The correlation of multivariate data is a common task in investigations of soil biology and in ecology in general. Procrustes analysis and the Mantel test are two approaches that often meet this objective and are considered analogous in many situations especially when used as a statistical test to assess the statistical significance between multivariate data tables. Here we call the attention of ecologists to the advantages of a less familiar application of the Procrustean framework, namely the Procrustean association metric (a vector of Procrustean residuals). These residuals represent differences in fit between multivariate data tables regarding homologous observations (e.g., sampling sites) that can be used to estimate local levels of association (e.g., some groups of sites are more similar in their association between biotic and environmental features than other groups of sites). Given that in the Mantel framework, multivariate information is translated into a pairwise distance matrix, we lose the ability to contrast homologous data points across dimensions and data matrices after their fit. In this paper, we attempt to familiarize ecologists with the benefits of using these Procrustean residual differences to further gain insights about the processes underlying the association among multivariate data tables using real and hypothetical examples.

It is of global concern to adopt measures to mitigate land degradation caused by agricultural production systems. One of the strategies proposed is to replace degraded pastures with agrosilvopastoral systems which integrate three different land-use types: crop production, livestock pasture and forestry plantation (denoted iCLF). However, little is known about the differences between iCLF and other land use types in terms of soil microbial community structure. Distance matrices based on individual soil chemical properties and individual soil microbial variables were correlated by Procrustes analysis and these relationships yielded vectors of residuals depicting these correlations (matches). These vectors were used as univariate response variables in an ANOVA framework in order to investigate how the match sizes (the strength of correlation/covariance) between individual soil chemical properties and individual soil microbial variables vary across land use types (levels: iCLF; degradated pasture; improved pasture; and a native cerrado fragment) and also across sample origin within iCLF (levels: soil samples under more influence of the exotic tree forest stand; soil samples under influence of the pasture; samples within the transition between the forest stand and the pasture). We were able to obtain insights into the fact that the land use distinction can be driven by more than just individual soil chemical and microbial variables. The integration of crop, livestock and forestry promoted a dominance of fungi in this low fertility and low pH environment. P availability and the composite variable exchangeable base cations (Ca þ2 , Mg þ2 , K þ) were the soil properties whose strengths of correlation (match sizes) with individual microbial variables were the most affected by land use type and sampling origin within iCLF. While the strength of the correlation between soil microbial structure variables and P availability was typically land use type dependent, the response of the microbial structure to exchangeable base cations was mainly affected by the sample origin within iCLF. Finally our results point towards the conclusion that increases in the heterogeneity of vegetation within integrated crop, pasture and forestry systems are an important driver of microbial community response to environmental changes, and may be one means by which to increase the sustainability of tropical agroecosystems.

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