Procrustes Shape Cannot be Analyzed, Interpreted or Visualized one Landmark at a Time

Abstract

Landmark-based geometric morphometrics using the Procrustes approach has become the dominant family of methods in morphometrics. However, the superimposition (and sliding, if semilandmarks are present), that transforms raw coordinates into shape coordinates is biologically arbitrary. Procrustes has desirable statistical properties, but is not based on a biological model. The same is true for sliding methods. These techniques allow powerful statistical analyses of a full set of shape coordinates, but make the use of subsets of landmarks/semilandmarks problematic, inaccurate and misleading, if not totally wrong. Crucially, the biological arbitrariness of the superimposition prevents any meaningful quantification, analysis and interpretation of variation one landmark/semilandmark at a time. We exemplify how misleading this type of analyses can be by using a real dataset, as well as simulated data with isotropic variation. Both show inconsistencies in ‘per-landmark/semilandmark’ variances. The simulation in fact helps to make even more obvious that the pattern of variance is strongly influenced by the biologically arbitrary choice of the mathematical treatment. Unfortunately, despite this limitation of all superimposition methods being known since the early days of Procrustean morphometrics, there has been a recent series of papers in leading journals presenting results of ‘per-landmark’ analyses. Thus, we further clarify why these analyses are wrong and represent misleading examples that should not be followed: Procrustes shape data cannot be analyzed, visualized or interpreted one landmark at a time. For users who are in doubt, in the Conclusions, we provide a short list of recommendations on how to easily avoid this type of mistakes.