Integration and modularity in Procrustes shape data: is there a risk of spurious results?

Abstract

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.