Figure 13.29 Mantel analysis of the relationships between matrices representing bacterial variables (a: BNA, b: MA, in matrix form), CHL A, and SPACE. Left tables, above the diagonals: simple Mantel statistics; below: partial Mantel statistics controlling for the effect of the third matrix. Asterisks (*) indicate significance (a = 0.05); tests of significance are one-tailed. Right: causal models supported by the results. Adapted from Legendre & Troussellier (1988).
Leduc et al. (1992) analysed the relationship between environmental conditions and the spatial distributions of adult trees and saplings, for 12 tree species in 198 vegetation quadrats from a 0.5 km2 forested area. Distance matrices were computed for the adults and saplings of each species separately. A matrix of geographic distances ("Space") was also computed among sites. "Environment" is a matrix computed among sites for the 6 drainage, soil and geomorphology variables, using the Estabrook-Rogers coefficient (S^, Chapter 7). Partial Mantel tests were used in conjunction with path analysis computed from the Mantel statistics, as in Ecological application 10.4b. The question here belonged to the second type mentioned in the introduction of Section 13.5: does the spatial structure of the environmental variables fully explain the spatial structure of the vegetation, or is there a part of the spatial structure of the vegetation which is not explained by the environmental variables in the model?
After analysing each species separately, the authors found that the spatial patterns of species associated with hydric conditions were largely explained by the spatial distributions of the environmental variables (Fig.13.30c, d), whereas mesic-site species still displayed significant spatial patterns after controlling for the environmental variables (Fig. 13.30a, b). Past events (disturbances) and forest cover dynamics were suggested as explanations for the latter.
Residual distance matrices, as computed in partial Mantel analysis, provide the basis for interesting illustrations of the relationships among sites, using ordination by principal coordinate analysis (PCoA, Section 9.2) or nonmetric multidimensional scaling (MDS, Sections 9.3).
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