Multivariate Mantel correlogram

Sokal (1986) and Oden & Sokal (1986) found an ingenious way to compute a correlogram for multivariate data, using the normalized Mantel statistic rM and test of significance (Subsection 10.5.1). This method is useful, in particular, to describe the spatial structure of species assemblages.

The principle is to quantify the ecological relationships among sampling sites by means of a matrix Y of multivariate similarities or distances (using, for instance, coefficients S17 or Du in the case of species abundance data), and compare Y to a model matrix X (Subsection 10.5.1) which is different for each geographic distance class (Fig. 13.12).

• For distance class 1 for instance, pairs of neighbouring stations (that belong to the first class of geographic distances) are coded 1, whereas the remainder of matrix X1 contains zeros. A first Mantel statistic (^1) is calculated between Y and X1.

• The process is repeated for the other distance classes d, building each time a modelmatrix Xd and recomputing the normalized Mantel statistic. Matrix Xd may contain 1's

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