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.
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Acknowledgements
I am deeply grateful to Paul O’Higgins for critically discussing with me some of the points presented in this communication, and to Dean Adams for his explanations on some of the methods commonly used in the analysis of modularity and integration. I owe a huge thank to Jim Rohlf for reading the quasi-final version of this paper, and for being most supportive and constructive in his assessment of this work. I am also greatly in debt to David Polly, Carmelo Fruciano and an anonymous reviewer for their in depth assessment of a previous version of this paper, including DP and the anonymous reviewer exploring the issues further using simulations: regardless of agreement or disagreement, all their comments and suggestions greatly improved this preliminary investigation and contributed to showing that there is an issue and that this is definitely more complicated that I originally thought! Last but not least, I wish to dedicate this paper to the memory of Paolo Tongiorgi (1936–2018): Paolo, you have been an extraordinary scientist; the most supportive mentor; a wonderful friend; and the greatest example of generosity I have known in my academic career.
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All simulated datasets are available online as Supplementary Material. Files use the NTS format, commonly employed in morphmetrics, easy to import in MorphoJ or R, and described in details in the help manuals of the TPS Series. The R-script with the simulation by the anonymous reviewer is available upon request; the flaw in the original version is corrected with a single change (to be done for all example datasets): increasing sample size from 100 to 500 in order to avoid most unfavourable p/N ratios and thus low power.
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Cardini, A. Integration and Modularity in Procrustes Shape Data: Is There a Risk of Spurious Results?. Evol Biol 46, 90–105 (2019). https://doi.org/10.1007/s11692-018-9463-x
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DOI: https://doi.org/10.1007/s11692-018-9463-x