Should the Mantel test be used in spatial analysis?. Issue 11 (25th July 2015) - Legendre, Pierre; Fortin, Marie‐Josée; Borcard, Daniel
Summary: The Mantel test is widely used in biology, including landscape ecology and genetics, to detect spatial structures in data or control for spatial correlation in the relationship between two data sets, for example community composition and environment. The study demonstrates that this is an incorrect use of that test. The null hypothesis of the Mantel test differs from that of correlation analysis; the statistics computed in the two types of analyses differ. We examined the basic assumptions of the Mantel test in spatial analysis and showed that they are not verified in most studies. We showed the consequences, in terms of power, of the mismatch between these assumptions and the Mantel testing procedure. The Mantel test H0 is the absence of relationship between values in two dissimilarity matrices, not the independence between two random variables or data tables. The Mantel R 2 differs from the R 2 of correlation, regression and canonical analysis; these two statistics cannot be reduced to one another. Using simulated data, we show that in spatial analysis, the assumptions of linearity and homoscedasticity of the Mantel test (H1 : small values ofD 1 correspond to small values ofD 2 and large values ofD 1 to large values ofD 2 ) do not hold in most cases, except when spatial correlation extends over the whole study area. Using extensive simulations of spatially correlated data involving different representations of geographic relationships, we show that the power of the Mantel test is always lower than that of distance‐based Moran's eigenvector map (dbMEM) analysis and that the Mantel R 2 is always smaller than in dbMEM analysis, and uninterpretable. These simulation results are novel contributions to the Mantel debate. We also show that regression on a geographic distance matrix does not remove the spatial structure from response data and does not produce spatially uncorrelated residuals. Our main conclusion is that Mantel tests should be restricted to questions that, in the domain of application, only concern dissimilarity matrices, and are not derived from questions that can be formulated as the analysis of the vectors and matrices from which one can compute dissimilarity matrices.