a topic of great interest in plant ecology. Univariate measurements of spatial autocorrelation such as Moran's I and Geary's c are widely used, but extensions to the multivariate case ( i. e. multi-species) are rare. Here, we propose a multivariate spatial analysis based on Moran's I (MULTISPATI) by introducing a row-sum standardized spatial weight matrix in the statistical triplet notation. This analysis, which is a generalization of Wartenberg's approach to multivariate spatial correlation, would imply a compromise between the relations among many variables ( multivariate analysis) and their spatial structure ( autocorrelation). MULTISPATI approach is very flexible and can handle various kinds of data ( quantitative and/or qualitative data, contingency tables). A study is presented to illustrate the method using a spatial version of Correspondence Analysis. Location: Territoire d'Etude et d'Experimentation de Trois-Fontaines ( eastern France). Results: Ordination of vegetation plots by this spatial analysis is quite robust with reference to rare species and highlights spatial patterns related to soil properties.