Shape coordinates or Procrustes distances? Biometric hypotheses over multiple spaces, with a suggestion for mixed bioinformatic–morphometric studies

Bioinformatics sample summaries often involve distances or the conversion of similarities to dissimilarities, while Procrustes methods can proceed either via distances or via the shape coordinates underlying those distances. There is a distance–distance statistical method, currently increasing in popularity in some of my applications domains, that is at once simple, intuitive, and quite wrongheaded: the method of Mantel matrix correlations. This note explains the error when the test is applied in most of our biometric contexts, and, in view of the unsuitability of the principal-coordinates model to most bioinformatic domains other than the morphometric, suggests a hybrid statistic bridging Procrustes analysis to bioinformatics that taps the power of Procrustes principal coordinates to the maximum