Figure 10.18 Relationships among fungi, trees, and environmental conditions. Left: Mantel statistics rM (above the diagonal) and partial Mantel statistics (below). Tests of significance: *, significant result; N.S., result not significant at the Bonferroni-corrected 0.05 level. Right: path diagram computed from the Mantel rM coefficients. The figures on the arrows are the path coefficients.
equivalent to a Pearson r correlation coefficient, the Mantel statistic values were used to carry out a path analysis in order to test a model of interdependence among the three matrices (Fig. 10.18). Partial t statistics (eq. 4.13 of Subsection 4.5.3) could not be used for testing in this case because the Mantel statistics had been computed from similarities, which were not independent of one another. Partial Mantel tests were used instead to determine the significance of the path coefficients. The study showed that, while both the trees and abiotic conditions were significantly related to the ectomycorrhizal basidiomycete community structure, the influence of the host trees was far greater. The influence of abiotic conditions on the fungus and tree communities was further studied using canonical correspondence analysis (Section 11.2).
Another application of Mantel statistics to path analysis, also coupled with partial Mantel tests (Subsection 10.5.1), is presented by Leduc et al. (1992), who tried to untangle the spatial component from the relationships between environmental conditions and the distributions of trees and saplings in a hardwood forest.
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