title: Much beyond Mantel: bringing Procrustes association metric to the plant and soil ecologist's toolbox.
abstract: 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.
authors: Soil Science Department, Agronomy Institute, Federal Rural University of Rio de Janeiro, Seropédica-RJ, Brazil; The James Hutton Institute, Craigiebuckler, Aberdeen, United Kingdom.
authors: Francy Junio Gonçalves
authors: FJ
authors: Lisboa
authors: Canada Research Chair in Spatial Modelling and Biodiversity; Université du Québec à Montréal, Département des sciences biologiques, Québec, Canada.
authors: Pedro R
authors: PR
authors: Peres-Neto
authors: Embrapa Agrobiologia, Seropédica-RJ, Brazil.
authors: Guilherme Montandon
authors: GM
authors: Chaer
authors: Embrapa Agrobiologia, Seropédica-RJ, Brazil.
authors: Ederson da Conceição
authors: Eda C
authors: Jesus
authors: The James Hutton Institute, Craigiebuckler, Aberdeen, United Kingdom.
authors: Ruth Joy
authors: RJ
authors: Mitchell
authors: The James Hutton Institute, Craigiebuckler, Aberdeen, United Kingdom.
authors: Stephen James
authors: SJ
authors: Chapman
authors: Soil Science Department, Agronomy Institute, Federal Rural University of Rio de Janeiro, Seropédica-RJ, Brazil.
authors: Ricardo Luis Louro
authors: RL
authors: Berbara
mesh_terms: D044822:Biodiversity; D004463:Ecology / Q000379:methods; D015233:Models, Statistical; D015999:Multivariate Analysis; D018521:Plant Physiological Phenomena; D012987:Soil
chemical_list: D012987:Soil