Dear All,
this (links and abstract below) is out right now in Evol.Biol., with many thanks to Benedikt for being such a great editor (plus more thanks to all those who read it and helped with comments etc.!).

One of the two main Procrustes approaches that produce data for analyses of modularity and/or integration seems to lead to very high rates of false positives in some of the most common tests used in the main programs/packages. The study has some simulations and explore a variety of cases (plus a few more in the R-script mentioned in the paper, and written by a reviewer). It happens all the time in those data (unless one uses such a small N relative to p, the number of variables, that unsurprisingly nothing is significant). However, it is mostly an empirical study and will require more work to understand how serious and general the issue is. This is clearly said in the paper, that also says (but I'd like to stress it) that: 1) the problem is not Procrustes but the way the data are used after Procrustes; 2) the alternative approach does not produce false positives, but may have low power and other issues (said multiple times but not a question addressed by the study), which is why there is no recommendation in favour of one or the other approach.

It might well be that in practice, if data have a real and strong covariance, the problem will have just a small effect. But it seems to be there all the time and there might be cases where it becomes much more serious.

I hope it may be useful for those interested in that type of evo-devo studies.



ALMOST (few differences!) FINAL PREPRINT:

Integration and Modularity in Procrustes Shape Data: Is There a Risk of Spurious Results?


Studies of morphological integration and modularity are a hot topic in evolutionary developmental biology. Geometric morphometrics using Procrustes methods offers powerful tools to quantitatively investigate morphological variation and, within this methodological framework, a number of different methods has been put forward to test if different regions within an anatomical structure behave like modules or, vice versa, are highly integrated and covary strongly. Although some exploratory techniques do not require a priori modules, commonly modules are specified in advance based on prior knowledge. Once this is done, most of the methods can be applied either by subdividing modules and performing separate Procrustes alignments or by splitting shape coordinates of anatomical landmarks into modules after a common superimposition. This second approach is particularly interesting because, contrary to completely separate blocks analyses, it preserves information on relative size and position of the putative modules. However, it also violates one of the fundamental assumptions on which Procrustes methods are based, which is that one should not analyse or interpret subsets of landmarks from a common superimposition, because the choice of that superimposition is purely based on statistical convenience (although with sound theoretical foundations) and not on a biological model of variance and covariance. In this study, I offer a first investigation of the effects of testing integration and modularity within a configuration of commonly superimposed landmarks using some of the most widely employed statistical methods available to this aim. When applied to simulated shapes with random non-modular isotropic variation, standard methods frequently recovered significant but arbitrary patterns of integration and modularity. Re-superimposing landmarks within each module, before testing integration or modularity, generally removes this artifact. The study, although preliminary and exploratory in nature, raises an important issue and indicates an avenue for future research. It also suggests that great caution should be exercised in the application and interpretation of findings from analyses of modularity and integration using Procrustes shape data, and that issues might be even more serious using some of the most common methods for handling the increasing popular semilandmark data used to analyse 2D outlines and 3D surfaces.


Dr. Andrea Cardini
Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy
tel. 0039 059 2058472

Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia

E-mail address:,

FREE Yellow BOOK on Geometric Morphometrics:


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